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PLAXIS 2D

Reference Manual

2012

Build 5848

TABLE OF CONTENTS

TABLE OF CONTENTS

1 Introduction 9

2 General information 112.1 Units and sign conventions 112.2 File handling 132.3 Help facilities 13

3 Input program — General overview 153.1 Starting the Input program 15

3.1.1 New project 163.1.2 Existing project 203.1.3 Importing a geometry 203.1.4 Packing a project 21

3.2 Layout of the Input program 233.3 Menus in the Menu bar 25

3.3.1 File menu 253.3.2 Edit menu 263.3.3 View menu 263.3.4 Geometry menu 263.3.5 Loads menu 273.3.6 Materials menu 283.3.7 Mesh menu 283.3.8 Help menu 28

3.4 Geometry 293.4.1 Points and lines 293.4.2 Plates 303.4.3 Embedded pile row 323.4.4 Geogrids 363.4.5 Interfaces 373.4.6 Node-to-node anchors 403.4.7 Fixed-end anchors 403.4.8 Tunnels 413.4.9 Hinges and rotation springs 463.4.10 Drains 473.4.11 Wells 48

3.5 Loads and boundary conditions 483.5.1 Standard fixities 483.5.2 Standard earthquake boundaries 493.5.3 Standard absorbent boundaries (dynamics) 493.5.4 Set dynamic load system 493.5.5 Fixities 493.5.6 Rotation fixities (plates) 503.5.7 Absorbent boundaries 503.5.8 Prescribed displacements 503.5.9 Distributed loads 523.5.10 Point loads 533.5.11 Bending moments 54

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3.6 Design approaches 543.6.1 Definition of design approaches 553.6.2 Definition of partial factors for loads 573.6.3 Definition of partial factors for materials 58

3.7 Mesh generation 603.7.1 Basic element type 613.7.2 Global coarseness 613.7.3 Global refinement 613.7.4 Local coarseness 613.7.5 Local refinement 623.7.6 Automatic refinement 62

4 Material properties and material database 654.1 Modelling soil and interface behaviour 67

4.1.1 General tabsheet 674.1.2 Parameters tabsheet 734.1.3 Flow parameters tabsheet 904.1.4 Interfaces tabsheet 964.1.5 Initial tabsheet 102

4.2 Modelling undrained behaviour 1044.2.1 Undrained (A) 1054.2.2 Undrained (B) 1054.2.3 Undrained (C) 106

4.3 Simulation of soil tests 1064.3.1 Triaxial test 1094.3.2 Oedometer 1104.3.3 CRS 1114.3.4 DSS 1124.3.5 General 1134.3.6 Results 1134.3.7 Parameter optimisation 114

4.4 Material data sets for plates 1214.4.1 Material set 1214.4.2 Properties 122

4.5 Material data sets for geogrids 1254.5.1 Material set 1264.5.2 Properties 126

4.6 Material data sets for embedded pile rows 1274.6.1 Material set 1284.6.2 Properties 1294.6.3 Interaction properties (pile bearing capacity) 1304.6.4 Interface stiffness factor 131

4.7 Material data sets for anchors 1334.7.1 Material set 1334.7.2 Properties 134

4.8 Assigning data sets to geometry components 136

5 Calculations 1375.1 Layout of the Calculations program 137

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5.2 Menus in the menu bar 1395.3 Calculation modes 141

5.3.1 Classical mode 1415.3.2 Advanced mode 1425.3.3 Flow mode 142

5.4 Defining calculation phases 1435.4.1 Calculation tabsheets 1435.4.2 Inserting and deleting calculation phases 1445.4.3 Phase identification and ordening 145

5.5 Types of analysis 1455.5.1 Initial stress generation 1465.5.2 Plastic calculation 1495.5.3 Consolidation calculation in Classical mode 1495.5.4 Consolidation calculation in Advanced mode 1505.5.5 Safety calculation (phi/c reduction) 1505.5.6 Dynamic calculation 1535.5.7 Free vibration 1535.5.8 Groundwater flow (steady-state) 1535.5.9 Groundwater flow (transient) 1545.5.10 Plastic nil-step 1545.5.11 Updated mesh analysis 154

5.6 Load stepping procedures 1575.6.1 Automatic step size procedure 1575.6.2 Load advancement — Ultimate level 1585.6.3 Load advancement — Number of steps 1605.6.4 Automatic time stepping (consolidation) 1605.6.5 Automatic time stepping (dynamics) 161

5.7 Calculation control parameters 1615.7.1 Iterative procedure control parameters 1615.7.2 Pore pressure limits 1685.7.3 Loading input 1685.7.4 Control parameters 173

5.8 Staged construction — geometry definition 1755.8.1 Changing geometry configuration 1765.8.2 Activating and deactivating clusters or structural objects 1765.8.3 Activating or changing loads 1785.8.4 Applying prescribed displacements 1795.8.5 Reassigning material data sets 1805.8.6 Applying a volumetric strain in volume clusters 1815.8.7 Prestressing of anchors 1825.8.8 Applying contraction of a tunnel lining 1835.8.9 Definition of design calculations 1835.8.10 Staged construction with ΣMstage < 1 1845.8.11 Unfinished staged construction calculation 185

5.9 Staged construction — water conditions 1865.9.1 Water unit weight 1875.9.2 Phreatic level 1885.9.3 Closed boundary 1915.9.4 Precipitation 192

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5.9.5 Cluster pore pressure distribution 1945.9.6 Boundary conditions for flow and consolidation 1965.9.7 Special objects 2025.9.8 Water pressure generation 203

5.10 Calculation using design approaches 2065.11 Load multipliers 206

5.11.1 Standard load multipliers 2075.11.2 Other multipliers and calculation parameters 2095.11.3 Dynamic multipliers 210

5.12 Sensitivity analysis & Parameter variation 2125.12.1 Sensitivity analysis 2135.12.2 Parameter variation 2135.12.3 Defining variations of parameters 2135.12.4 Starting the analysis 2145.12.5 Sensitivity — View results 2155.12.6 Parameter variation — Calculate boundary values 2175.12.7 Viewing upper and lower values 2185.12.8 Viewing results of variations 2185.12.9 Delete results 218

5.13 Starting a calculation 2185.13.1 Previewing a construction stage 2185.13.2 Selecting points for curves 2195.13.3 Execution of the calculation process 2195.13.4 Aborting a calculation 2205.13.5 Output during calculations 2205.13.6 Selecting calculation phases for output 2255.13.7 Reset staged construction settings 2255.13.8 Adjustment to input data in between calculations 2265.13.9 Automatic error checks 226

6 Output program — General overview 2296.1 Layout of the output program 2306.2 Menus in the Menu bar 231

6.2.1 File menu 2316.2.2 View menu 2316.2.3 Project menu 2336.2.4 Geometry menu 2336.2.5 Mesh menu 2346.2.6 Deformations menu 2356.2.7 Stresses menu 2356.2.8 Forces menu 2356.2.9 Tools menu 2356.2.10 Window menu 2366.2.11 Help menu 236

6.3 Tools in the Output program 2376.3.1 Accessing the Output program 2376.3.2 Exporting output data 2376.3.3 Curves manager 2396.3.4 Store the view for reports 239

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6.3.5 Zooming the plot 2396.3.6 Relocation of the plot 2406.3.7 Scaling the displayed results 2406.3.8 Tables 2406.3.9 Selection of results 2416.3.10 Display type of results 2416.3.11 Select structures 2426.3.12 Partial geometry 2436.3.13 Viewing results in cross sections 2446.3.14 Plot annotations 2456.3.15 Miscellaneous tools 247

6.4 Display area 2506.4.1 Legend 2506.4.2 Modifying the display settings 251

6.5 Views in Output 2536.5.1 Model view 2536.5.2 Structures view 2536.5.3 Cross section view 2536.5.4 Forces view 253

6.6 Report generation 2546.6.1 Configuration of the document 256

6.7 Creating animations 256

7 Results available in Output program 2597.1 Connectivity plot 2597.2 Deformations 259

7.2.1 Deformed mesh 2597.2.2 Total displacements 2607.2.3 Phase displacements 2607.2.4 Sum phase displacements 2607.2.5 Incremental displacements 2607.2.6 Extreme total displacements 2617.2.7 Velocities 2617.2.8 Accelerations 2617.2.9 Accelerations in ‘g’ 2627.2.10 Total cartesian strains 2627.2.11 Phase cartesian strains 2627.2.12 Incremental cartesian strains 2627.2.13 Total strains 2637.2.14 Phase strains 2637.2.15 Incremental strains 263

7.3 Stresses 2647.3.1 Cartesian effective stresses 2647.3.2 Cartesian total stresses 2647.3.3 Principal effective stresses 2647.3.4 Principal total stresses 2667.3.5 State parameters 2667.3.6 Pore pressures 2687.3.7 Groundwater flow 269

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7.3.8 Plastic points 2707.3.9 Fixed end anchors 2717.3.10 Node to node anchors 2717.3.11 Wells 2727.3.12 Drains 272

7.4 Structures and interfaces 2727.4.1 Deformation in structural elements 2727.4.2 Resulting forces in Plates 2727.4.3 Resulting forces in Geogrids 2737.4.4 Resulting forces in embedded pile rows 2737.4.5 Anchors 2747.4.6 Interfaces 2747.4.7 Results in Hinges and rotation springs 2757.4.8 Structural forces in volumes 275

8 Curves 2798.1 Selecting points for curves 279

8.1.1 Mesh point selection 2798.1.2 Pre-calculation points 2808.1.3 Post-calculation points 280

8.2 Generating curves 2818.2.1 Load-displacement curves 2838.2.2 Force-displacement curves 2838.2.3 Displacement-time or force-time curves 2848.2.4 Stress and strain diagrams 2848.2.5 Curves in Dynamic calculations 284

8.3 Formatting curves 2878.3.1 Menus for curves 2888.3.2 Editing curve data in table 2898.3.3 Value indication 291

8.4 Formatting options 2918.4.1 Chart settings 2918.4.2 Curve settings 292

8.5 Regeneration of curves 2948.6 Multiple curves in one chart 294

9 References 295

Index

Appendix A — Possibilities and limitations of PLAXIS 2D 301

Appendix B — Program and Data File Structure 315

Appendix C — Shortcuts Output program 319

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INTRODUCTION

1 INTRODUCTION

The PLAXIS 2D program is a special purpose two-dimensional finite element programused to perform deformation and stability analysis for various types of geotechnicalapplications. Real situations may be modelled either by a plane strain or an axisymmetricmodel. The program uses a convenient graphical user interface that enables users toquickly generate a geometry model and finite element mesh based on a representativevertical cross section of the situation at hand. Users need to be familiar with the Windowsenvironment. To obtain a quick working knowledge of the main features of the PLAXISprogram, users should work through the example problems contained in the TutorialManual.

The Reference Manual is intended for users who want more detailed information aboutprogram features. The manual covers topics that are not covered exhaustively in theTutorial Manual. It also contains practical details on how to use the PLAXIS program fora wide variety of problem types. The user interface consists of three sub-programs(Input, Calculations and Output).

The Input program is a pre-processor,which is used to define the problem geometry and to create the finite element mesh.

The Calculations program is a separate partof the user-interface that is used to define and execute finite element calculations.

The Output program is a post-processor, which is used to inspect the resultsof calculations in a two dimensional view or in cross sections, and to plot graphs

(curves) of output quantities of selected geometry points.

The contents of this Reference Manual are arranged according to the sub-programs andtheir respective options as listed in the corresponding menus. This manual does notcontain detailed information about the constitutive models, the finite element formulationsor the non-linear solution algorithms used in the program. For detailed information onthese and other related subjects, users are referred to the various papers listed in theScientific Manual and the Material Models Manual.

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GENERAL INFORMATION

2 GENERAL INFORMATION

Before describing the specific features in the three parts of the PLAXIS 2D user interface,the information given in this chapter applies to all parts of the program.

2.1 UNITS AND SIGN CONVENTIONS

It is important in any analysis to adopt a consistent system of units. At the start of theinput of a geometry, a suitable set of basic units should be selected. The basic unitscomprise a unit for length, force and time. These basic units are defined in the Modeltabsheet of the Project properties window in the Input program. The default units aremeters [m] for length, kiloNewton [kN] for force and day [day] for time. Table 2.1 gives anoverview of all available units, the [default] settings and conversion factors to the defaultunits. All subsequent input data should conform to the selected system of units and theoutput data should be interpreted in terms of the same system. From the basic set ofunits, as defined by the user, the appropriate unit for the input of a particular parameter isgenerally listed directly behind the edit box or, when using input tables, above the inputcolumn. In all of the examples given in the PLAXIS manuals, the standard units are used.

Table 2.1 Available units and their conversion factor to the default units

Length Conversion Force Conversion Time Conversion

mm = 0.001 m N = 0.001 kN s (sec) = 1/86400 day

[m] = 1 m [kN] = 1 kN min = 1/1440 day

in (inch) = 0.0254 m MN = 1000 kN [h] = 1/24 day

ft (feet) = 0.3048 m lbf (pounds force) = 0.0044482 kN [day] = 1 day

kip (kilo pound) = 4.4482 kN

For convenience, the units of commonly used quantities in two different sets of units arelisted below:

Int. system (SI) Imperial system

Basic units: Length [m] [in]

Force [kN] [lbf]

Time [day] [sec]

Geometry: Coordinates [m] [in]

Displacements [m] [in]

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Material properties: Young’s modulus [kN/m2]=[kPa] [psi]=[lbf/in2]

Cohesion [kN/m2] [psi]

Friction angle [deg.] [deg.]

Dilatancy angle [deg.] [deg.]

Unit weight [kN/m3] [lbf/cu in]

Permeability [m/day] [in/sec]

Forces & stresses: Point loads [kN] [lbf]

Line loads [kN/m] [lbf/in]

Distributed loads [kN/m2] [psi]

Stresses [kN/m2] [psi]

Units are generally only used as a reference for the user but, to some extent, changingthe basic units in the Project properties window will automatically convert existing inputvalues to the new units. This applies to parameters in material data sets and othermaterial properties in the Input program. It does not apply to geometry related inputvalues like geometry data, loads, prescribed displacements or phreatic levels or to anyvalue outside the Input program. If it is the user’s intention to use a different system ofunits in an existing project, the user has to modify all geometrical data manually and redoall calculations.

In a plane strain analysis, the calculated forces resulting from prescribed displacementsrepresent forces per unit length in the out of plane direction (z-direction; see Figure 2.1).In an axisymmetric analysis, the calculated forces (Force − X , Force − Y ) are those thatact on the boundary of a circle subtending an angle of 1 radian. In order to obtain theforces corresponding to the complete problem therefore, these forces should bemultiplied by a factor of 2π. All other output for axisymmetric problems is given per unitwidth and not per radian.

Sign convention

The generation of a two-dimensional (2D) finite element model in the PLAXIS 2Dprogram is based on the creation of a geometry model. This geometry model is createdin the x-y -plane of the global coordinate system (Figure 2.1), whereas the z-direction isthe out-of-plane direction. In the global coordinate system the positive z-direction ispointing towards the user. In all of the output data, compressive stresses and forces,including pore pressures, are taken to be negative, whereas tensile stresses and forcesare taken to be positive. Figure 2.1 shows the positive stress directions.

Although PLAXIS 2D is a 2D program, stresses are based on the 3D Cartesiancoordinate system shown in Figure 2.1. In a plane strain analysis σzz is the out-of-planestress. In an axisymmetric analysis, x represents the radial coordinate, y represents theaxial coordinate and z represents the tangential direction. In this case, σxx represents theradial stress and σzz represents the hoop stress.

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GENERAL INFORMATION

y

z

x

σσ

σ

σ

σ

σσ

σ

σ

xx

xy

xz

yy

yxyz

zz zx

zy

Figure 2.1 Coordinate system and indication of positive stress components

2.2 FILE HANDLING

All file handling in PLAXIS is done using a modified version of the general Windows® filerequester (Figure 2.2).

Figure 2.2 PLAXIS file requester

With the file requester, it is possible to search for files in any admissible directory of thecomputer (and network) environment. The main file used to store information for aPLAXIS project has a structured format and is named <project>.P2D, where <project> isthe project title. Besides this file, additional data is stored in multiple files in thesub-directory <project>.P2DAT. It is generally not necessary to enter such a directorybecause it is not possible to read individual files in this directory.

If a PLAXIS project file (*.P2D) is selected, a small bitmap of the corresponding projectgeometry is shown in the file requester to enable a quick and easy recognition of aproject.

2.3 HELP FACILITIES

To inform the user about the various program options and features, PLAXIS 2D providesa link in the Help menu to a digital version of the Manuals. Moreover, the Help menu maybe used to generate a file with software license information as stored in the security lock(to be used for license updates and extensions). A more detailed description of the Help

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menu of the Input and Output program is given in Sections 3.3.8 and 6.2.11 respectively.Many features are available as buttons in a toolbar. When the mouse pointer ispositioned on a button for more than a second, a short description (‘hint’) appears,indicating the function of the button. For some input parameters side panels appear tohelp the user decide which value to select.

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INPUT PROGRAM — GENERAL OVERVIEW

3 INPUT PROGRAM — GENERAL OVERVIEW

To carry out a finite element analysis using the PLAXIS 2D program, the user has tocreate a two dimensional geometry model composed of points, lines and othercomponents, in the x − y -plane and specify the material properties and boundaryconditions. This is done in the Input program. The generation of an appropriate finiteelement mesh and the generation of properties and boundary conditions on an elementlevel is automatically performed by the PLAXIS mesh generator based on the input of thegeometry model. Users may also customise the finite element mesh in order to gainoptimum performance.

When a geometry model is created in the Input program it is suggested that the differentinput items are selected in the order given by the model toolbar (from left to right). Inprinciple, first draw the geometry contour, then add the soil layers, then structural objects,then construction layers, then boundary conditions and then loadings. Using thisprocedure, the model toolbar acts as a guide through the Input program and ensures thatall necessary input items are dealt with. Of course, not all input options are generallyrequired for any particular analysis. For example, some structural objects or loadingtypes might not be used when only soil loading is considered. Nevertheless, by followingthe toolbar the user is reminded of the various input items and will select the ones thatare of interest. The program will also give warning messages if some necessary inputhas not been specified. It is important to realise that the finite element mesh must beregenerated when the geometry of an existing model is changed. This is also checked bythe program. On following these procedures the user can be confident that a consistentfinite element model is obtained.

3.1 STARTING THE INPUT PROGRAM

This icon represents the Input program. At the start of the Input program the Quickselect window appears in which a choice must be made between the selection of

an existing project and the creation of a new project (Figure 3.1).

Figure 3.1 Quick select window

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3.1.1 NEW PROJECT

When the Start a new project option is selected, the Project properties window (Figure3.4) appears in which the basic model parameters of the new project can be defined. TheProject properties window contains the Project and the Model tabsheets. The Projecttabsheet (Figure 3.4) contains the project name and description, the type of model andacceleration data. The Model tabsheet (Figure 3.5) contains the basic units for length,force and time (see Section 2.1), the initial dimensions of the model contour and the gridspecifications. The default values can be replaced by the current values when selectingSet as default and clicking the OK button. A more detailed description of all theseoptions is given below.

Project

The title, directory and the file name of the project are available in the Project group boxavailable in the Project tabsheet.

Title The defined title appears as a default name for the file of theproject when it is saved.

Directory The address to the folder where the project is saved is displayed.For a new project, there is no information shown.

File name The name of the project file is displayed. For a new project, thereis no information shown.

Comments

The Comments box in the Project tabsheet gives the possibility to add some extracomments about the project.

General options

The general options of the project are available in the Project tabsheet of the Projectproperties window.

Model

PLAXIS 2D may be used to carry out two-dimensional finite element analysis. The finiteelement model is defined by selecting the corresponding option in the Model dropdown-menu in the Project tabsheet.

Plane strain: A Plane strain model is used for geometries with a (more or less) uniformcross section and corresponding stress state and loading scheme over a certain lengthperpendicular to the cross section (z-direction). Displacements and strains in z-directionare assumed to be zero. However, normal stresses in z-direction are fully taken intoaccount.

In earthquake problems the dynamic loading source is usually applied along the bottomof the model resulting in shear waves that propagate upwards. This type of problems isgenerally simulated using a plane strain model.

Axisymmetric: An Axisymmetric model is used for circular structures with a (more orless) uniform radial cross section and loading scheme around the central axis, where thedeformation and stress state are assumed to be identical in any radial direction. Note that

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INPUT PROGRAM — GENERAL OVERVIEW

for axisymmetric problems the x-coordinate represents the radius and the y -axiscorresponds to the axial line of symmetry. Negative x-coordinates cannot be used.

Single-source vibration problems are often modelled with axisymmetric models. This isbecause waves in an axisymmetric system radiate in a manner similar to that in a threedimensional system. In this case, the energy disperses leading to wave attenuations withdistance. Such effect can be attributed to the geometric damping (or radiation damping),which is by definition included in the axisymmetric model.

The selection of Plane strain or Axisymmetric results in a two dimensional finite elementmodel with only two translational degrees of freedom per node (x- and y -direction).

x

y y

x

Figure 3.2 Example of a plane strain (left) and axisymmetric problem (right)

Elements

The user may select either 6-node or 15-node triangular elements (Figure 3.4) to modelsoil layers and other volume clusters.

nodes stress points

a. 15-node triangle

nodes stress points

b. 6-node triangle

Figure 3.3 Position of nodes and stress points in soil elements

15-Node: The 15-node triangle is the default element. It provides a fourth orderinterpolation for displacements and the numerical integration involves twelve Gausspoints (stress points). The type of element for structural elements and interfaces isautomatically taken to be compatible with the soil element type as selected here.

The 15-node triangle is a very accurate element that has produced high quality stressresults for difficult problems, as for example in collapse calculations for incompressible

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soils (Nagtegaal, Parks & Rice,1974, Sloan,1981 and Sloan & Randolph,1982). The15-node triangle is particularly recommended to be used in axi-symmetric analysis. Theuse of 15-node triangles leads to more memory consumption and slower calculation andoperation performance. Therefore a more simple type of elements is also available.

6-Node: The 6-node triangle provides a second order interpolation for displacementsand the numerical integration involves three Gauss points. The type of element forstructural elements and interfaces is automatically taken to be compatible with the soilelement type as selected here.

The 6-node triangle is a fairly accurate element that gives good results in standarddeformation analyses, provided that a sufficient number of elements are used. However,care should be taken with axisymmetric models or in situations where (possible) failureplays a role, such as a bearing capacity calculation or a safety analysis by means of phi-creduction. Failure loads or safety factors are generally overpredicted using 6-nodedelements. In those cases the use of 15-node elements is preferred.

One 15-node element can be thought of a composition of four 6-node elements, since thetotal number of nodes and stress points is equal. Nevertheless, one 15-node element ismore powerful than four 6-node elements.

In addition to the soil elements, compatible plate elements are used to simulate thebehaviour of walls, plates and shells (Section 3.4.2) and geogrid elements are used tosimulate the behaviour of geogrids and wovens (Section 3.4.4). Moreover, compatibleinterface elements are used to simulate soil-structure interaction (Section 3.4.5). Finally,the geometry creation mode allows for the input of fixed-end anchors and node-to-nodeanchors (Sections 3.4.6 and 3.4.7).

Gravity and acceleration

By default, the earth gravity acceleration, g, is set to 9.8 m/s2 and the direction of gravitycoincides with the negative y -axis, i.e. an orientation of -90◦ in the x-y -plane. Gravity isimplicitly included in the unit weights given by the user (Section 4.1). In this way, thegravity is controlled by the total load multiplier for weights of materials, ΣMweight(Section 5.11.1).

In addition to the normal gravity the user may prescribe an independent acceleration tomodel dynamic forces in a pseudo-static way. The input values of the x- andy -acceleration components are expressed in terms of the normal gravity acceleration gand entered in the Project tabsheet of the Project properties window. The activation ofthe additional acceleration in calculations is controlled by the load multipliers Maccel andΣMaccel (Section 5.11.1).

In dynamic calculations, the value of the gravity acceleration, g, is used to calculate thematerial density, ρ, from the unit of weight, γ (ρ = γ/g).

Units

Units for length, force and time to be used in the analysis need to be specified. Thesebasic units are entered in the Model tabsheet of the Project properties window (Figure3.5).

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Figure 3.4 Project properties window (Project tabsheet)

The default units, as suggested by the program, are m (meter) for length, kN (kiloNewton)for force and day for time. The corresponding units for stress and unit weights are listedin the box below the basic units.

In a dynamic analysis, the time is usually measured in [seconds] rather than the defaultunit [days]. Hence, for dynamic analysis the unit of time could be changed in the Projecttabsheet of the Project properties window. However, this is not strictly necessary since inPLAXIS Time and Dynamic time are different parameters. The time interval in a dynamicanalysis is always the dynamic time and PLAXIS always uses seconds [s] as the unit ofDynamic time. In the case where a dynamic analysis and a consolidation analysis areinvolved, the unit of Time can be left as [days] whereas the Dynamic time is in seconds[s].

All input values should be given in a consistent set of units (Section 2.1). The appropriateunit of a certain input value is usually given directly behind the edit box, based on thebasic set of units.

Geometry dimensions

At the start of a new project, the user needs to specify the dimensions of the draw area insuch a way that the geometry model that is to be created will fit within the dimensions.The dimensions are entered in the Model tabsheet of the Project properties window. Thedimensions of the draw area do not influence the geometry itself and may be changedwhen modifying an existing project, provided that the existing geometry fits within themodified dimensions. Clicking on the rulers in the geometry creation mode may be usedas a shortcut to proceed to the input of the geometry dimensions in the Project propertieswindow.

Grid

To facilitate the creation of the geometry model, the user may define a grid for the drawarea. This grid may be used to snap the pointer into certain ‘regular’ positions. The grid isdefined by means of the parameters Spacing and Number of snap intervals. The Spacingis used to set up a coarse grid, indicated by the small dots on the draw area. The actualgrid is the coarse grid divided into the Number of snap intervals. The default number ofintervals is 1, which gives a grid equal to the coarse grid. The grid specification is entered

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in the Model tabsheet of the Project properties window. The View menu may be used toactivate or deactivate the grid and snapping options.

Figure 3.5 Project properties window (Model tabsheet)

3.1.2 EXISTING PROJECT

When the Input program is started, a list of the recent projects appears in the Quick selectwindow. In the case when a project other than the listed recent ones is required, the Openan existing project option should be selected. As this selection is made, the Windows®

file requester (Figure 2.2) pops up. It enables the user to browse through all availabledirectories and to select the desired PLAXIS project file (*.P2D). After the selection of anexisting project, the corresponding geometry is presented in the main window.

An existing PLAXIS 2D project can also be read by selecting the Open option in the Filemenu. In the file requester, the type of the file is, by default, set to ‘PLAXIS 2D files(*.P2D)’.

3.1.3 IMPORTING A GEOMETRY

It is possible to import tab-separated value (.txt) or comma-separated value (.csv) textfiles to import a geometry in PLAXIS. Such files need to include a table with thecoordinates of the points (preceded by the command Points; each new line starting with anumber which serves as the point’s ID, followed by the point coordinates) and lines(preceded by the command Lines; each new line starting with a number , which servesas the line’s ID, followed by the starting and ending point ID’s). Examples of such files areon given in Table 3.1 and 3.2. Note that PLAXIS only supports the English notation ofdecimal numbers using a dot.

It is possible to import a geometry composed of points and straight lines (with theAcdbLine property) from external sources in different formats like AutoCAD native(*.DWG) and interchange (*.DXF) file formats. Lines as part of polylines(AcdbPolyLine)are not imported. In the cases where the imported geometry contains curved elementsas well (like arcs), the geometry will be partly imported (only points and straight lines).

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Table 3.1 Example of a tab-separated value file (.txt)

Points

0 0.0 0.0

1 20.0 0.0

2 20.0 10.0

3 0.0 10.0

Lines

0 0 1

1 1 2

2 2 3

3 3 0

Table 3.2 Example of a comma-separated value file (.csv)

Points

0 , 0.0 , 0.0

1 , 20.0 , 0.0

2 , 20.0 , 10.0

3 , 0.0 , 10.0

Lines

0 , 0 , 1

1 , 1 , 2

2 , 2 , 3

3 , 3 , 0

Scaling of the imported geometry

When a geometry is imported the Import scale factor (Figure 3.6) pops up where ascaling factor can be defined for the imported geometry. The scale factor is relevant whenthe imported geometry is defined in a unit of length different from the one used in thePLAXIS project. The scaled geometry will be displayed when the OK button is clicked.

Figure 3.6 Import scale factor window

3.1.4 PACKING A PROJECT

The created project can be compressed using the Pack project application whichis available in the File menu of the Input program. This application can be executed

directly from the PLAXIS 2D installation folder by double clicking the corresponding file(PackProject.exe). A shortcut to the application can be created as well. In the Packproject window (Figure 3.7) the information archiving process and information can

The project to be compressed and the archive can be located using the Browse button.The options available in the Purpose box are:

Backup All the files in the project are included in the compressed projectas well as the mesh information, phase specification and theresults of all the saved calculation steps. The extension of the

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project file, indicating in which program it was created, and thearchiving date are included in the archive name.

Support Selecting this option enables including all the informationrequired to give support for the project at hand. Note thatsupport is only provided to VIP users.

Custom The user can define the information to be included in the archive.

Figure 3.7 Pack project window

The options for compression and volume size are available in the Archiveoptions window (Figure 3.8), displayed by clicking the button in the Purpose box.

Figure 3.8 Archive options window

The Content box displays the options for the information to be included in the archive isshown. The options available are:

Mesh The information related to geometry is imported when the Meshoption is selected.

Phases The options available are:Smart When a phase is selected in the tree,

the parent phase is selectedautomatically in order to provide aconsistent chain of phases.

All All the phases available in the project

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are selected.

Manual Specific phases can be selected by theuser.

Results The results to be included in the archive can be selected. Theoptions available are:All steps The results of all the calculation steps

are included in the archive.

Last step only The results of only the last calculationstep of each phase are included in thearchive.

Manual The results of specific calculation stepscan be selected by the user.

Note that when the Backup or the Support option is selected, the Content options areautomatically selected by the program.

3.2 LAYOUT OF THE INPUT PROGRAM

The general layout of the Input program for a new project is shown in Figure 3.9.

Figure 3.9 Layout of the Input program

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The main window of the Input program contains the following items:

Title bar

The name of the program and the title of the project is displayed in the title bar. Unsavedmodifications in the project are indicated by a ‘∗’ in the project name.

Menu bar

The menu bar contains drop-down menus covering the options available in the Inputprogram.

General toolbar

The general toolbar contains buttons for general actions such as disk operations,printing, zooming or selecting objects. It also contains buttons to start the othersub-programs (Calculations, Output).

Hint: If the mouse is moved over a button in a toolbar, a hint about the function ofthis button is displayed.

Mode tabs

The mode tabs are used to separate different modelling modes. The following tabs areavailable:

Geometry The geometry of the model is defined.

Calculations The calculation phases and calculation process are defined andthe project is calculated.

Model toolbar

The model toolbar contains buttons for actions that are related to the creation of ageometry model. The buttons are ordered in such a way that, in general, following thebuttons on the tool bar from the left to the right results in a fully defined model.

Draw area

The draw area is the drawing sheet on which the geometry model is created andmodified. The geometry model can be created by means of the mouse and using thebuttons available in the Model toolbar.

The physical origin is indicated by the intersection of the x− and y− axes. Each axis isdisplayed in a different colour and their positive directions are indicated by arrows.

Rulers

At both the left and the top of the draw area, rulers indicate the physical x- andy -coordinates of the geometry model. This enables a direct view of the geometrydimensions. The rulers can be switched off in the View menu. When clicking on the

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rulers the Project properties window appears in which the geometry dimensions can bechanged.

Status bar

The status bar displays information about the location of the mouse cursor in the drawarea. The cursor position is given in both in physical units (x , y -coordinates) and inscreen pixels.

Command line

If drawing with the mouse does not give the desired accuracy, the Manual input line canbe used. Values for the x- and y -coordinates can be entered here by typing the requiredvalues separated by a space (x-value <space> y -value <Enter>) or by a semicolon(x-value;y -value <Enter>). Manual input of coordinates can be given for all objects,except for Hinges and Rotation fixities.

Instead of the input of absolute coordinates, increments with respect to the previous pointcan be given by typing an @ directly in front of the value (@x-value <space> @y -value<Enter>). In addition to the input of coordinates, existing geometry points may beselected by their number.

3.3 MENUS IN THE MENU BAR

The menu bar of the Input program contains drop-down menus covering most options forhandling files, transferring data, viewing graphs, creating a geometry model, generatingfinite element meshes and entering data in general.

The menus available in the Input program are:

3.3.1 FILE MENU

New To create a new project. In case of a new project, the Projectproperties window is automatically displayed to define itsproperties.

Open To open an existing project. The file requester is displayed.

Recent projects To quickly open one of the most recent projects.

Import To import geometry data from other file types (Section 3.1.3).

Save To save the current project under the existing name. If a namehas not been given before, the file requester is presented.

Save as To save the current project under a new name. The file requesteris displayed.

Pack project To compress the current project.

Project properties To activate the Project properties window (Section 3.1.1).

Print To print the geometry model on a selected printer.

Exit To leave the Input program.

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3.3.2 EDIT MENU

Undo To restore a previous status of the geometry model (after aninput error). Repetitive use of the undo option is limited to the 10most recent actions.

Copy to clipboard To copy the view of the model displayed in the draw area toclipboard.

3.3.3 VIEW MENU

Zoom in To zoom into a rectangular area for a more detailed view.Alternatively, the mouse wheel may be used for zooming.

Zoom out To restore the view to before the most recent zoom action.

Reset view To restore the full draw area.

Table To view the table with the x- and y -coordinates of all geometrypoints. The table may be used to adjust existing coordinates.

Rulers To show or hide the rulers along the draw area.

Cross hair To show or hide the cross hair during the creation of a geometrymodel.

Grid To show or hide the grid in the draw area.

Axes To show or hide the arrows indicating the x- and y -axes.

Snap to grid To activate or deactivate the snapping into the regular grid points.

Change color scheme To change the intensity of the colours indicating the material datasets assigned to soil layers.

Point numbers To show or hide the geometry point numbers.

Chain numbers To show or hide the ‘chain’ numbers of geometry objects.’Chains’ are clusters of similar geometry objects that are drawnin one drawing action without intermediately clicking the righthand mouse button or the <Esc> key.

3.3.4 GEOMETRY MENU

Geometry line To create points and lines in the draw area.

Plate To create structural objects with a significant flexural rigidity (orbending stiffness)

Geogrid To create slender structures with a normal stiffness but with nobending stiffness.

Interface To model the soil-structure interaction.

Node-to-node anchor To create springs that are used to model ties between two points.

Fixed-end anchor To create springs that are used to model a tying of a single point.

Tunnel To create circular and non-circular tunnel cross sections whichare to be included in the geometry model.

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Hinge and rotation springTo create a plate connection that allows for a discontinuousrotation in the point of connection.

Drain To prescribe lines inside the geometry model where (excess)pore pressures are reduced.

Well To prescribe points inside the geometry model where a specificdischarge is extracted from or infiltrated into the soil.

Check consistency To check the geometry consistency. The program gives amessage indicating whether consistency issues exist. Possibleinconsistencies are overlapping lines or multiple points at thesame location.

3.3.5 LOADS MENU

Standard fixities To impose a set of general boundary conditions to the geometrymodel.

Standard earthquake boundariesTo impose standard boundary conditions for earthquake loading.

Standard absorbent boundaries (dynamics)To impose standard absorbent boundaries for single sourcevibrations.

Set dynamic load systemTo specify which of the load system(s) will be used as a dynamicload.

Total fixities To impose total fixities.

Vertical fixities To impose vertical fixities.

Horizontal fixities To impose horizontal fixities.

Rotation fixities (plates) To fix the rotational degree of freedom of a plate around the z−axis.

Absorbent boundaries To define a boundary that absorbs the increments of stressescaused by dynamic loading.

Prescribed displacementsTo impose special conditions on the model to control thedisplacement of certain points.

Distributed load — static load system ATo define distributed loads for load system A.

Distributed load — static load system BTo define distributed loads for load system B.

Point load — static load system ATo define point loads for load system A.

Point load — static load system BTo define point loads for load system B.

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Design approaches To define partial factors according to a design approach and toselect the design approaches for the current project.

Hint: Note that point loads actually represent line loads in the out-of-planedirection.

3.3.6 MATERIALS MENU

Soil & interfaces To activate the data base engine for the creation andmodification of material data sets for soil and interfaces.

Plates To activate the data base engine for the creation andmodification of material data sets for plates.

Geogrids To activate the data base engine for the creation andmodification of material data sets for geogrids.

Anchors To activate the data base engine for the creation andmodification of material data sets for anchors.

The use of the data base and the parameters contained in the data sets are described indetail in Chapter 4.

3.3.7 MESH MENU

Basic element type To display the Project tabsheet of the Project properties windowwhere the basic element type can be selected.

Global coarseness To select one of the available options for the global meshcoarseness.

Refine global To refine the mesh globally.

Refine cluster To locally refine the selected clusters.

Refine line To locally refine the mesh around selected lines.

Refine around point To locally refine the mesh around selected points.

Reset all To reset all the refinements.

Generate To generate the mesh.

The options in this menu are explained in detail in Section 3.7.

3.3.8 HELP MENU

Manuals To display the manuals.

Instruction movies To reach the PLAXIS TV website where instruction movies aredisplayed.

Update license To update the PLAXIS 2D license via e-mail.

http://www.plaxis.nl/ To reach the PLAXIS website.

Disclaimer The complete disclaimer text is displayed.

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About Information about the program version and license are displayed.

3.4 GEOMETRY

The generation of a finite element model begins with the creation of a geometry model,which is a representation of the problem of interest. A geometry model consists of points,lines and clusters. Points and lines are entered by the user, whereas clusters aregenerated by the program. In addition to these basic components, structural objects orspecial conditions can be assigned to the geometry model to simulate tunnel linings,walls, plates, soil-structure interaction or loadings.

It is recommended to start the creation of a geometry model by drawing the full geometrycontour. In addition, the user may specify material layers, structural objects, lines usedfor construction phases, loads and boundary conditions. The geometry model should notonly include the initial situation, but also situations that occur in the various calculationphases.

After the geometry components of the geometry model have been created, the usershould compose data sets of material parameters and assign the data sets to thecorresponding geometry components (Section 4). When the full geometry model hasbeen defined and all geometry components have their initial properties, the finite elementmesh can be generated (Section 3.7).

Selecting geometry components

When the Selection tool is active, a geometry component may be selectedby clicking once on that component in the geometry model. Multiple selection is

possible by holding down the <Shift> key on the keyboard while selecting the desiredcomponents.

Properties of geometry components

Most geometry components have certain properties, which can be viewed and altered inproperty windows. After double clicking a geometry component the correspondingproperty window appears. If more than one object is located on the indicated point, aselection dialog box appears from which the desired component can be selected.

3.4.1 POINTS AND LINES

The basic input item for the creation of a geometry model is the Geometry line. Thisitem can be selected from the Geometry menu as well as from the second tool bar.

When the Geometry line option is selected, the user may create points and lines in thedraw area by clicking with the mouse pointer (graphical input) or by typing coordinates atthe command line (keyboard input). As soon as the left hand mouse button is clicked inthe draw area a new point is created, provided that there is no existing point close to thepointer position. If there is an existing point close to the pointer, the pointer snaps into theexisting point without generating a new point. After the first point is created, the user maydraw a line by entering another point, etc. The drawing of points and lines continues untilthe right hand mouse button is clicked at any position or the <Esc> key is pressed.

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If a point is to be created on or close to an existing line, the pointer snaps onto the lineand creates a new point exactly on that line. As a result, the line is split into two newlines. If a line crosses an existing line, a new point is created at the crossing of both lines.As a result, both lines are split into two new lines. If a line is drawn that partly coincideswith an existing line, the program makes sure that over the range where the two linescoincide only one line is present. All these procedures accomplish that a consistentgeometry is created without double points or lines. The Check consistency option in theGeometry menu may be used to check the consistency of the geometry model.

Existing points or lines may be modified or deleted by first choosing the Selection toolfrom the tool bar. To move a point or line, select the point or the line in the cross sectionand drag it to the desired position. To delete a point or line, select the point or the line inthe cross section and press <Delete> on the keyboard. If more than one object is presentat the selected position, a delete dialog box appears from which the object(s) to bedeleted can be selected. If a point is deleted where one or more geometry lines cometogether, then all these connected geometry lines will be deleted as well.

After each drawing action the program determines the clusters that can be formed. Acluster is a closed loop of different geometry lines. In other words, a cluster is an areafully enclosed by geometry lines. The detected clusters are lightly shaded. Each clustercan be given certain material properties to simulate the behaviour of the soil in that partof the geometry (Section 4.1). The clusters are divided into soil elements during meshgeneration (Section 3.7).

3.4.2 PLATES

Plates are structural objects used to model slender structures in the ground witha significant flexural rigidity (or bending stiffness) and a normal stiffness. Plates can

be used to simulate the influence of walls, plates, shells or linings extending inz-direction. In a geometry model, plates without assigned material properties appear as’light blue lines’, whereas plates with assigned material properties appear in their materialset colour. Examples of geotechnical structures involving plates are shown in Figure 3.10.

Figure 3.10 Applications in which plates, anchors and interfaces are used

Plates can be selected from the Geometry menu or by clicking on the correspondingbutton in the tool bar. The creation of plates in the geometry model is similar to thecreation of geometry lines (Section 3.4.1). When creating plates, the correspondinggeometry lines are created simultaneously. Hence, it is not necessary to create first ageometry line at the position of a plate. Plates can be erased by selecting them in thegeometry and pressing the <Delete> key.

The material properties of plates are contained in material data sets (Section 4.2). Themost important parameters are the flexural rigidity (bending stiffness) EI and the axialstiffness EA.

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From these two parameters an equivalent plate thickness deq is calculated from theequation:

deq =√

12EIEA

Plates can be activated or de-activated in calculation phases using Staged constructionas Loading input.

Plate elements

Plates in the 2D finite element model are composed of plate elements (line elements)with three degrees of freedom per node: two translational degrees of freedom (ux , uy )and one rotational degrees of freedom (rotation in the x-y plane: φz ). When 6-node soilelements are employed then each plate element is defined by three nodes whereas5-node plate elements are used together with the 15-node soil elements (Figure 3.15).The plate elements are based on Mindlin’s plate theory (Bathe, 1982). This theory allowsfor plate deflections due to shearing as well as bending. In addition, the element canchange length when an axial force is applied. Plate elements can become plastic if aprescribed maximum bending moment or maximum axial force is reached.

Bending moments and axial forces are evaluated from the stresses at the stress points. A3-node plate element contains two pairs of Gaussian stress points whereas a 5-nodeplate element contains four pairs of stress points. Within each pair, stress points arelocated at a distance 1/6

√3deq above and below the plate centre-line.

Figure 3.15 shows a single 3-node and 5-node plate element with an indication of thenodes and stress points.

stress pointnode

3-node plate element 5-node plate element

Figure 3.11 Position of nodes and stress points in plate elements

It is important to note that a change in the ratio EI/EA will change the equivalentthickness deq and thus the distance separating the stress points. If this is done whenexisting forces are present in the plate element, it would change the distribution ofbending moments, which is unacceptable. For this reason, if material properties of aplate are changed during an analysis (for example in the framework of StagedConstruction) it should be noted that the ratio EI/EA must remain unchanged.

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3.4.3 EMBEDDED PILE ROW

Since the stress state and deformation pattern around piles is fully three-dimensional, it isimpossible to model piles realistically in a 2D model. Hence, the 2D embedded pileelement is only a simplified approach to deal with a row of piles in the out-of-planedirection in a 2D plane strain model.

The idea behind the 2D embedded pile is that the pile (represented by a Mindlin beamelement) is not ‘in’ the 2D mesh, but superimposed ‘on’ the mesh, while the soil elementmesh itself is continuous (Figure 3.12, after Sluis (2012)). A special out-of-plane interfaceconnects the beam with the underlying soil elements. The beam is supposed to representthe deformations of an out-of-plane row of individual piles, whereas displacements of thesoil elements are supposed to represent the ‘average’ soil displacement in theout-of-plane direction. The interface stiffness should be chosen such that it accounts forthe difference between the (average) soil displacement and the pile displacement whiletransferring loads from the pile onto the soil and vice versa. This requires at least theout-of-plane spacing of the piles to be taken into account in relation to the pile diameter.

Figure 3.12 Schematic representation of embedded pile (after Sluis (2012))

An embedded pile row can be utilised to model a row of long slender structuralmembers used to transmit loads to the ground at lower levels. The Embedded pile

row feature is available only for Plane strain models. The information required for anembedded pile row consists of the properties of a single pile and the spacing of the pilesin the out-of-plane direction.

Hint: Since installation effects cannot be considered, the Embedded pile rowfeature should be primarily used for pile types that cause a limiteddisturbance of the surrounding soil during installation. This may include sometypes of bored piles, but obviously not driven piles or soil displacement piles.

The feature can be selected from the Geometry menu or by clicking on the correspondingbutton in the toolbar. The creation of embedded pile rows in the geometry model is

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similar to the creation of a geometry line (Section 3.4.1). Note that one row is indicatedby one line in the model. When creating embedded pile rows, the correspondinggeometry line is created simultaneously. Hence it is not necessary to create first ageometry line at the position of an embedded pile row. It is also not necessary to createinterface elements around the embedded pile row, since special interface elements areautomatically created with the embedded pile elements. An embedded pile row can beerased by selecting the corresponding pile in the geometry and pressing the <Delete>key. Figure 3.13 is displayed as the <Delete> key is pressed and it indicates that both anembedded pile and a line have been created simultaneously. In a geometry model,embedded pile rows without assigned material properties appear as ‘pink lines’, whereasembedded pile rows with assigned material properties appear in their material set colour.

Figure 3.13 Indication of an embedded pile and a line created simultaneously

The order of drawing an embedded pile row is relevant in defining the connection of theembedded pile to the surrounding (soil or structure) and the application of the bearingcapacity. By default the first drawn point corresponds to the top point of the pile and thesecond drawn point corresponds to the tip of the pile. Note that the top point is the pointwhere the connection type may be defined. The user may redefine the top point of thepile, as well as modify the connection of the top point of the pile to the surroundinggeometry. To define the connection of the embedded pile:

• Select the embedded pile row in the model.

• In the select window select the embedded pile and press OK. The Embedded pilerow window (Figure 3.14) is displayed. Note that the connection type can only bedefined for the top point.

Figure 3.14 Embedded pile row window

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The options available are:

Free: The top of the pile is not directly coupled with the soil element inwhich the pile top is located, but the interaction through theinterface elements is still present.

Hinged: The displacement at the top point of the pile is directly coupledwith the displacement of the element in which the top point islocated, which means that they undergo exactly the samedisplacement.

Rigid: The displacement and rotation at the pile top are both coupledwith the displacement and rotation of the element in which thepile top is located, provided that this element has rotationaldegrees of freedom. This option only applies if the pile topcoincides with plates elements.

Hint: When embedded pile rows are located in a volume cluster with linear elasticmaterial behaviour, the specified values of the shaft resistance and spacingare ignored. The reason for this is that the linear elastic material is notsupposed to be soil, but part of the structure. The connection between thepile and the structure is supposed to be rigid to avoid, for example, punchingof piles through a concrete deck.

» When an embedded pile row and a structure are both active and share thesame geometry point, the node created at the top point of the embedded pileis by default rigidly connected to the structure node. However, if the structureis not active, the embedded pile node is by default connected (hinged) to thesoil node at that location.

» Note that when an interface is available, the embedded pile row is NOTconnected to the interface but to the structure or soil node at that location.

The material properties of embedded pile rows are contained in material data sets(Section 4.6). Embedded pile rows can be activated or de-activated in calculation phasesusing Staged construction as Loading input.

Embedded pile elements

Embedded piles in the 2D finite element model are composed of line elements with threedegrees of freedom per node: two translational degrees of freedom (ux , uy ) and onerotational degrees of freedom (rotation in the x-y plane: φz ). When 6-node soil elementsare employed then each embedded pile element is defined by three nodes whereas5-node embedded pile elements are used together with the 15-node soil elements(Figure 3.15). The elements are based on Mindlin’s beam theory (Bathe, 1982). Thistheory allows for deflections due to shearing as well as bending. In addition, the elementcan change length when an axial force is applied. Figure 3.15 shows a single 3-node and5-node embedded pile element with an indication of the nodes and stress points.

Bending moments and axial forces are evaluated from the stresses at the stress points. A3-node embedded pile element contains two pairs of Gaussian stress points whereas a5-node embedded pile element contains four pairs of stress points. Within each pair,

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stress pointnode

3-node plate element 5-node plate element

Figure 3.15 Position of nodes and stress points in embedded pile elements

stress points are located at a distance 1/6

√3deq above and below the embedded pile

centre-line.

The interaction between the pile and the surrounding soil may involve a skin resistance aswell as a foot resistance. Therefore, special out-of-plane interface elements (line-to-lineinterface along the shaft and point-to-point interface at the base) are used to connect thepile elements to the surrounding soil elements. The interface elements involve springs inthe longitudinal and transverse pile direction and a slider in the longitudinal direction.

Figure 3.16 Embedded pile interaction with soil (after Sluis (2012))

Pile forces (structural forces) are evaluated at the embedded pile element integrationpoints and extrapolated to the beam element nodes. These forces can be viewedgraphically and tabulated in the Output program. Details about the embedded pileelement formulations are given in the Material Models Manual.

Embedded pile row properties

The material properties of embedded pile rows are contained in Embedded pile rowsmaterial data sets (Section 4.6). In the material dataset geometric features of the pile,material properties, spacing of the piles in the out of plane direction, skin friction andbearing capacity of the pile as well as the interface stiffness factor can be defined.

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3.4.4 GEOGRIDS

Geogrids are slender structures with a normal stiffness but with no bendingstiffness. Geogrids can only sustain tensile forces and no compression. These

objects are generally used to model soil reinforcements. Examples of geotechnicalstructures involving geotextiles are presented in Figure 3.17.

Figure 3.17 Applications in which geogrids are used

Geogrids can be selected from the Geometry menu or by clicking on the correspondingbutton in the tool bar. The creation of geogrids in the geometry model is similar to thecreation of geometry lines (Section 3.4.1). In a geometry model geogrids withoutassigned material properties appear as ‘light yellow lines’, whereas geogrids withassigned properties appear in their material colour. When creating geogrids,corresponding geometry lines are created simultaneously. The only material property of ageogrid is an elastic normal (axial) stiffness EA, which can be specified in the materialdata base (Section 4.5). Geogrids can be erased by selecting them in the geometry andpressing the <Delete> key. Geogrids can be activated or de-activated in calculationphases using Staged construction as Loading input.

Geogrid elements

Geogrids are composed of geogrid elements (line elements) with two translationaldegrees of freedom in each node (ux , uy ). When 15-node soil elements are employedthen each geogrid element is defined by five nodes whereas 3-node geogrid elementsare used in combination with 6-node soil lements. Axial forces are evaluated at theNewton-Cotes stress points. These stress points coincide with the nodes. The locationsof the nodes and stress points in geogrid elements are indicated in Figure 3.18.

nodesa. 3-node geogrid element

stress pointnodes

b. 5-node geogrid element

Figure 3.18 Position of nodes and stress points in geogrid elements

Modelling ground anchors

Geogrids may be used in combination with node-to-node anchors to simulate a groundanchor. In this case the geogrid is used to model the grouted anchor section and thenode-to-node anchor is used to model the ungrouted part of the anchor (free length)(Section 3.4.6).

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3.4.5 INTERFACES

Each interface has assigned to it a ‘virtual thickness’ which is an imaginarydimension used to define the material properties of the interface. The higher the

virtual thickness is, the more elastic deformations are generated. In general, interfaceelements are supposed to generate very little elastic deformations and therefore thevirtual thickness should be small. On the other hand, if the virtual thickness is too small,numerical ill-conditioning may occur. The virtual thickness is calculated as the Virtualthickness factor times the global element size. The global element size is determined bythe global coarseness setting for the mesh generation (Section 3.7.2). The default valueof the Virtual thickness factor is 0.1. This value can be changed by double clicking on thegeometry line and selecting the interface from the selection dialog box. In general, careshould be taken when changing the default factor. However, if interface elements aresubjected to very large normal stresses, it may be required to reduce the Virtual thicknessfactor. Further details of the significance of the virtual thickness are given in Section4.1.4.

The creation of an interface in the geometry model is similar to the creation of a geometryline. The interface appears as a dashed line at the right hand side of the geometry line(considering the direction of drawing) to indicate at which side of the geometry line theinteraction with the soil takes place. The side at which the interface will appear is alsoindicated by the arrow on the cursor pointing in the direction of drawing. To place aninterface at the other side, it should be drawn in the opposite direction. Note thatinterfaces can be placed at both sides of a geometry line. This enables a full interactionbetween structural objects (walls, plates, geogrids, etc.) and the surrounding soil. To beable to distinguish between the two possible interfaces along a geometry line, theinterfaces are indicated by a plus-sign (+) or a minus-sign (-). This sign is just foridentification purposes; it does not have a physical meaning and it has no influence onthe results. Interfaces can be erased by selecting them in the geometry and pressing the<Delete> key.

A typical application of interfaces would be in a region which is intermediate betweensmooth and fully rough. The roughness of the interaction is modelled by choosing asuitable value for the strength reduction factor in the interface (Rinter ). This factor relatesthe interface strength (wall friction and adhesion) to the soil strength (friction angle andcohesion). Instead of entering Rinter as a direct interface property, this parameter isspecified together with the soil strength parameters in a material data set for soil andinterfaces. For detailed information about the interface material properties, see Section4.1.4.

Interfaces can be activated or de-activated in calculation phases using Stagedconstruction as Loading input.

Interface elements

Interfaces are composed of interface elements. Figure 3.19 shows how interfaceelements are connected to soil elements. When using 15-node soil elements, thecorresponding interface elements are defined by five pairs of nodes, whereas for 6-nodesoil elements the corresponding interface elements are defined by three pairs of nodes.In the figure, the interface elements are shown to have a finite thickness, but in the finiteelement formulation the coordinates of each node pair are identical, which means that theelement has a zero thickness.

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nodesa. 6-node soil element

stress pointnodes

b. 15-node soil element

Figure 3.19 Distribution of nodes and stress points in interface elements and their connection to soilelements

The stiffness matrix for interface elements is obtained by means of Newton Cotesintegration. The position of the Newton Cotes stress points coincides with the node pairs.Hence, five stress points are used for a 10-node interface element whereas three stresspoints are used for a 6-node interface element.

Interface properties

The basic property of an interface element is the associated material data set for soil andinterfaces. This property is contained in the interface properties window, which can beentered by double clicking an interface in the geometry model and selecting the positiveor negative interface element or interface chain from the selection window. Alternatively,the right-hand mouse button may be clicked, then the Properties option should beselected and finally the positive or negative interface element or interface chain may beselected from the right-hand mouse button menu. As a result, the Interface windowappears showing the associated Material set. By default, the Material set is set to<Cluster material> indicating that the material of the associated cluster has beenassigned. However, any other existing material data set for soil and interfaces can beselected in the Material set drop down menu to change the associated material data set.

In addition, the interface properties window shows the Virtual thickness factor. This factoris used to calculate the Virtual thickness of interface elements (see Page 37). Thestandard value of the Virtual thickness factor is 0.1. Care should be taken when changingthe standard value. The standard value can be restored using the Standard button.

In a consolidation analysis or a groundwater flow analysis, interface elements can beused to block the flow perpendicular to the interface, for example to simulate animpermeable screen. In fact, when interfaces are used in combination with plates, theinterface is used to block the flow since plate elements are fully permeable. In situationswhere interfaces are used in a mesh where they should be fully permeable, it is possibleto de-activate the interface (see Sections 5.9.8, 5.9.6 and 5.8.1).

Interfaces around corner points

Figure 3.20 and Figure 3.21 show that problems of soil-structure interaction may involvepoints that require special attention. Corners in stiff structures and an abrupt change inboundary condition may lead to high peaks in the stresses and strains. Volume elementsare not capable of reproducing these sharp peaks and will, as a result, producenon-physical stress oscillations. This problem can be solved by making use of interface

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elements as shown in Figure 3.21.

Figure 3.20 Inflexible corner point, causing poor quality stress results

Figure 3.21 Flexible corner point with improved stress results

Figure 3.21 shows that the problem of stress oscillation may be prevented by specifyingadditional interface elements inside the soil body. These elements will enhance theflexibility of the finite element mesh and will thus prevent non-physical stress results.However, these elements should not introduce an unrealistic weakness in the soil.Therefore special attention should be made to the properties of these interface elements(Section 4.1.4).

It is advised to extend the interface beyond the end (ends) of the plate in the soil. Thisavoids the end (ends) of the plate becoming fixed to the soil. Figure 3.22 displays theeffect of extending the interface in the mesh. A possible result of not extending theinterface may be an unrealistic end bearing capacity or unrealistic contact stresses.

a. Not extended interface b. Extended interface

Figure 3.22 Effect of the interface extension in the mesh

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Additional theoretical details on this special use of interface elements is provided byGoodman, Taylor & Brekke (1968) and van Langen & Vermeer (1991).

3.4.6 NODE-TO-NODE ANCHORS

Node-to-node anchors are springs that are used to model ties between two points.This type of anchors can be selected from the Geometry menu or by clicking on the

corresponding button in the tool bar. Typical applications include the modelling of acofferdam as shown in Figure 3.10. It is not recommended to draw a geometry line at theposition where a node-to-node anchor is to be placed. However, the end points ofnode-to-node anchors must always be connected to geometry lines, but not necessarilyto existing geometry points. In the latter case a new geometry point is automaticallyintroduced. The creation of node-to-node anchors is similar to the creation of geometrylines (Section 3.4.1) but, in contrast to other types of structural objects, geometry linesare not simultaneously created with the anchors. Hence, node-to-node anchors will notdivide clusters nor create new ones.

A node-to-node anchor is a two-node elastic spring element with a constant springstiffness (normal stiffness). This element can be subjected to tensile forces (for anchors)as well as compressive forces (for struts). Both the tensile force and the compressiveforce can be limited to allow for the simulation of anchor or strut failure. The propertiescan be entered in the material data base for anchors (Section 4.7). Node-to-nodeanchors can be activated, de-activated or prestressed in a calculation phase usingStaged construction as Loading input.

3.4.7 FIXED-END ANCHORS

Fixed-end anchors are springs that are used to model a tying of a single point.This type of anchor can be selected from the Geometry menu or by clicking on the

corresponding button in the tool bar. An example of the use of fixed-end anchors is themodelling of struts (or props) to sheet-pile walls, as shown in Figure 3.10. Fixed-endanchors must always be connected to existing geometry lines, but not necessarily toexisting geometry points. A fixed-end anchor is visualised as a rotated T (—|). The lengthof the plotted T is arbitrary and does not have any particular physical meaning. Bydefault, a fixed-end anchor is pointing in the positive x-direction, i.e. the angle in thex ,y -plane is zero. By double clicking in the middle of the T the Fixed-end anchor windowappears in which the angle can be changed. The angle is defined in the anticlockwisedirection, starting from the positive x-direction towards the y -direction. In addition to theangle, the equivalent length of the anchor may be entered in the Fixed-end anchorwindow. The equivalent length is defined as the distance between the anchor connectionpoint and the fictitious point in the longitudinal direction of the anchor where thedisplacement is assumed to be zero.

A fixed-end anchor is a one-node elastic spring element with a constant spring stiffness(or normal stiffness). The other end of the spring (defined by the equivalent length andthe direction) is fixed. The properties can be entered in the material database for anchors(Section 4.7).

Fixed-end anchors can be activated, de-activated or prestressed in a calculation phaseusing Staged construction as Loading input.

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3.4.8 TUNNELS

The Tunnel option can be used to create circular and non-circular tunnel crosssections which are to be included in the geometry model. A tunnel cross section is

composed of arcs and lines, optionally supplied with a lining and an interface. A tunnelcross section can be stored as an object on the hard disk (i.e. as a file with the extension.TNL) and included in other projects. The tunnel option is available from the Geometrymenu or from the tool bar.

Tunnel designer

Once the tunnel option has been selected, the Tunnel designer window appears. TheTunnel designer contains the following items (Figure 3.23):

Figure 3.23 Tunnel designer with standard tunnel shape

Tunnel menu Menu with options to open and save a tunnel object and to settunnel attributes.

Tool bar Bar with buttons as shortcuts to set tunnel attributes.

Display area Area in which the tunnel cross section is plotted.

Rulers The rulers indicate the dimension of the tunnel cross section inlocal coordinates. The origin of the local coordinate system isused as a reference point for the positioning of the tunnel in thegeometry model.

Section group box Box containing shape parameters and attributes of individualtunnel sections. Use the buttons to select other sections.

Other parameters See further.

Standard buttons To accept (OK ) or to cancel the created tunnel.

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Basic tunnel shape

Once the tunnel option has been selected, the following toolbar buttons can be used toselect a basic tunnel shape:

A Whole tunnel should be used if the full tunnel cross section is included in thegeometry model.

A half tunnel should be used if the geometry model includes only one symmetric half ofthe problem where the symmetry line of the geometry model corresponds to thesymmetry line of the tunnel. Depending on the side of the symmetry line that is used inthe geometry model the user should select the right half of a tunnel or the left half.

Half a tunnel — Left half

Half a tunnel — Right half

Hint: A half tunnel can also be used to define curved sides of a larger structure,such as an underground storage tank. The remaining linear parts of thestructure can be added in the draw area using geometry lines or plates.

Type of tunnel

Before creating the tunnel cross section the type of tunnel must be selected.

None: Select this option when you want to create an internal geometry contourcomposed of different sections and have no intention to create a tunnel. Each section isdefined by a line, an arc or a corner. The outline consists of two lines if you enter apositive value for the Thickness parameter. The two lines will form separate clusters witha corresponding thickness when inserting the outline in the geometry model.

Bored tunnel: Select this option to create a circular tunnel that includes a homogeneoustunnel lining (composed of a circular shell) an outside and an inside interface. The tunnelshape consists of different sections that can be defined with arcs. Since the tunnel liningis circular, each section has the radius that is defined in the first section. The tunneloutline consists of two lines if you enter a positive value for the Thickness parameter.This way a thick tunnel lining can be created that is composed of volume elements.

The tunnel lining (shell) is considered to be homogeneous and continuous. As a result,assigning material data and the activation or deactivation of the shell in the framework ofstaged construction can only be done for the lining as a whole (and not individually foreach section). If the shell is active, a contraction of the tunnel lining (shrinkage) can bespecified to simulate the volume loss due to the tunnel boring process (Section 5.8.8).

NATM tunnel: The tunnel lining (shell) is considered to be discontinuous. As a result,assigning material data and the activation or deactivation of lining parts in the frameworkof staged construction is done for each section individually. It is not possible to apply acontraction of the shell (shrinkage) for NATM tunnels. To simulate the deformations dueto the excavation and construction in NATM tunnels other calculation methods areavailable (Sections 5.8.6 and 5.8.10).

The tunnel lining (shell) is considered to be discontinuous. As a result, assigning materialdata and the activation or deactivation of lining parts in the framework of staged

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construction is done for each section individually. It is not possible to apply a contractionof the shell (shrinkage) for NATM tunnels. To simulate the deformations due to theexcavation and construction in NATM tunnels other calculation methods are available(Sections 5.8.6 and 5.8.10).

Geometrical features of tunnel sections

The creation of a tunnel cross section starts with the definition of the inner tunnelboundary, which is composed of sections. Each section is either an Arc (part of a circle,defined by a centre point, a radius and an angle), or a Line increment (defined by astarting point and a length). In addition, sharp corners can be defined, i.e. a suddentransition in the inclination angle of two adjacent tunnel sections. When entering thetunnel designer, a standard circular tunnel is presented composed of 6 sections (3sections for half a tunnel).

The first section starts with a horizontal tangent at the lowest point on the local y -axis(highest point for a left half), and runs in the anti-clockwise direction. The position of thisfirst start point is determined by the Center coordinates and the Radius (if the first sectionis an Arc) or by the Starting point coordinates (if the first section is a Line). The end pointof the first section is determined by the Angle (in the case of an arc) or by the Length (inthe case of a line).

The start point of a next section coincides with the end point of the previous section. Thestart tangent of the next section is equal to the end tangent of the previous section. Ifboth sections are arcs, the two sections have the same radial (normal of the tunnelsection), but not necessarily the same radius (Figure 3.24). Hence, the centre point of thenext section is located on this common radial and the exact position follows from thesection radius.

If the tangent of the tunnel outline in the connection point is discontinuous, a sharp cornermay be introduced by selecting the Corner option for the next section. In this case asudden change in the tangent can be specified by the Angle parameter. The radius andthe angle of the last tunnel section are automatically determined such that the end radialcoincides again with the y -axis.

For a whole tunnel the start point of the first section should coincide with the end point ofthe last section. This is not automatically guaranteed. The distance between the startpoint and the end point (in units of length) is defined as the closing error. The closingerror is indicated on the status line of the tunnel designer. A well-defined tunnel crosssection must have a zero closing error. When a significant closing error exists, it isadvisable to carefully check the section data.

The number of sections follows from the sum of the section angles. For whole tunnels thesum of the angles is 360 degrees and for half tunnels this sum is 180 degrees. Themaximum angle of a section is 90.0 degrees. The automatically calculated angle of thelast section completes the tunnel cross section and it cannot be changed. If the angle ofan intermediate section is decreased, the angle of the last section is increased by thesame amount, until the maximum angle is reached. Upon further reduction of theintermediate section angle or by reducing the last section angle, a new section will becreated. If the angle of one of the intermediate tunnel sections is increased, the angle ofthe last tunnel section is automatically decreased. This may result in elimination of thelast section.

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R2

R2

R1

R1 commonradial

Figure 3.24 Detail of connection point between two tunnel sections

When the creation of the tunnel cross section is finished, it can be saved as a tunnelobject on the hard disk by using the Save as option from the File menu in the Tunneldesigner window.

Symmetric tunnel: The option Symmetric is only relevant for whole tunnels. When thisoption is selected, the tunnel is made fully symmetric. In this case the input proceduresare similar to those used when entering half a tunnel (right half). The left half of thetunnel is automatically made equal to the right half.

Circular tunnel: When changing the radius of one of the tunnel sections, the tunnelceases to be circular. To enforce the tunnel to be circular, the Circular option may beselected. If this option is selected, all tunnel sections will be arcs with the same radius. Inthis case the radius can only be entered for the first tunnel section. This option isautomatically selected when the type of tunnel is a bored tunnel.

Structural features of tunnel sections

Beside the geometric features, structural features can be assigned as well to the tunnelsections. The available structural features for tunnel sections are:

Shell To model the boring machine in shield tunneling or shotcretelining in NATM. Note that final lining can be modelled by defininga thickness greater than 0.

Outside interface To model the interaction of the tunnel lining with the surroundingsoil in the selected section.

Inside interface To model for example the interaction between the shotcrete andthe final lining in the selected section.

Load To assign loads to the selected segment. When this option isselected, the options to define the distribution, the referencepoint (for varying loads), and the necessary numerical values (σ,σref are displayed. More description on load options is given asfollows.

Hint: Selecting the For all segments option enables assigning all the selectedoptions and the defined values to all the segments in the tunnel.

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Load options for tunnel segments

The information required to define a load assigned to a segment in the tunnel consists ofload distribution, load value and the point of reference (in case of linear loads).

The distribution options for loads are:

Perpendicular: To create a uniformly distributed load perpendicular to theselected segment. The value of the load (σn) needs to bespecified.

Perpendicular, vertical increment:To create a load perpendicular to the selected segment varyingin y direction by defining the components and the magnitude ofthe load at the reference point and its increment in y direction.The values of the reference load (σn,ref ) and the load increment(σn,inc) as well as the reference point need to be specified.

X direction: To create a uniformly distributed horizontal load. The value of theload (σx ) needs to be specified.

X direction, vertical increment:To create a linearly distributed horizontal load varying iny -direction. The values of the reference load (σx ,ref ) and the loadincrement (σx ,inc) as well as the reference point need to bespecified.

X direction, horizontal increment:To create a linearly distributed horizontal load varying inx-direction. The values of the reference load (σn,ref ) and the loadincrement (σn,inc) as well as the reference point need to bespecified.

Y direction: To create a uniformly distributed vertical load. The value of theload (σy ) needs to be specified.

Y direction, vertical increment:To create a linearly distributed vertical load varying in y -direction.The values of the reference load (σy ,ref ) and the load increment(σy ,inc) as well as the reference point need to be specified.

Y direction, horizontal increment:To create a linearly distributed vertical load varying in y -direction.The values of the reference load (σy ,ref ) and the load increment(σy ,inc) as well as the reference point need to be specified.

The reference point to be considered when linear loads are defined can be specified byselecting the corresponding option in the drop down menu.

The options available for the reference point are:

Top of the tunnel: To specify the highest point in the tunnel cross section as thereference point.

Bottom of the tunnel: To specify the lowest point in the tunnel cross section as thereference point.

Start point of segment: To specify the start point of the segment as the reference point.

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End point of segment: To specify the end point of the segment as the reference point.

Hint: The coordinates of the reference point are displayed under the drop downmenu containing the available options. The location of the coordinated iscalculated according to the coordinate system displayed in the plot shown inthe Tunnel designer window.

Including tunnel in geometry model

After clicking on the OK button in the Tunnel designer the window is closed and the maininput window is displayed again. A tunnel symbol is attached to the cursor to emphasizethat the reference point for the tunnel must be selected. The reference point will be thepoint where the origin of the local tunnel coordinate system is located. When thereference point is entered by clicking with the mouse in the geometry model or byentering the coordinates in the manual input line, the tunnel is included in the geometrymodel, taking into account eventual crossings with existing geometry lines or objects.

Editing an existing tunnel

An existing tunnel can be edited by double clicking its reference point or one of the othertunnel points. As a result, the Tunnel designer window reappears showing the existingtunnel cross section. Desired modifications can now be made. On clicking the OK buttonthe ‘old’ tunnel is removed and the ‘new’ tunnel is directly included in the geometry modelusing the original reference point. Note that previously assigned material sets of a liningmust be reassigned after modification of the tunnel.

Moving an existing tunnel

An existing tunnel can be moved in the geometry by dragging the tunnel reference point.Note that this is only possible if the tunnel reference point does not coincide with anotherpoint.

3.4.9 HINGES AND ROTATION SPRINGS

A hinge is a plate connection that allows for a discontinuous rotation in the point ofconnection (joint). By default, in a geometry point where plate ends come together,

the rotation is continuous and the point contains only one rotational degree of freedom. Inother words, the default plate connection is rigid (clamped). If it is desired to create ahinge connection (a joint where plate ends can rotate freely with respect to each other) ora rotation spring (a joint where the rotation of plate ends with respect to each otherrequires a finite torque), the option Hinges and rotation springs can be selected from theGeometry menu or by clicking the corresponding button in the tool bar.

When this option is selected and an existing geometry point is clicked where at least twoplates come together, the Hinges and rotation springs window appears presenting adetailed view of the joint with all connected plates. For each individual plate end it can beindicated whether the connection is a hinge or a clamp. A hinge is indicated by an opencircle whereas a clamp is indicated by a solid circle.

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Figure 3.25 Example of a joint in the hinges and rotation springs window

After selecting a particular plate connection by clicking on the corresponding circle, theconnection can be toggled from a clamp into a hinge or vice versa by clicking again onthe circle. For each hinge, an additional rotational degree of freedom is introduced inorder to allow for an independent rotation.

In reality, plate connections may allow for rotations, but this generally requires a torque.To simulate such a situation, PLAXIS enables the input of rotation springs andcorresponding relative rotation spring stiffnesses between two plates. This option is onlyuseful if at least one of the two individual plate connections is a hinge (otherwise theconnection between the two plates is rigid). To define rotation springs in a joint, the jointis surrounded by large circle sections in which rotation springs can be activated. Possiblelocations of rotation springs are indicated by small circles (comparable with the hinges)on the large circle sections. In the case of a straight plate there are no large circlesaround the joint. In that case the central circle represents the rotation spring. Afterselecting a particular rotation spring by clicking on the corresponding circle, the rotationspring can be toggled on and off by clicking again on the circle.

When a rotation spring is created, the properties of the rotation spring must be entereddirectly in the right part of the window. The properties of a rotation spring include thespring stiffness and the maximum torque that it can sustain. The spring stiffness isdefined as the torque per radian (in the unit of Force times Length per Radian per Lengthout of plane).

In the project geometry, a hinge and a rotation spring are indicated by a white and a cyancircle respectively. To modify the hinges and rotation spring properties in a plateconnection, the Hinge and rotation spring button is clicked in the toolbar and theconnection is clicked in the model. The modification can be done in the appearing Hingesand rotation springs window.

3.4.10 DRAINS

Drains are used to prescribe lines inside the geometry model where (excess)pore pressures are reduced. Together with the creation of a drain, the input of a

groundwater head is required. This option is only relevant for consolidation analyses orgroundwater flow calculations. In such calculations, the pore pressure in all nodes of thedrain is reduced such that it is equivalent to the given head. Pore pressures lower thanthe equivalent to the given head are not affected by the drain.

The Drain option can be selected from the Geometry menu or by clicking on the

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corresponding button in the tool bar. The creation of a drain in the geometry model issimilar to the creation of a geometry line (Section 3.4.1). In a geometry model drainsappear as blue dashed lines.

Drains can be activated or de-activated in calculation phases when the Loading input isdefined as Staged construction. Drains can be activated by clicking on them in the Waterconditions mode. Active drains are indicated by a blue colour. A description of theproperties of the drains is given in Section 5.9.7.

3.4.11 WELLS

Wells are used to prescribe points inside the geometry model where a specificdischarge is extracted from or infiltrated into the soil. This option is only relevant for

groundwater flow calculations. The Well option can be selected from the Geometry menuor by clicking on the corresponding button in the tool bar. The creation of a well in thegeometry model is similar to the creation of a fixed-end anchor, but it is not restricted toexisting geometry lines. In a geometry model wells appear as a blue circles attached tosmall black lines.

After creating a well, the discharge of the well can be specified by double clicking the wellin the geometry model. This may require zooming into the area where the well is located.As a result, the Well window appears. In this window the discharge can be specified as apositive value in the unit of volume per unit time per unit of width out of plane. In addition,it can be selected whether the well is used to apply Extraction from the soil or to applyInfiltration in the soil. In the case of an Extraction well, the minimum groundwater headmust be specified in [m] with respect to the global system of axes. The default Equal towell location means that the extraction is automatically stopped if the groundwater leveldrops below the well level.

Wells can be activated or de-activated in calculation phases using Staged construction asLoading input. A description of the properties of the wells is given in Section 5.9.7.

3.5 LOADS AND BOUNDARY CONDITIONS

The Loads menu contains the options to introduce boundary conditions, prescribeddisplacements and loads in the geometry model. Loads and prescribed displacementscan be applied at the model boundaries as well as inside the model.

3.5.1 STANDARD FIXITIES

On selecting Standard fixities from the Loads menu or by clicking the correspondingbutton in the tool bar PLAXIS automatically imposes a set of general boundary

conditions to the geometry model. These boundary conditions are generated accordingto the following rules:

• Vertical geometry lines for which the x-coordinate is equal to the lowest or highestx-coordinate in the model obtain a horizontal fixity (ux = 0).

• Horizontal geometry lines for which the y -coordinate is equal to the lowesty -coordinate in the model obtain a full fixity (ux = uy = 0).

• Plates that extend to the boundary of the geometry model obtain a fixed rotation in

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the point at the boundary (φz = 0) if at least one of the displacement directions ofthat point is fixed.

Standard fixities can be used as a convenient and fast input option for many practicalapplications.

3.5.2 STANDARD EARTHQUAKE BOUNDARIES

PLAXIS has a convenient default setting to generate standard boundary conditions forearthquake loading. This option can be selected from the Loads menu. On selectingStandard earthquake boundaries, the program will automatically generate absorbentboundaries at the left-hand and right-hand vertical boundaries and prescribeddisplacements with ux = 0.01 m and uy = 0.00 m at the bottom boundary (see alsobelow).

3.5.3 STANDARD ABSORBENT BOUNDARIES (DYNAMICS)

An absorbent boundary is aimed to absorb the increments of stresses on the boundariescaused by dynamic loading, that otherwise would be reflected inside the soil body.

For single-source vibrations, PLAXIS has a default setting for generating appropriateabsorbent boundaries. This option can be selected from the Loads menu. For planestrain models, the standard absorbent boundaries are generated at the left-hand, theright-hand and the bottom boundary. For axisymmetric models, the standard absorbentboundaries are only generated at the bottom and the right-hand boundaries.

For manual setting, however, the input of an absorbent boundary is similar to the input offixities (Section 3.5.5).

3.5.4 SET DYNAMIC LOAD SYSTEM

In PLAXIS 2D, the input of a dynamic load is similar to that of a static load. Here, thestandard external load options (point loads and distributed loads in system A and B andprescribed displacements) can be used. In the Input program, the user must specifywhich of the load system(s) will be used as a dynamic load. This can be done using theSet dynamic load system option in the Loads menu. Load systems that are set asdynamic, cannot be used for static loading. Load systems that are not set as dynamic,are considered to be static.

3.5.5 FIXITIES

Fixities are prescribed displacements equal to zero. These conditions can be applied togeometry lines as well as to geometry points. Fixities can be selected from the Loadsmenu. The following options can be selected:

Total fixities Displacements in both x and y directions are equal to zero(ux = uy = 0).

Vertical fixities Displacements in y directions are equal to zero (uy = 0).

Horizontal fixities Displacements in x directions are equal to zero (ux = 0).

To introduce a sharp transition in different prescribed displacements or betweenprescribed displacements and fixities (for example to model a trap-door problem; Figure

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3.26), it is necessary to introduce an interface at the point of transition perpendicular tothe geometry line. As a result, the thickness of the transition zone between the twodifferent displacements is zero. If no interface is used then the transition will occur withinone of the elements connected to the transition point. Hence, the transition zone will bedetermined by the size of the element. The transition zone will therefore be unrealisticallywide.

Figure 3.26 Modelling of a trap-door problem using interfaces

Only one type of boundary conditions can be applied to individual points. In points wherefixities as well as loads are defined, the fixities have priority over the loads. In pointswhere fixities as well as prescribed displacements are defined, the prescribeddisplacements have priority over fixities.

3.5.6 ROTATION FIXITIES (PLATES)

Rotations fixities are used to fix the rotational degree of freedom of a plate aroundthe z-axis. Rotation fixities can be selected from the Loads menu or by clicking on

the corresponding button in the tool bar. Rotation fixities must always act on plates, butnot necessarily on existing geometry points. In the latter case a new geometry point isautomatically introduced.

Existing rotation fixities can be eliminated by selecting the rotation fixity in the geometrymodel and pressing the <Delete> key on the keyboard.

3.5.7 ABSORBENT BOUNDARIES

An absorbent boundary is aimed to absorb the increments of stresses on the boundariescaused by dynamic loading, that otherwise would be reflected inside the soil body.

3.5.8 PRESCRIBED DISPLACEMENTS

Prescribed displacements are special conditions that can be imposed on the modelto control the displacements of certain points. Prescribed displacements can be

selected from the Loads menu or by clicking on the corresponding button in the tool bar.The input of Prescribed displacements in the geometry model is similar to the creation ofgeometry lines (Section 3.4.1). By default, the input values of prescribed displacementsare set such that the vertical displacement component is one unit in the negative verticaldirection (uy = −1) and the horizontal displacement component is free.

The input values of prescribed displacements can be changed by double clicking thecorresponding geometry line and selecting Prescribed displacements from the selectiondialog box. As a result, the Prescribed displacements window appears in which the input

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Figure 3.27 Input window for prescribed displacements

values of the prescribed displacements of both end points of the geometry line can bechanged (Figure 3.5.8). The distribution is always linear along the line. The input valuemust be in the range [-9999, 9999]. In the case that one of the displacement directions isprescribed whilst the other direction is free, one can use the check boxes in the Freedirections group to indicate which direction is free. The Perpendicular button can be usedto impose a prescribed displacement of one unit perpendicular to the correspondinggeometry line. For internal geometry lines, the displacement is perpendicular to the rightside of the geometry line (considering that the line goes from the first point to the secondpoint). For geometry lines at a model boundary, the displacement direction is towards theinside of the model.

On a geometry line where both prescribed displacements and loads are applied, theprescribed displacements have priority over the loads during the calculations, except ifthe prescribed displacements are not activated. On a geometry line where bothprescribed displacements and full fixities are applied, the prescribed displacements havepriority over the fixities during the calculations, except if the prescribed displacements arenot activated.

Although the input values of prescribed displacements can be specified in the geometrymodel, the actual values that are applied during a calculation may be changed in theframework of Staged construction (Section 3.4.1). Moreover, an existing composition ofprescribed displacements may be increased globally by means of the load multipliersMdisp and ΣMdisp (Section 5.11.1).

During calculations, the reaction forces corresponding to prescribed displacements in x-and y -direction are calculated and stored as output parameters (Force-X, Force-Y ).

Hint: Prescribed displacements should be interpreted as specified totaldisplacements at the end of the phase instead of additional phasedisplacements.

Prescribed displacements in dynamics

A special method for introducing dynamic loads in a model is by means of prescribeddisplacements. Earthquakes are usually modelled by means of prescribed horizontaldisplacements. When the Standard earthquake boundaries in the Loads menu is

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selected the horizontal displacement component is defined automatically by PLAXIS.

To define the prescribed displacement for an earthquake manually:

• Enter a prescribed displacement in the geometry model (usually at the bottom).

• Double click on the prescribed displacement.

• Select Prescribed displacement in the window that appears.

• Change the x-values of both geometry points to 1 (or 0.01 when working withstandard SMC files with unit of length in meters, or 0.0328 with unit of length in feet)and the y -values to 0. Now the given displacement is one unit in horizontal direction.

• Optionally, the same input value can be entered for both x- and y-values to allow for(independent) horizontal and vertical motions (see Section 5.11.3 for the applicationof dynamic loads).

• In the Loads menu, set the dynamic load system to Prescribed displacements.

3.5.9 DISTRIBUTED LOADS

The creation of a distributed load in the geometry model is similar to the creationof a geometry line (Section 3.4.1). Two load systems (A and B) are available for a

combination of distributed loads or point loads. The load systems A and B can beactivated independently. Distributed loads for load system A or B can be selected fromthe Loads menu or by clicking on the corresponding button in the tool bar.

The input values of a distributed load are given in force per area (for example kN/m2).Distributed loads may consist of a x- and/or y -component. By default, when applyingloads to the geometry boundary, the load will be a unit pressure perpendicular to theboundary. The input value of a load may be changed by double clicking thecorresponding geometry line and selecting the corresponding load system from theselection dialog box. As a result, the Distributed load window is opened in which the twocomponents of the load can be specified for both end points of the geometry line in thegeometry model. The distribution is always linear along the line.

Figure 3.28 Input window for distributed loads

Although the global input values of distributed loads can be specified in the geometrymodel, the actual value that is applied in a calculation may be changed in the frameworkof Staged construction (Section 5.8.3). Moreover, an existing composition of loads maybe increased globally by means of the load multipliers MloadA (or ΣMloadA) for loadsystem A and MloadB (or ΣMloadB) for load system B (Section 5.11.1).

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On a geometry line where both prescribed displacements and distributed loads areapplied, the prescribed displacements have priority over the distributed loads during thecalculations, provided that the prescribed displacements are active. Hence, it is notuseful to apply distributed loads on a line with fully prescribed displacements. When onlyone displacement direction is prescribed whilst the other direction is free, it is possible toapply a distributed load in the free direction.

3.5.10 POINT LOADS

This option may be used to create point loads, which are actually line loads in theout-of-plane direction. The input values of point loads are given in force per unit of

width (for example kN/m). In axisymmetric models, point loads are in fact line loads on acircle section of 1 radian. In that case the input value of is still given in force per unit ofwidth, except when the point load is located at x = 0. In the latter case (axisymmetry;point load in x = 0) the point load is a real point load and the input value is given in theunit of force (for example kN, though the input window still shows kN/m). Note that thisforce is acting on a circle section of 1 radian only. To derive the input value from a realsituation, the real point force must be divided by 2π to get the input value of the pointforce at the centre of the axisymmetric model.

The creation of a point or line load in the geometry model is similar to the creation of ageometry point (Section 3.4.1). Two load systems (A and B) are available for acombination of distributed loads and line loads or point loads. The load systems A and Bcan be activated independently. Point loads for load system A or B can be selected fromthe Loads menu or by clicking on the corresponding button in the tool bar.

The input values of a point load (or line load) are given in force per unit of length (forexample kN/m). Point loads may consist of a x- and/or y -component. By default, whenapplying point loads, the load will be one unit in the negative y -direction. The input valueof a load may be changed by double clicking the corresponding point and selecting thecorresponding load system from the selection dialog box. As a result, the Point loadwindow is opened in which the two components of the load can be specified (Figure3.5.10).

Figure 3.29 Input window for point loads

A bending moment can be specified in the Point load window as well. For moreinformation on Bending moments see Section 3.5.11.

Although the input values of point loads can be specified in the geometry model, theactual value that is applied in a calculation may be changed in the framework of Stagedconstruction. Moreover, an existing composition of loads may be increased globally bymeans of the load multipliers MloadA (or ΣMloadA) for load system A and MloadB (orΣMloadB) for load system B (Section 5.11.1).

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On a part of the geometry where both prescribed displacements and point loads areapplied, the prescribed displacements have priority over the point loads during thecalculations, provided that the prescribed displacements are active. Hence, it is notuseful to apply point loads on a line with fully prescribed displacements. When only onedisplacement direction is prescribed whilst the other direction is free, it is possible toapply a point load in the free direction.

3.5.11 BENDING MOMENTS

Bending moments can be assigned as a value at a specific point in a plate. The bendingmoment can be defined by clicking the Point load button in the toolbar and clicking on thelocation on the plate where the bending moment is to be assigned. The value of thebending moment can be specified in the corresponding cell in the Point load window(Figure 3.5.11). A positive value indicates a counter clockwise bending moment whereasa negative sign indicates a clockwise one.

Figure 3.30 Definition of bending moment

Hint: Note that the Bending moment option is not accessible in the Point loadwindow (Figure 3.5.10) when the point is not located on a plate.

Although the input values of bending moment can be specified in the geometry model,the actual value that is applied in a calculation may be changed in the framework ofStaged construction. Moreover, an existing composition of loads may be increasedglobally by means of the load multipliers MloadA (or ΣMloadA) for load system A andMloadB (or ΣMloadB) for load system B (Section 5.11.1).

On a part of the geometry where both a rotation fixity and a bending moment are applied,the rotation fixity has priority over the bending moment during the calculations, providedthat the rotation fixity is active. Hence, it is not useful to apply bending moment on a pointwith a rotation fixity.

3.6 DESIGN APPROACHES

PLAXIS 2D has a facility to deal with partial factors for loads and model parameters. Thisfacility is called ‘Design approaches’ and enables PLAXIS 2D to be used for designcalculations in the framework of the Eurocode, LRFD or other design methods based onpartial factors.

The main idea is that a project is first analyzed for a Serviceability Limit State (SLS)situation, without using Design approaches. The input values of loads and the model

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parameters are supposed to be representative or characteristic values. The result wouldbe a cautious estimate of deformations, stresses and structural forces.

If satisfactory results have been obtained for the serviceability state, one may considerusing Design approaches to deal with Ultimate Limit State (ULS) design. In order toperform design calculations, new phases need to be defined in addition to theserviceability state calculations. There are two main schemes to perform designcalculations in relation to serviceability calculations (Bauduin, Vos & Simpson (2000)).

Scheme 1:

0. Initial phase

1. Phase 1 (SLS) → 4. Phase 4 (ULS)

2. Phase 2 (SLS) → 5. Phase 5 (ULS)

3. Phase 3 (SLS) → 6. Phase 6 (ULS)

In this scheme, the design calculations (ULS) are performed for each serviceability statecalculation separately. This means that Phase 4 starts from Phase 1, Phase 5 starts fromPhase 2, etc. Note that in this case a partial factor on a stiffness parameter is only usedto calculate additional displacements as a result of stress redistribution due to thefactored (higher) loads and the factored (reduced) strength parameters.

Scheme 2:

0. Initial phase → 4. Phase 4 (ULS)

1. Phase 1 (SLS) 5. Phase 5 (ULS)

2. Phase 2 (SLS) 6. Phase 6 (ULS)

3. Phase 3 (SLS)

In this scheme, the design calculations (ULS) start from the initial situation and areperformed subsequently. This means that Phase 4 starts from the Initial phase, Phase 5starts from Phase 4, etc.

It is the responsibility of the geotechnical engineer to consider all the different conditionsthat effect the design. Engineering judgment plays a vital role in the determination ofdifferent combinations to be considered in the design.

3.6.1 DEFINITION OF DESIGN APPROACHES

Different design approaches, i.e. coherent sets of partial factors, can be defined for loadsand model parameters according to the applicable design methods (for example:Eurocode 7 — DA 3). After defining such a coherent set of partial factors by the user, itmay then be exported (stored) under an appropriate name in a global data base, afterwhich it can be imported and re-used in other projects. Hence, once complete sets ofpartial factors have been defined and stored, it is a relatively small effort to make designcalculations in addition to serviceability calculations.

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Figure 3.31 Design approaches window

• To add a new design approach click the corresponding option under the designapproaches list. The New design approach window pops up where the name of thenew design approach can be defined (Figure 3.32). The new approach is added inthe list when OK is clicked in the New design approach window.

Figure 3.32 New design approach window

• To delete a design approach from the list select the design in the list and click thecorresponding button under the list.

• To create a copy of a predefined design approach select the design approach in thelist and click the Copy button.

• To import design approaches from other projects or from the global repository ofdesign approaches. Click the corresponding button under the list. As a result, theImport/Export to global repository window appears.The global repository is adatabase of the design approaches contained in other projects, simplifying theirreuse. The address to the location of the global repository is given under the list ofthe global design approaches. A different repository can be selected by clicking theSelect button and selecting the new repository. Global design approaches can beremoved from the depository by selecting them first in the list and by clicking Deletebutton.

Within a design approach, distinction is made between partial factors for loads (actions)and partial factors for model parameters (providing resistances). Design approachesavailable in the model can be defined and managed in the Design approaches window

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Figure 3.33 Import design approach window

that appears when the corresponding option, available in the Loads menu is selected.The Design approaches window consists of two parts. In the upper part of the window alist of the design approaches is displayed. By default no design approaches areavailable. The buttons available under the design approaches list enable adding anddeleting of the approaches in the list as well as importing and exporting designapproaches between different projects.

3.6.2 DEFINITION OF PARTIAL FACTORS FOR LOADS

Loads to be considered in the design approaches for a geotechnical project are:

• Distributed loads

• Point loads

• Prescribed displacements

Different partial factors may apply to different loads or groups of loads. This can bearranged by assigning Labels to individual loads or groups of loads. Considering partialfactors for loads, distinction can be made between different load cases, for examplepermanent unfavourable, permanent favourable, variable unfavourable, variablefavourable, etc.

To change a label, double click it and type the new label. Up to 10 labels and theircorresponding partial factors can be defined. The partial factors for loads are used as amultiplication factor to the reference values of the loads.

Hint: The partial factors for loads are defined such that the design value of aparameter is the reference value multiplied with the partial factor.

By default, the first load case (permanent unfavourable) is assigned to external loads inthe model, but this may be changed when defining a design calculation. Other labels canbe assigned to loads in the Staged construction tabsheet, as part of the definition of acalculation phase. However, the partial factors corresponding to the load labels are onlyapplied when the calculation is performed according to the selected design approach(see Section 5.8.9); otherwise reference values of loads are used.

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3.6.3 DEFINITION OF PARTIAL FACTORS FOR MATERIALS

The partial factors for materials for a selected design approach in the list can be definedin the corresponding tabsheet in the Design approaches window. A list of all the availablematerial models for soil and the materials for structural elements, for which partial factorsare supported is displayed (Figure 3.34).

Figure 3.34 Partial factors for materials tabsheet

Considering partial factors for model parameters, a first distinction is made between thedifferent material models, because different models have different sets of parameters. If aproject contains Mohr-Coulomb material as well as Hardening Soil material, separate setsof partial factors are needed for MC and for HS, even when the parameters to be factoredhappen to be the same (e.g. ϕ’ and c’).

A further distinction can be made between different cases of how the parameters or thematerial model are used. For example, when using the Mohr-Coulomb model, soilstrength may be defined in terms of effective strength (using ϕ’ and c’, i.e. the Drained orUndrained A approach) or in terms of undrained strength (using su , i.e. the Undrained Bor Undrained C approach), for which different partial factors may apply. Hence, separatesets of partial factors may be defined for a case named ‘Effective strength’ (= defaultcase) and a case named ‘Undrained strength’.

To add a case:

• Click the Add case button. The corresponding window pops up (Figure 3.35).

Figure 3.35 Add materialcase window

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• Specify the name of the new case and select the material set and the materialmodel from the corresponding drop-down menus. Note that the Model option is notapplicable for the structural elements.

• Click OK to add the new material case. Note that a new column is added for thenew material case, where the selected material model is indicated by a greenbutton. The window for the soil material set pops up where the partial factors can bedefined for the material parameters.

Hint: The partial factors for materials are defined such that the design value of aparameter is the reference value divided by the partial factor.

» In the case of a partial factor on the friction angle ϕ or the dilatancy angle ψ,the partial factor is applied to tanϕ and tanψ respectively.

» By default, all partial factors are set to 1.0.

In addition to partial factors for soil model parameters, partial factors for structural modelparameters may be defined as well. After creating the different material cases, theyshould be assigned to the materials in the current project, listed in the table namedaccordingly (Figure 3.36). The first two columns in the table give the name of the materialdataset and the material model respectively. The cells in the third column aretransformed into drop-down menus where the material cases available in the selecteddesign approach are listed. Clicking on the options will assign the material case to theselected material in the model. Make sure all material data sets have been assigned acorresponding material case other than the default ‘none’.

Figure 3.36 Assignment of material cases

Subsequently, the material data sets can be opened via the material data base to view(and modify, if necessary!) the actual values of model parameters that will be used whendesign calculations are performed.

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To complete the definition of a design calculation it is necessary to proceed to the Stagedconstruction tabsheet (Section 5.8.9) where the design approach to be used for a specificphase is selected and the loads in the model are labelled. Make sure that the requiredload labels with corresponding partial factors are properly assigned to the external loadsin the model.

When using Design approaches in combination with advanced soil models, these modelswill continue to behave as advanced models, maintaining all their features, such asstress-dependent stiffness behaviour and hardening effects. This is different than whenusing a Safety analysis with advanced models (Section 5.5.5), since in the latter caseadvanced models loose their advanced features and basically switch to Mohr-Coulomb.When comparing a Safety analysis to a target value of ΣMsf with a Design approachesanalysis using the same partial factor for c and tanϕ, it should be realized that the resultscould be different because of this reason.

3.7 MESH GENERATION

When the geometry model is fully defined and material properties have been assigned toall clusters and structural objects, the geometry has to be divided into finite elements inorder to perform finite element calculations. A composition of finite elements is called amesh. The basic type of element in a mesh is the 15-node triangular element or the6-node triangular element, as described in Section 3.1.1. In addition to these elements,there are special elements for structural behaviour (plates, embedded pile rows, geogridsand anchors), as described in Section 3.4.2 to 3.4.7. PLAXIS 2D allows for a fullyautomatic mesh generation of finite element meshes. The generation of the mesh isbased on a robust triangulation procedure.

Although PLAXIS 2D automatically applies local mesh refinements (Section 3.7.6),meshes that are automatically generated by PLAXIS may not be accurate enough toproduce acceptable numerical results. Please note that the user remains responsible tojudge the accuracy of the finite element meshes and may need to consider further globaland local refinement options.

The required input for the mesh generator is a geometry model composed of points, linesand clusters, of which the clusters (areas enclosed by lines) are automatically generatedduring the creation of the geometry model. Geometry lines and points may also be usedto influence the position and distribution of elements.

The generation of the mesh is started by clicking on the mesh generationbutton in the tool bar or by selecting the Generate option from the Mesh menu. The

generation is also activated directly after the selection of a refinement option from theMesh menu.

After the mesh generation the Output program is started and a plot of the mesh isdisplayed. Although interface elements have a zero thickness, the interfaces in the meshare drawn with a certain thickness to show the connections between soil elements andinterfaces. This so-called Connectivity plot is also available as a regular output option(Section 7.1). The scale factor (Section 6.3.7) may be used to reduce the graphicalthickness of the interfaces. To return to the Input program, the green Close arrow mustbe clicked.

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3.7.1 BASIC ELEMENT TYPE

On selecting Basic element type from the Mesh menu, the Project properties window isopened. The user may select either 15-Node or 6-Node triangular elements (Figure 3.3)as the basic type of element to model soil layers and other volume clusters. The type ofelement for structures and interfaces is automatically taken to be compatible with thebasic type of soil element.

3.7.2 GLOBAL COARSENESS

The mesh generator requires a general meshing parameter which represents the averageelement size, le. In PLAXIS this parameter is calculated from the outer geometrydimensions (xmin, xmax , ymin, ymax ) and a Global coarseness setting as defined in theMesh menu:

le =nc

12

√(xmax − xmin)(ymax − ymin)

Distinction is made between five levels of global coarseness: Very coarse, Coarse,Medium, Fine and Very fine. By default, the global coarseness is set to Medium. Theglobal element size and the number of generated triangular elements depends on thisglobal coarseness setting. A rough estimate is given below (based on a generationwithout local refinement):

Very coarse: nc = 2.0 Around 70 elements

Coarse: nc = 1.4 Around 150 elements

Medium: nc = 1.0 Around 200 elements

Fine: nc = 0.7 Around 500 elements

Very fine: nc = 0.5 Around 1000 elements

The exact number of elements depends on the shape of the geometry and optional localrefinement settings. The number of elements is not influenced by the Type of elementsparameter, as set in the Project properties window. Note that a mesh composed of15-node elements gives a much finer distribution of nodes and thus much more accurateresults than a similar mesh composed of an equal number of 6-node elements. On theother hand, the use of 15-node elements is more time consuming than using 6-nodeelements.

3.7.3 GLOBAL REFINEMENT

A finite element mesh can be refined globally by selecting the Refine global option fromthe Mesh menu. When selecting this option, the global coarseness parameter isincreased one level (for example from Medium to Fine) and the mesh is automaticallyregenerated.

3.7.4 LOCAL COARSENESS

In areas where large stress concentrations or large deformation gradients are expected, itis desirable to have a more accurate (finer) finite element mesh, whereas other parts ofthe geometry might not require a fine mesh. Such a situation often occurs when thegeometry model includes edges or corners or structural objects. For these cases PLAXIS

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uses local coarseness parameters in addition to the global coarseness parameter. Thelocal coarseness parameter is the Local element size factor, which is contained in eachgeometry point. These factors give an indication of the relative element size with respectto the average element size as determined by the Global coarseness parameter. Bydefault, the Local element size factor is set to 1.0 at all geometry points. Automaticrefinement will be applied where necessary (see Section 3.7.6). To reduce the length ofan element to half the global element size, the Local element size factor should be set to0.5.

The local element size factor can be changed by double clicking the correspondinggeometry point. Alternatively, when double clicking a geometry line, one can set the localelement size factor for both points of the geometry line simultaneously. Values in therange from 0.05 to 5.0 are acceptable.

3.7.5 LOCAL REFINEMENT

Instead of specifying local element size factors, a local refinement can be achieved byselecting clusters, lines or points and selecting a local refinement option from the Meshmenu.

When selecting one or more clusters, the Mesh menu allows for the option Refine cluster .Similarly, when selecting one or more geometry lines, the Mesh menu provides the optionRefine line. When selecting one or more points, the option Refine around point isavailable.

Using one of the options for the first time will give a local element size factor of 0.5 for allselected geometry points or all geometry points that are included in the selected clustersor lines. Repetitive use of the local refinement option will result in a local element sizefactor which is half the current factor, however, the minimum and maximum value arerestricted to the range [0.05, 5.0]. After selecting one of the local refinement options, themesh is automatically regenerated.

3.7.6 AUTOMATIC REFINEMENT

To supply a good quality mesh for every geometry which also takes into account thenecessary mesh refinement around structural elements, loads and prescribeddisplacements, PLAXIS will apply automatic mesh refinements. These automaticrefinements in terms of an implicit local element size multiplication factor will be applied incase of:

• structural elements, loads and prescribed displacements: the Local element sizefactor will be multiplied by 0.25, except when prescribed displacements or loadshave been applied along a whole edge of the geometry. The implicit multiplicationfactors can be compensated in the Input program by setting the Local element sizefactor manually to 4.0.

• the distance between points and/or lines is rather close, which requires a smallerelement size to avoid large aspect ratios.

• an angle between geometry lines other than a multiple of 900, to allow for moreaccurate stresses around geometry discontinuities. The Local element size factorwill be multiplied according to Figure 3.37.

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Figure 3.37 The implicit Local element size multiplication factor as a function of the angle betweentwo lines.

Note that the Local element size factors are implicitly applied, and are not visible to theuser. In order to ‘compensate’ implicitly applied Local element size factors, an inverseLocal element size factor can be given manually to the corresponding geometry point(e.g. a Local element size factor of 4 will compensate the implicit factor of 0.25 for loadssuch that the global coarseness is retained).

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4 MATERIAL PROPERTIES AND MATERIAL DATABASE

In PLAXIS, soil properties and material properties of structures are stored in materialdata sets. There are four different types of material sets grouped as data sets for soil andinterfaces, data sets for plates, data sets for geogrids, data sets for embedded pile rowsand data sets for anchors. All data sets are stored in the material database. From thedatabase, the data sets can be assigned to the soil clusters or to the correspondingstructural objects in the geometry model.

The material database can be activated by selecting one of the options from theMaterials menu or by clicking the Materials button in the tool bar. As a result, the

Material sets window appears showing the contents of the project material database. Thewindow can be extended to show the global database by clicking the Show global buttonin the upper part of the window. The Material sets window displaying the material definedin the current project and the ones available in a selected global database is shown inFigure 4.1.

Figure 4.1 Material sets window showing the project and the global database

The database of a new project is empty. The global database can be used to storematerial data sets in a global folder and to exchange data sets between different projects.

At both sides of the window (Project materials and Global materials) there are twodrop-down menus and a tree view. The Set type can be selected from the drop-downmenu on the left hand side. The Set type parameter determines which type of materialdata set is displayed in the tree view (Soil and interfaces, Plates, Embedded pile rows,Geogrids, Anchors).

The data sets in the tree view are identified by a user-defined name. The data sets forSoil and interfaces can be ordered in groups according to the material model, thematerial type or the name of the data set by selecting this order in the Group orderdrop-down menu. The None option can be used to discard the group ordering.

The small buttons between the two tree views can be used to copy individual data setsfrom the project database to the selected global database or vice versa.

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To copy the selected project material set to the global database.

To copy all the project material sets of the specified type to the global database.

To copy the selected global material set to the project database.

The location of the selected global database is shown below its tree view. The buttonsbelow the tree view of the global database enable actions in the global database.

Select To select an existing global database.

Delete To delete a selected material data set from the selected globaldatabase.

By default, the global database for soil and interface data contains the data sets of all thetutorials and it is contained in the file ‘SoilMat.matdb’. This file is compatible with otherPLAXIS database files for soil and interfaces and is stored in the installation folder ofPLAXIS 2D. Material data sets for structural elements will be contained in separate files.Similarly, the global data bases for plates, geogrids and anchors are contained in the files’PlateMat2D.matdb’, ‘GeogridMat.matdb’, ‘EmbeddedPile2DMat.matdb’ and’AnchorMat2D.matdb’ respectively.

Note that besides the global material files (*.matdb), it is possible to select projectmaterial files (*.plxmat) and legacy project material files (*.mat) as global database.

In addition, databases with data sets of standard sheet-pile wall profiles are availablefrom the Plaxis Knowledge Base(http://kb.plaxis.nl/downloads/material-parameter-datasets-sheetpiles-and-beams).

Hint: A new global database can be created by clicking the Select button, definingthe name of the new global database and clicking Open.

The project data base can be managed using the buttons below the tree view of theproject database.

New To create a new data set in the project. As a result, a newwindow appears in which the material properties or modelparameters can be entered. The first item to be entered isalways the Identification, which is the user-defined name of thedata set. After completing a data set, it will appear in the treeview, indicated by its name as defined by the Identification.

Edit To modify the selected data set in the project material database.

SoilTest To perform standard soil lab tests. A separate window will openwhere several basic soil tests can be simulated and thebehaviour of the selected soil material model with the givenmaterial parameters can be checked (Section 4.3).

Copy To create a copy of a selected data set in the project materialdatabase.

Delete To delete a selected material data set from the project materialdatabase.

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4.1 MODELLING SOIL AND INTERFACE BEHAVIOUR

The material properties and model parameters for soil clusters are entered in materialdata sets (Figure 4.2). The properties in the data sets are divided into five tabsheets:General, Parameters , Flow parameters, Interfaces and Initial.

4.1.1 GENERAL TABSHEET

The General tabsheet contains the type of soil model, the drainage type and the generalsoil properties such as unit weights. Several data sets may be created to distinguishbetween different soil layers. A user may specify any identification title for a data set inthe General tabsheet of the Soil window. It is advisable to use a meaningful name sincethe data set will appear in the database tree view by its identification.

For easy recognition in the model, a colour is given to a certain data set. This colour alsoappears in the database tree view. PLAXIS 2D selects a unique default colour for a dataset, but this colour may be changed by the user. Changing the colour can be done byclicking on the colour box in the General tabsheet.

Figure 4.2 General tabsheet of the Soil window

Material model

Soil and rock tend to behave in a highly non-linear way under load. This non-linearstress-strain behaviour can be modelled at several levels of sophistication. Clearly, thenumber of model parameters increases with the level of sophistication. PLAXIS supportsdifferent models to simulate the behaviour of soil and other continua. The models andtheir parameters are described in detail in the Material Models Manual. A shortdiscussion of the available models is given below:

Linear elastic model: This model represents Hooke’s law of isotropic linear elasticity.The linear elastic model is too limited for the simulation of soil behaviour. It is primarilyused for stiff structures in the soil.

Mohr-Coulomb model (MC): This well-known linear elastic perfectly-plastic model isused as a first approximation of soil behaviour in general. It is recommended to use thismodel for a first analysis of the problem considered. A constant average stiffness is

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estimated for the soil layer. Due to this constant stiffness, computations tend to berelatively fast and a first estimate of deformations can be obtained.

Hardening Soil model (HS): This is an advanced model for the simulation of soilbehaviour. The Hardening Soil model is an elastoplastic type of hyperbolic model,formulated in the framework of shear hardening plasticity. Moreover, the model involvescompression hardening to simulate irreversible compaction of soil under primarycompression. This second-order model can be used to simulate the behaviour of sandsand gravel as well as softer types of soil such as clays and silts.

Hardening Soil model with small-strain stiffness (HSsmall): This is an elastoplastictype of hyperbolic model, similar to the Hardening Soil model. Moreover, this modelincorporates strain dependent stiffness moduli, simulating the different reaction of soilsfrom small strains (for example vibrations with strain levels below 10-5) to large strains(engineering strain levels above 10-3).

Soft Soil model (SS): This is a Cam-Clay type model that can be used to simulate thebehaviour of soft soils like normally consolidated clays and peat. The model performsbest in situations of primary compression.

Soft Soil Creep model (SSC): This is a second order model formulated in theframework of viscoplasticity. The model can be used to simulate the time-dependentbehaviour of soft soils like normally consolidated clays and peat. The model includeslogarithmic primary and secondary compression.

Jointed Rock model (JR): This is an anisotropic elastic-perfectly plastic model whereplastic shearing can only occur in a limited number of shearing directions. This modelcan be used to simulate the anisotropic behaviour of stratified or jointed rock.

Modified Cam-Clay model (MCC): This well-known critical state model can be used tosimulate the behaviour of normally consolidated soft soils. The model assumes alogarithmic relationship between the volumetric strain and the mean effective stress.

NGI-ADP model (NGI-ADP): The NGI-ADP model may be used for capacity,deformation and soil-structure interaction analysis involving undrained loading of clay.Distinct anisotropic stress strengths may be defined for different stress paths.

Hoek-Brown model (HB): This well-known elastic perfectly-plastic model is used tosimulate the isotropic behaviour of rock. A constant stiffness is used for the rock mass.Shear failure and tension failure are described by a non-linear stress curve.

Sekiguchi-Ohta model (Inviscid): The Sekiguchi-Ohta model (Inviscid) is a Cam-Claytype effective stress model for time-independent behaviour of clay-type soils.

Sekiguchi-Ohta model (Viscid): The Sekiguchi-Ohta model (Viscid) is a Cam-Claytype effective stress model for time-dependent behaviour (creep) behaviour of clay-typesoils.

User-defined soil models (UDSM): With this option it is possible to use otherconstitutive models than the standard PLAXIS models. For a detailed description of thisfacility, reference is made to the Material Models Manual. Links to existing User-definedsoil models are available on the Plaxis Knowledge Base (http://kb.plaxis.nl/models).

Drainage type

In principle, all model parameters in PLAXIS are meant to represent the effective soilresponse, i.e. the relation between the stresses and strains associated with the soil

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skeleton. An important feature of soil is the presence of pore water. Pore pressuressignificantly influence the soil response. To enable incorporation of the water-skeletoninteraction in the soil response PLAXIS offers a choice of different types of drainage:

Drained behaviour: Using this setting no excess pore pressures are generated. This isclearly the case for dry soils and also for full drainage due to a high permeability (sands)and/or a low rate of loading. This option may also be used to simulate long-term soilbehaviour without the need to model the precise history of undrained loading andconsolidation.

Undrained behaviour: This setting is used for saturated soils in cases where porewater cannot freely flow through the soil skeleton. Flow of pore water can sometimes beneglected due to a low permeability (clays) and/or a high rate of loading. All clusters thatare specified as undrained will indeed behave undrained, even if the cluster or a part ofthe cluster is located above the phreatic level.

Distinction is made between three different methods of modelling undrained soilbehaviour. Method A is an undrained effective stress analysis with effective stiffness aswell as effective strength parameters. This method will give a prediction of the porepressures and the analysis can be followed by a consolidation analysis. The undrainedshear strength (su) is a consequence of the model rather then an input parameter. It isrecommended to check this shear strength with known data. To consider this type ofanalysis, the Undrained (A) option should be selected in the Drainage type drop-downmenu.

Method B is an undrained effective stress analysis with effective stiffness parameters andundrained strength parameters. The undrained shear strength su is an input parameter.This method will give a prediction of pore pressures. However, when followed by aconsolidation analysis, the undrained shear strength (su) is not updated, since this is aninput parameter. To consider this type of analysis, the Undrained (B) option should beselected in the Drainage type drop-down menu.

Method C is an undrained total stress analysis with all parameters undrained. Thismethod will not give a prediction of pore pressures. Therefore it is not useful to perform aconsolidation analysis. The undrained shear strength (su) is an input parameter. Toconsider this type of analysis, the Undrained (C) option should be selected in theDrainage type drop-down menu.

More information about modelling undrained behaviour can be found in Section 4.2 andthe Material Models Manual.

Non-porous behaviour: Using this setting neither initial nor excess pore pressures willbe taken into account in clusters of this type. Applications may be found in the modellingof concrete or structural behaviour. Non-porous behaviour is often used in combinationwith the Linear elastic model. The input of a saturated weight is not relevant fornon-porous materials or intact rock.

In a consolidation analysis it is the permeability parameter in the Flow tabsheet thatdetermines the drainage capacity of a layer rather than the drainage type. Still, thedrainage type has influence on the applied compressibility of water in a consolidationanalysis. For more information see Appendix A.

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Saturated and unsaturated weight (γsat and γunsat )

The saturated and the unsaturated weight refer to the total unit weight of the soil skeletonincluding the fluid in the pores. The unsaturated weight γunsat applies to all materialabove the phreatic level and the saturated weight γsat applies to all material below thephreatic level. The unit weights are entered as a force per unit volume.

For non-porous material only the unsaturated weight is relevant, which is just the total unitweight. For porous soils the unsaturated weight is obviously smaller than the saturatedweight. For sands, for example, the saturated weight is generally around 20 kN/m3

whereas the unsaturated weight can be significantly lower, depending on the degree ofsaturation.

Note that soils in practical situations are never completely dry. Hence, it is advisable notto enter the fully dry unit weight for γunsat . For example, clays above the phreatic levelmay be almost fully saturated due to capillary action. Other zones above the phreaticlevel may be partially saturated. However, the steady-state pore pressures above thephreatic level are always set equal to zero. In this way tensile capillary stresses aredisregarded. However, excess pore stresses (both pressure and suction) may occurabove the phreatic line as a result of undrained behaviour A or B. The latter does notaffect the unit weight of the soil.

In the Advanced mode (Section 5.3.2), the actual unit weight for the soil that is used inthe calculations depends on the effective degree of saturation Se as calculated in theprevious calculation step.

γ = (1− Se)γunsat + Seγsat (4.1)

where

Se = (S − Smin)/(Smax − Smin) (4.2)

S is the actual degree of saturation, Smin is the minimum degree of saturation and Ssat isthe maximum degree of saturation.

Weights are activated by means of Gravity loading or K0 procedure in the Calculationmode, which is always the first calculation phase (Initial phase) (see Section 5.5.1).

Advanced general properties

Additional properties for advanced modelling features can be defined in the Advancedsubtree in the General tabsheet (Figure 4.2).

Void ratio (einit , emin, emax ): The void ratio, e, is related to the porosity, n(e = n/(1− n)). This quantity is used in some special options. The initial value einit is thevalue in the initial situation. The actual void ratio is calculated in each calculation stepfrom the initial value and the volumetric strain ∆εv . These parameters are used tocalculate the change of permeability when input is given for the ck value (in the Flowtabsheet). In addition to einit , a minimum value emin and a maximum value emax can beentered. These values are related to the maximum and minimum density that can bereached in the soil. When the Hardening Soil model or Hardening Soil model withsmall-strain stiffness is used with a certain (positive) value of dilatancy, the mobiliseddilatancy is set to zero as soon as the maximum void ratio is reached (this is termed

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dilatancy cut-off). For other models this option is not available. To avoid the dilatancycut-off in the Hardening Soil model or Hardening Soil model with small-strain stiffnessthe option may be deselected in the Advanced general properties subtree.

Rayleigh α and β: Material damping in dynamic calculations is caused by the viscousproperties of soil, friction and the development of irreversible strains. All plasticity modelsin PLAXIS 2D can generate irreversible (plastic) strains, and may thus cause materialdamping. However, this damping is generally not enough to model the dampingcharacteristics of real soils. For example, most soil models show pure elastic behaviourupon unloading and reloading which does not lead to damping at all. There is one modelin PLAXIS that includes viscous behaviour, which is the Soft Soil Creep model. Using themodel in dynamic calculations may lead to viscous damping, but also the Soft Soil Creepmodel hardly shows any creep strain in load / reload cycles. There is also one model inPLAXIS that includes hysteretic behaviour in loading / reload cycles, which is the HSsmall model (Chapter 7 of the Material Models Manual). When using this model, theamount of damping that is obtained depends on the amplitude of the strain cycles.Considering very small vibrations, even the HS small model does not show materialdamping, whereas real soils still show a bit of viscous damping. Hence, additionaldamping is needed to model realistic damping characteristics of soils in dynamiccalculations. This can be done by means of Rayleigh damping.

Rayleigh damping is a numerical feature in which a damping matrix C is composed byadding a portion of the mass matrix M and a portion of the stiffness matrix K :

C = αM + βK

The parameters α and β are the Rayleigh coefficients. α is the parameter thatdetermines the influence of mass in the damping of the system. The higher α is, the morethe lower frequencies are damped. β is the parameter that determines the influence ofstiffness in the damping of the system. The higher β is, the more the higher frequenciesare damped. In PLAXIS 2D, these parameters can be specified for each material data setfor soil and interfaces as well as for material data sets for plates. In this way, the (viscous)damping characteristics can be specified for each individual material in the finite elementmodel. The values for α and β can be specified in the corresponding cells in theParameters tabsheet of the Soil window.

Figure 4.3 Damping parameters in the General tabsheet

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Despite the considerable amount of research work in the field of dynamics, little has beenachieved yet for the development of a commonly accepted procedure for dampingparameter identification. Instead, for engineering purposes, some measures are made toaccount for material damping. A commonly used engineering parameter is the dampingratio ξ. The damping ratio is defined as ξ = 1 for critical damping, i.e. exactly the amountof damping needed to let a single degree-of-freedom system that is released from aninitial excitation u0, smoothly stop without rebouncing.

Considering Rayleigh damping, a relationship can be established between the dampingratio ξ and the Rayleigh damping parameters α and β:

α + β ω2 = 2ω ξ and ω = 2π f

where ω is the angular frequency in rad/s and f is the frequency in Hz (1/s).

u

t

Critically damped (ξ = 1)

Underdamped (ξ < 1)

Overdamped (ξ > 1)

Figure 4.4 Role of damping ratio ξ in free vibration of a single degree-of-freedom system

Solving this equation for two different target frequencies and corresponding targetdamping ratios gives the required Rayleigh damping coefficients:

α = 2ω1ω2ω1ξ2 − ω2ξ1

ω21 − ω2

2and β = 2

ω1ξ1 − ω2ξ2

ω21 − ω2

2

For example, when it is desired to have a target damping of 8% at the target frequenciesf = 1.5 Hz and 8.0 Hz, the corresponding Rayleigh damping ratios are α = 1.2698 andβ = 0.002681. From Figure 4.5 it can be seen that within the range of frequencies asdefined by the target frequencies the damping is less than the target damping, whereasoutside this range the damping is more than the target damping.

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0.1

0.1

0.2

0.3

0.4

0.5

1.5 8.0

10

10 100

8%

Dam

ping

ratio

(-)

Frequency (Hz)

Influence of β Influence of α

Damping curve

Figure 4.5 Rayleigh damping parameter influence

The damping parameters (α and β) can be automatically calculated by the program whenthe target damping ratio (ξ) and the target frequencies (f) are specified in the panedisplayed in the General tabsheet when one of the cells corresponding to the dampingparameters is clicked (Figure 4.6). A graph shows the damping ratio as a function of thefrequency.

Figure 4.6 Input of ξ and f

4.1.2 PARAMETERS TABSHEET

The Parameters tabsheet contains the stiffness and strength parameters of the selectedsoil model. These parameters depend on the selected soil model as well as on theselected drainage type.

Linear Elastic model (LE): The Parameters tabsheet for the Linear Elastic model(drained behaviour) is shown in Figure 4.7.

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Hint: Optional drainage types when the Linear Elastic model is selected are:Drained, Undrained (A), Undrained (C), and Non-porous.

» In the case of Undrained (A) or Non-porous drainage types, the sameparameters are used as for drained behaviour.

» In the case of Undrained (C) drainage type, an undrained Young’s modulus(Eu) and undrained Poisson’s ratio (νu) are used.

The model involves two elastic stiffness parameters, namely the effective Young’smodulus E ‘ and the effective Poisson’s ratio ν ‘.

E ‘ : Effective Young’s modulus [kN/m2]

ν ‘ : Effective Poisson’s ratio [-]

During the input for the Linear Elastic model the values of the shear modulus G and theoedometer modulus Eoed are presented as auxiliary parameters (alternatives).

G : Shear modulus, where G = E ‘2(1 + ν ‘)

[kN/m2]

Eoed : Oedometer modulus, where Eoed = E ‘(1− ν ‘)(1 + ν ‘)(1− 2ν ‘)

[kN/m2]

Figure 4.7 Parameters tabsheet for the Linear Elastic model (drained behaviour)

Note that the alternatives are influenced by the input values of E ‘ and ν ‘. Entering aparticular value for one of the alternatives G or Eoed results in a change of the Young’smodulus E ‘.

It is possible for the Linear Elastic model to specify a stiffness that varies linearly withdepth. Therefore, the increment of stiffness per unit of depth, E ‘inc , can be defined.Together with the input of E ‘inc the input of yref becomes relevant. For any y -coordinateabove yref the stiffness is equal to E ‘ref . For any y -coordinate below yref the stiffness is

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given by:

E ‘(y ) = E ‘ +(yref − y )E ‘inc y < yref (4.3)

The Linear Elastic model is usually inappropriate to model the highly non-linear behaviourof soil, but it is of interest to simulate structural behaviour, such as thick concrete walls orplates, for which strength properties are usually very high compared with those of soil.For these applications, the Linear Elastic model will often be selected together withNon-porous type of material behaviour in order to exclude pore pressures from thesestructural elements.

Hint: When embedded piles penetrate a volume cluster with linear elastic materialbehaviour, the specified value of the shaft resistance is ignored. The reasonfor this is that the linear elastic material is not supposed to be soil, but part ofthe structure. The connection between the pile and the structure is supposedto be rigid to avoid, for example, punching of piles through a concrete deck.

Beside the parameters related to strength and stiffness of the soil, the velocities of wavepropagation in soil can be defined in the Parameters tabsheet of the Soil window whenthe Dynamics module of the program is available. These velocities are:

Vs : Shear wave velocity, where Vs =√

G/ρ [m/s]

Vp : Compression wave velocity, where Vp =√

Eoed/ρ [m/s]

Note that ρ = γ/g.

Hint: Note that the wave velocities are influenced by the input values of E ‘ and ν ‘.Entering a particular value for one of the wave velocities results in a changeof the Young’s modulus.

» Velocities of wave propagation in soil can be defined only for models withstress independent stiffness.

Mohr-Coulomb model (MC): The linear-elastic perfectly-plastic model withMohr-Coulomb failure contour (in short the Mohr-Coulomb model) requires a total of fiveparameters (two stiffness parameters and three strength parameters), which aregenerally familiar to most geotechnical engineers and which can be obtained from basictests on soil samples.

The stiffness parameters of the Mohr-Coulomb model (drained behaviour) are:

E ‘ : Effective Young’s modulus [kN/m2]

ν ‘ : Effective Poisson’s ratio [-]

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Figure 4.8 Parameters tabsheet for the Mohr-Coulomb model (drained behaviour)

Hint: Optional drainage types when Mohr-Coulomb model is selected are:Drained, Undrained (A), Undrained (B), Undrained (C), and Non-porous.

» In the case of Undrained (A) or Non-porous drainage types, the sameparameters are used as for drained behaviour.

» In the case of Undrained (B) drainage type, ϕ = ϕu = 0, ψ = 0 and theundrained shear strength su is used instead of the effective cohesion (c’).

» In the case of Undrained (C) drainage type all parameters are undrained. i.e.Eu , νu and su as undrained Young’s modulus, undrained Poisson’s ratio andundrained shear strength respectively, and ϕ = ψ = 0.

Instead of using the Young’s modulus as a stiffness parameter, alternative stiffnessparameters can be entered. These parameters, the relations and their standard units arelisted below:

G : Shear modulus, where G = E ‘2(1 + ν ‘)

[kN/m2]

Eoed : Oedometer modulus, where Eoed = E ‘(1− ν ‘)(1 + ν ‘)(1− 2ν ‘)

[kN/m2]

Note that the alternatives are influenced by the input values of E ‘ and ν ‘. Entering aparticular value for one of the alternatives G or Eoed results in a change of the Young’smodulus E ‘.

Stiffness varying with depth can be defined in Mohr-Coulomb model by entering a valuefor E ‘inc which is the increment of stiffness per unit of depth. Together with the input ofE ‘inc the input of yref becomes relevant. For any y -coordinate above yref the stiffness isequal to E ‘ref . For any y -coordinate below yref the stiffness is given by:

E ‘(y ) = E ‘ +(yref − y )E ‘inc y < yref (4.4)

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The strength parameters for the Mohr-Coulomb model are:

c’ref : Effective cohesion [kN/m2]

ϕ’ : Effective friction angle [◦]

ψ : Dilatancy angle [◦]

A cohesion varying with depth can be defined in Mohr-Coulomb model by entering avalue for c’inc which is the increment of effective cohesion per unit of depth. Together withthe input of c’inc the input of yref becomes relevant. For any y -coordinate above yref thecohesion is equal to c’ref . For any y -coordinate below yref the cohesion is given by:

c'(y ) = c’ref +(yref − y )c’inc y < yref (4.5)

In some practical problems an area with tensile stresses may develop. This is allowedwhen the shear stress is sufficiently small. However, the soil surface near a trench in claysometimes shows tensile cracks. This indicates that soil may also fail in tension insteadof in shear. Such behaviour can be included in a PLAXIS analysis by selecting theTension cut-off option. When selecting the Tension cut-off option the allowable tensilestrength (σt ,soil ) may be entered. For the Mohr-Coulomb model model the default value ofthe tension cut-off is zero.

Beside the parameters related to strength and stiffness of the soil, the velocities of wavepropagation in soil can be defined in the Parameters tabsheet of the Soil window. Thesevelocities are:

Vs : Shear wave velocity, where Vs =√

G/ρ [m/s]

Vp : Compression wave velocity, where Vp =√

Eoed/ρ [m/s]

Note that ρ = γ/g.

Hint: Note that the wave velocities are influenced by the input values of E ‘ and ν ‘.Entering a particular value for one of the wave velocities results in a changeof the Young’s modulus.

» Velocities of wave propagation in soil can be defined only for models withstress independent stiffness.

Hardening Soil model (HS): The Parameters tabsheet for the Hardening Soil model isshown in Figure 4.9.

Hint: Optional drainage types when Hardening Soil model is selected are:Drained, Undrained (A), and Undrained (B).

» In the case of Undrained (A) drainage type, the same parameters are usedas for drained behaviour.

» In the case of Undrained (B) drainage type, ϕ = ϕu = 0 , ψ = 0 and theundrained shear strength su is used instead of the effective cohesion (c’).

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Figure 4.9 Parameters tabsheet for the Hardening Soil model (drained behaviour)

The stiffness parameters of the Hardening Soil model are:

E ref50 : Secant stiffness in standard drained triaxial test [kN/m2]

E refoed : Tangent stiffness for primary oedometer loading [kN/m2]

E refur : Unloading / reloading stiffness (default E ref

ur = 3E ref50 ) [kN/m2]

m : Power for stress-level dependency of stiffness [-]

Instead of entering the basic parameters for soil stiffness, alternative parameters can beentered. These parameters are listed below:

Cc : Compression index [-]

Cs : Swelling index or reloading index [-]

einit : Initial void ratio [-]

In addition, advanced parameters can be defined for stiffness (it is advised to use thedefault setting):

νur : Poisson’s ratio for unloading-reloading (default ν = 0.2) [-]

pref : Reference stress for stiffnesses (default pref = 100kN/m2)

[kN/m2]

K nc0 : K0-value for normal consolidation (default K nc

0 =1− sinϕ)

[-]

The strength parameters of the present hardening model coincide with those of thenon-hardening Mohr-Coulomb model:

c’ref : Effective cohesion [kN/m2]

ϕ’ : Effective angle of internal friction [◦]

ψ : Angle of dilatancy [◦]

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In addition, advanced parameters can be defined for strength:

c’inc : As in Mohr-Coulomb model (default cinc = 0) [kN/m3]

Rf : Failure ratio qf / qa (default Rf = 0.9) [-]

σtension : Tensile strength (default σtension = 0 stress units) [kN/m2]

In some practical problems an area with tensile stresses may develop. This is allowedwhen the shear stress is sufficiently small. However, the soil surface near a trench in claysometimes shows tensile cracks. This indicates that soil may also fail in tension insteadof in shear. Such behaviour can be included in a PLAXIS analysis by selecting theTension cut-off option. When selecting the Tension cut-off option the allowable tensilestrength may be entered. For the Hardening Soil model the default value of the tensioncut-off is zero.

Hardening Soil model with small-strain stiffness (HSsmall): Compared to thestandard HS model, the HS small model requires two additional stiffness parameters asinput: γ0.7 and Gref

0 . The Parameters tabsheet for the HS small model is shown in Figure4.10.

Hint: Optional drainage types when Hardening Soil model with small-strainstiffness is selected are: Drained, Undrained (A), and Undrained (B).

» In the case of Undrained (A) drainage type, the same parameters are usedas for drained behaviour.

» In the case of Undrained (B) drainage type, ϕ = ϕu = 0, ψ = 0 and theundrained shear strength su is used instead of the effective cohesion (c’).

Figure 4.10 Parameters tabsheet for the HS small model (drained behaviour)

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All other parameters, including the alternative stiffness parameters, remain the same asin the standard Hardening Soil model. In summary, the input stiffness parameters of theHS small model are listed below:

Parameters for stiffness:

E ref50 : Secant stiffness in standard drained triaxial test [kN/m2]

E refoed : Tangent stiffness for primary oedometer loading [kN/m2]

E refur : unloading / reload stiffness at engineering strains

(ε ≈ 10−3 to 10−2)[kN/m2]

m : Power for stress-level dependency of stiffness [-]

Alternative parameters for stiffness:

Cc : Compression index [-]

Cs : Swelling index or reloading index [-]

einit : Initial void ratio [-]

Advanced parameters for stiffness:

νur : Poisson’s ratio for unloading-reloading (default ν = 0.2) [-]

pref : Reference stress for stiffnesses (default pref = 100kN/m2)

[kN/m2]

K nc0 : K0-value for normal consolidation (default K nc

0 =1− sinϕ)

[-]

Parameters for strength:

c’ref : Effective cohesion [kN/m2]

ϕ’ : Effective angle of internal friction [◦]

ψ : Angle of dilatancy [◦]

Advanced parameters for strength:

c’inc : As in Mohr-Coulomb model (default c’inc = 0) [kN/m3]

Rf : Failure ratio qf / qa (default Rf = 0.9) [-]

σtension : Tensile strength (default σtension = 0 stress units) [kN/m2]

Parameters for small strain stiffness:

γ0.7 : shear strain at which Gs = 0.722G0 [-]

Gref0 : reference shear modulus at very small strains

(ε < 10−6)[kN/m2]

Hysteretic damping

The elastic modulus ratio is plotted as a function of the shear strain (γ) in a side panewhen specifying the small-strain stiffness parameters (Modulus reduction curve). The HSsmall model shows typical hysteretic behaviour when subjected to cyclic shear loading. Indynamic calculations this leads to hysteretic damping. The damping ratio is plotted as afunction of the cyclic shear strain γc . Details are given in Brinkgreve, Kappert & Bonnier(2007).

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Figure 4.11 Effect of small strain stiffness parameters on dumping

Hint: Note that the Modulus reduction curve and the Damping curve are based onfully elastic behaviour. Plastic strains as a result of hardening or local failuremay lead to significant lower stiffness and higher damping.

Soft Soil model (SS): The Parameters tabsheet for the Soft Soil model is shown inFigure 4.12.

Hint: Optional drainage types when Soft Soil model is selected are: Drained andUndrained (A).

» In the case of Undrained (A) drainage type, the same parameters are usedas for drained behaviour.

The parameters for stiffness are:

λ∗ : Modified compression index [-]

κ∗ : Modified swelling index [-]

Alternative parameters can be used to define stiffness:

Cc : Compression index [-]

Cs : Swelling index or reloading index [-]

einit : Initial void ratio [-]

The parameters for strength are:

c’ref : Effective cohesion [kN/m2]

ϕ’ : Effective friction angle [◦]

ψ : Dilatancy angle [◦]

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Figure 4.12 Parameters tabsheet for the Soft Soil model (drained behaviour)

Advanced parameters (use default settings):

νur : Poisson’s ratio for unloading / reloading (defaultνur = 0.15)

[-]

K nc0 : Coefficient of lateral stress in normal consolidation

(default K nc0 = 1− sinϕ)

[-]

M : K nc0 — related parameter [-]

Soft Soil Creep model (SSC): The Parameters tabsheet for the Soft Soil Creep modelis shown in Figure 4.13.

Hint: Optional drainage types when Soft Soil Creep model is selected are: Drainedand Undrained (A).

» In the case of Undrained (A) drainage type, the same parameters are usedas for drained behaviour.

The parameters for stiffness are:

λ∗ : Modified compression index [-]

κ∗ : Modified swelling index [-]

The parameter taking time effect into account is:

µ∗ : Modified creep index [-]

Alternative parameters can be used to define stiffness:

Cc : Compression index [-]

Cs : Swelling index or reloading index [-]

Cα : Secondary compression index [-]

einit : Initial void ratio [-]

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Figure 4.13 Parameters tabsheet for the Soft Soil Creep model (drained behaviour)

The parameters for strength are:

c’ref : Cohesion [kN/m2]

ϕ’ : Friction angle [◦]

ψ : Dilatancy angle [◦]

Advanced parameters (use default settings):

νur : Poisson’s ratio for unloading / reloading (defaultνur = 0.15)

[-]

K nc0 : Coefficient of lateral stress in normal consolidation

(default K nc0 = 1− sinϕ)

[-]

M : K nc0 — related parameter [-]

Jointed Rock model (JR): The Parameters tabsheet for the Jointed Rock model isshown in Figure 4.14.

Hint: Optional drainage types when Jointed Rock model is selected are: Drainedand Non-porous.

» In the case of Non-porous drainage type, the same parameters are used asfor drained behaviour.

Parameters for stiffness:

E1 : Young’s modulus for rock as a continuum [kN/m2]

ν1 : Poisson’s ratio for rock as a continuum [-]

Anisotropic elastic parameters ‘Plane 1’ direction (e.g. stratification direction):

E2 : Young’s modulus in ‘Plane 1’ direction [kN/m2]

G2 : Shear modulus in ‘Plane 1’ direction [kN/m2]

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Figure 4.14 Parameters tabsheet for the Jointed Rock model (drained behaviour)

ν2 : Poisson’s ratio in ‘Plane 1’ direction [-]

Parameters for strength:

Strength parameters in joint directions (Plane i=1, 2, 3):

ci : Cohesion [kN/m2]

ϕi : Friction angle [◦]

ψi : Dilatancy angle [◦]

σt ,i : Tensile strength [kN/m2]

Definition of joint directions (Plane i=1, 2, 3):

n : Number of joint directions (1 ≤ n ≤ 3) [-]

α1,i : Dip angle [◦]

α2,i : Dip direction [◦]

Modified Cam-Clay model (MCC): This is a critical state model that can be used tosimulate the behaviour of normally consolidated soft soils. The model assumes alogarithmic relationship between the volumetric strain and the mean effective stress. TheParameters tabsheet for the Modified Cam-Clay model is shown in Figure 4.15.

Hint: Optional drainage types when Modified Cam-Clay model is selected are:Drained and Undrained (A).

» In the case of Undrained (A) drainage type, the same parameters are usedas for drained behaviour.

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Figure 4.15 Parameters tabsheet for the Modified Cam-Clay model (drained behaviour)

Parameters for stiffness:

λ : Cam-Clay compression index [-]

κ : Cam-Clay swelling index [-]

ν : Poisson’s ratio [-]

einit : Initial void ratio for loading/unloading [-]

Parameters for strength:

M : Tangent of the critical state line [-]

K nc0 : Coefficient of lateral stress in normal consolidation

derived from M . The relationship between M and K nc0

is given in Section 9.7 of the Material Models Manual

[-]

NGI-ADP model (NGI-ADP): The NGI-ADP model may be used for capacity,deformation and soil-structure interaction analysis involving undrained loading of clay.The Parameters tabsheet for the NGI-ADP model is shown in Figure 4.16.

Hint: Optional drainage types when NGI-ADP model is selected are: Drained,Undrained (B) and Undrained (C).

» In the case of Undrained (B) drainage type, the same parameters are usedas for drained behaviour.

Parameters for stiffness:

Gur/sAu : Ratio unloading/reloading shear modulus over (plane

strain) active shear strength[-]

γCf : Shear strain in triaxial compression (|γC

f = 3/2εC1 |) [%]

γEf : Shear strain in triaxial extension [%]

γDSSf : Shear strain in direct simple shear [%]

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Figure 4.16 Parameters tabsheet for the NGI-ADP model

Parameters for strength:

sA,refu : Reference (plane strain) active shear strength [kN/m2/m]

sC,TXu /sA

u : Ratio triaxial compressive shear strength over (planestrain) active shear strength (default = 0.99)

[-]

yref : Reference depth [m]

sAu,inc : Increase of shear strength with depth [kN/m2/m]

sPu /sA

u : Ratio of (plane strain) passive shear strength over(plane strain) active shear strength

[-]

τ0/sAu : Initial mobilization (default = 0.7) [-]

sDSSu /sA

u : Ratio of direct simple shear strength over (plain strain)active shear strength

[-]

Advanced parameters:

ν ‘ : Effective Poisson’s ratio [-]

νu : Undrained Poisson’s ratio [-]

Hoek-Brown model (HB): The Parameters tabsheet for the Hoek-Brown model isshown in Figure 4.17.

Hint: Optional drainage types when Hoek-Brown model is selected are: Drainedand Non-porous.

» In the case of Non-porous drainage type, the same parameters are used asfor drained behaviour.

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Figure 4.17 Parameters tabsheet for the Hoek-Brown model (drained behaviour)

The stiffness parameters of the Hoek-Brown model are:

E : Young’s modulus [kN/m2]

ν : Poisson’s ratio [-]

The Hoek-Brown parameters are:

σci : Uniaxial compressive strength [kN/m2]

mi : Material constant for the intact rock [-]

GSI : Geological Strength Index [-]

D : Disturbance factor which depends on the degree ofdisturbance to which the rock mass has beensubjected.

[-]

ψmax : Dilatancy at zero stress level [◦]

σψ : Stress level at which dilatancy is fully suppressed [◦]

Sekiguchi-Ohta model (Inviscid): The Parameters tabsheet for the Sekiguchi-Ohtamodel (Inviscid) is shown in Figure 4.18.

Hint: Optional drainage types when Sekiguchi-Ohta model (Inviscid) is selectedare: Drained and Undrained (A).

» In the case of Undrained (A) drainage type, the same parameters are usedas for drained behaviour.

The stiffness parameters of the Sekiguchi-Ohta model (Inviscid) are:

λ∗ : Modified compression index [-]

κ∗ : Modified swelling index [-]

Alternative parameters can be used to define stiffness:

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Figure 4.18 Parameters tabsheet for the Sekiguchi-Ohta model (drained behaviour)

Cc : Compression index [-]

Cs : Swelling index or reloading index [-]

einit : Initial void ratio [-]

Advanced parameters for stiffness:

νur : Poisson’s ratio for unloading-reloading [-]

K nc0 : Coefficient of lateral stress in normal consolidation [-]

Parameters for strength:

M : Tangent of the critical state line [-]

Sekiguchi-Ohta model (Viscid): The Parameters tabsheet for the Sekiguchi-Ohtamodel (Viscid) is shown in Figure 4.19.

Hint: Optional drainage types when Sekiguchi-Ohta model (Viscid) is selected are:Drained and Undrained (A).

» In the case of Undrained (A) drainage type, the same parameters are usedas for drained behaviour.

The stiffness parameters of the Sekiguchi-Ohta model (Viscid) are:

λ∗ : Modified compression index [-]

κ∗ : Modified swelling index [-]

α∗ : Coefficient of secondary compression [-]

dot v0 : Initial volumetric strain rate [day−1]

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Figure 4.19 Parameters tabsheet for the Sekiguchi-Ohta model (Viscid) (drained behaviour)

Alternative parameters can be used to define stiffness:

Cc : Compression index [-]

Cs : Swelling index or reloading index [-]

Cα : Secondary compression index [-]

einit : Initial void ratio [-]

Advanced parameters for stiffness:

νur : Poisson’s ratio for unloading-reloading [-]

K nc0 : Coefficient of lateral stress in normal consolidation [-]

Parameters for strength:

M : Tangent of the critical state line [-]

User-defined soil models (UDSM): The Parameters tabsheet shows two drop-downmenus; the top combo box lists all the DLLs that contain valid User-defined soil modelsand the next combo box shows the models defined in the selected DLL. Each UD modelhas its own set of model parameters, defined in the same DLL that contains the modeldefinition.

When an available model is chosen PLAXIS will automatically read its parameter namesand units from the DLL and fill the parameter table below. For a detailed description ofthis facility, reference is made to the Material Models Manual.

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Hint: Available drainage types when User-defined soil models is selected are:Drained, Undrained (A) and Non-porous.

Advanced parameters for Undrained behaviour

The advanced parameters available in the Parameters tabsheet can be used to model theUndrained behaviour of soils. The advanced parameters for the Undrained behaviourare:

Skempton-B : A measure of how the applied stress is distributedbetween the skeletal framework and the fluid

[-]

νu : Undrained Poisson’s ratio [-]

Kw ,ref/n : The corresponding reference bulk stiffness of thepore fluid

[kN/m2]

A more detailed information is available in Section 2.4 of the Material Models Manual.

4.1.3 FLOW PARAMETERS TABSHEET

The flow parameters are defined in the corresponding tabsheet of the Soil window.

The flow parameters involve the (saturated) permeability as well as the models andparameters for flow in the unsaturated zone. These parameters define the relationshipbetween the degree of saturation S and the suction height ψ as well as the relativepermeability Kr and the suction height ψ. In order to enable an easy selection of theunsaturated flow parameters, predefined data sets are available for common soil types.These data sets can be selected based on standardized soil classification systems.

Hint: Although the predefined data sets have been created for the convenience ofthe user, the user remains at all times responsible for the model parametersthat he/she uses. Note that these predefined data sets have limited accuracy.

Hydraulic data sets and models

The program provides different data sets and models to model the flow in the saturatedzone in soil. The data sets available in the program are:

Standard: This option allows for a simplified selection of the most common soil types(Coarse, Medium, Medium fine, Fine and Very fine non-organic materials and Organicmaterial) and is based on the Hypres topsoil classification series.

The only model available for this data set is Van Genuchten (see Section 16.1 of theMaterial Models Manual).

When one of the soil type options is selected, the particle fractions are automaticallydefined and the soil type is indicated in the soil texture triangle (Figure 4.20). The particlefractions can also be defined by clicking on the corresponding location in the soil texturetriangle or by directly typing the values.

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Figure 4.20 Flow parameters for Standard data set

Hypres: The Hypres series is an international soil classification system. The hydraulicmodels available for Hypres data set are the Van Genuchten model and the ApproximateVan Genuchten (see Sections 16.1 and 16.2 of the Material Models Manual).

A distinction can be made between Topsoil and Subsoil. In general, soils are consideredto be subsoils. The Type drop-down menu for the Hypres data set includes Coarse,Medium, Medium fine, Fine, Very fine and Organic soils.

Hint: Only soil layers that are located not more than 1 m below the ground surfaceare considered to be Upper soils.

The selected soil type and grading (particle fractions) is indicated in the soil texturetriangle. As an alternative, the user can also select the type of soil by clicking one of thesections in the triangle or by manually specifying the particle fraction values (Figure 4.21).

Figure 4.21 Flow parameters for Hypres data set

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The predefined parameters for both the Van Genuchten model as well as theApproximate Van Genuchten model are shown in Table 4.1 and 4.2.

Table 4.1 Hypres series with Van Genuchten parameters

θr (-) θs (-) Ksat (m/day) ga (1/m) gl (-) gn (-)

Topsoil:

coarse 0.025 0.403 0.600 3.83 1.2500 1.3774

medium 0.010 0.439 0.121 3.14 -2.3421 1.1804

medium fine 0.010 0.430 0.0227 0.83 -0.5884 1.2539

fine 0.010 0.520 0.248 3.67 -1.9772 1.1012

very fine 0.010 0.614 0.150 2.65 2.5000 1.1033

Subsoil:

coarse 0.025 0.366 0.700 4.30 1.2500 1.5206

medium 0.010 0.392 0.108 2.49 -0.7437 1.1689

medium fine 0.010 0.412 0.0400 0.82 0.5000 1.2179

fine 0.010 0.481 0.0850 1.98 -3.7124 1.0861

very fine 0.010 0.538 0.0823 1.68 0.0001 1.0730

organic 0.010 0.766 0.0800 1.30 0.4000 1.2039

Table 4.2 Hypres series with Approximate Van Genuchten parameters

ψs (m) ψk (m)

Topsoil:

coarse -2.37 -1.06

medium -4.66 -0.50

medium fine -8.98 -1.20

fine -7.12 -0.50

very fine -8.31 -0.73

Subsoil:

coarse -1.82 -1.00

medium -5.60 -0.50

medium fine -10.15 -1.73

fine -11.66 -0.50

very fine -15.06 -0.50

organic -7.35 -0.97

USDA: The USDA series is another international soil classification system. Thehydraulic models available for USDA data set are the Van Genuchten model and theApproximate Van Genuchten (see Sections 16.1 and 16.2 of the Material ModelsManual).

The Type drop-down menu for the USDA date set includes Sand, Loamy sand, Sandyloam, Loam, Silt, Silt loam, Sandy clay loam, Clay loam, Silty clay loam, Sandy clay, Siltyclay and Clay. The selected soil type and grading (particle fractions) are different fromthe Hypres data sets and can be visualised in the soil texture triangle. As an alternative,the user can also select the type of soil by clicking one of the sections in the triangle or bymanually specifying the particle fraction values (Figure 4.22).

The parameters for the Van Genuchten and the Approximate Van Genuchten models areshown in Table 4.3 and 4.4.

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Figure 4.22 Flow parameters for USDA data set

Table 4.3 USDA series with Van Genuchten parameters (gl = 0.5 for all sets)

θr (-) θs (-) Ksat (m/day) ga (1/m) gn (-)

sand 0.045 0.430 7.13 14.5 2.68

loamy sand 0.057 0.410 3.50 12.4 2.28

sandy loam 0.065 0.410 1.06 7.5 1.89

loam 0.078 0.430 0.250 3.6 1.56

silt 0.034 0.460 0.600 1.6 1.37

silty loam 0.067 0.450 0.108 2.0 1.41

sandy clay loam 0.100 0.390 0.314 5.9 1.48

clayey loam 0.095 0.410 0.624 1.9 1.31

silty clayey loam 0.089 0.430 0.168 1.0 1.23

sandy clay 0.100 0.380 0.288 2.7 1.23

silty clay 0.070 0.360 0.00475 0.5 1.09

clay 0.068 0.380 0.0475 0.8 1.09

Table 4.4 USDA series with Approximate Van Genuchten parameters

ψs (m) ψk (m)

sand -1.01 -0.50

loamy sand -1.04 -0.50

sandy loam -1.20 -0.50

loam -1.87 -0.60

silt -4.00 -1.22

silty loam -3.18 -1.02

sandy clay loam -1.72 -0.50

clayey loam -4.05 -0.95

silty clayey loam -8.23 -1.48

sandy clay -4.14 -0.55

silty clay -31.95 -0.95

clay -21.42 -0.60

Staring: The Staring series is a soil classification system which is mainly used in TheNetherlands. The hydraulic models available for Staring data set are the Van Genuchtenmodel and the Approximate Van Genuchten (see Sections 16.1 and 16.2 of the MaterialModels Manual).

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Figure 4.23 Flow parameters for Staring data set

A distinction can be made between Topsoil and Subsoil. In general, soils are consideredto be subsoils. The Type drop-down menu for the Staring series (Figure 4.23) containsthe following subsoils: Non-loamy sand (O1), Loamy sand (O2), Very loamy sand (O3),Extremely loamy sand (O4), Coarse sand (O5), Boulder clay (O6), River loam (O7),Sandy loam (O8), Silt loam (O9), Clayey loam (O10), Light clay (O11), Heavy clay (O12),Very heavy clay (O13), Loam (O14), Heavy loam (O15), Oligotrophic peat (O16),Eutrophic peat (O17) and Peaty layer (O18), and the following topsoils: Non-loamy sand(B1), Loamy sand (B2), Very loamy sand (B3), Extremely loamy sand (B4), Coarse sand(B5), Boulder clay (B6), Sandy loam (B7), Silt loam (B8), Clayey loam (B9), Light clay(B10), Heavy clay (B11), Very heavy clay (B12), Loam (B13), Heavy loam (B14), Peatysand (B15), Sandy peat (B16), Peaty clay (B17) and Clayey peat (B18). The selected soiltype and grading (particle fractions) are different from the Hypres and the USDA datasets. The parameters of the hydraulic model for the selected soil type are displayed in theSoil tab at the right side of the Flow parameters tabsheet.

Hint: Only soil layers that are located not more than 1 m below the ground surfaceare considered to be Upper soils.

User defined: The User defined option enables the user to define both saturated andunsaturated properties manually. Please note that this option requires adequateexperience with unsaturated groundwater flow modelling. The hydraulic models availableare:

Van Genuchten This well-known and widely accepted model requires direct inputof the residual saturation Sres, the saturation at p = 0 Ssat andthe three fitting parameters gn, ga and gl (see Section 16.1 in theMaterial Models Manual).

Spline The Spline function requires direct input of the capillary height ψ(in unit of length), the relative permeability Kr (-), and the degreeof saturation Sr (-). Data for the Spline function can be enteredby clicking the Table tab. During the calculations, PlaxFlow will

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use ‘smooth’ relationships based on a spline function betweenthe relative permeability and the capillary height and alsobetween the relative saturation and the capillary height.

Saturated When the Saturated option is selected, no extra data input isrequired. During the calculations, PlaxFlow will continuously usethe saturated permeabilities for soil layers where a Saturateddata set was assigned.

Figure 4.24 Flow parameters for User defined data set

Permeabilities (kx and ky )

Permeabilities have the dimension of discharge per area, which simplifies to unit of lengthper unit of time. This is also known as the coefficient of permeability. The input ofpermeability parameters is required for consolidation analyses and groundwater flow.

For those types of calculations, it is necessary to specify permeabilities for all clusters,including almost impermeable layers that are considered to be fully impervious. PLAXIS2D distinguishes between a horizontal permeability, kx , and a vertical permeability, ky ,since in some types of soil (for example peat) there can be a significant differencebetween horizontal and vertical permeability.

In real soils, the difference in permeabilities between the various layers can be quitelarge. However, care should be taken when very high and very low permeabilities occursimultaneously in a finite element model, as this could lead to ill-conditioning of the flowmatrix. In order to obtain accurate results, the ratio between the highest and lowestpermeability value in the geometry should not exceed 105.

Note that the input field for permeabilities are greyed out when the Non-porous option isselected.

One of the advanced features is to account for the change of permeability during aconsolidation analysis. This can be applied by entering a proper value for the change ofpermeability parameter ck and the void ratio’s einit , emin and emax in the General tabsheetof the Soil window.

In case of a Standard, Hypres, USDA or Staring data set default values for the

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permeability can be automatically set by selecting the Set to default values option. Thesevalues can be modified by unselecting the Set to default values option.

Unsaturated zone (ψunsat )

ψunsat (in unit of length relative to the phreatic level) sets the maximum pressure headuntil which the Mualem-Van Genuchten functions are used for calculation of relativepermeability and degree of saturation. The negative sign indicates suction. Above thelevel of ψunsat , the value of Kr and S remain constant. In this way a minimum degree ofsaturation (Smin) is guaranteed (Figure 4.25). It is used to limit the relative permeabilityKr and degree of saturations for high unsaturated zones.

Figure 4.25 Relative permeability vs. Degree of saturation

By default a very large value is assigned to ψunsat (= 104). This value is only an indicationthat the unsaturated zone is by default unlimited.

Change of permeability (ck ): This advanced feature is to account for the change ofpermeability during a consolidation analysis. This can be applied by entering a propervalue for the ck parameter and the void ratio’s. On entering a real value, the permeabilitywill change according to the formula:

log(

kk0

)=

∆eck

where ∆e is the change in void ratio, k is the permeability in the calculation and k0 is theinput value of the permeability in the data set (= kx and ky ). Note that a proper input ofthe initial void ratio einit , in the General tabsheet is required. It is recommended to use achanging permeability only in combination with the Hardening Soil model, Hardening Soilmodel with small-strain stiffness , Soft Soil model or the Soft Soil Creep model. In thatcase the ck -value is generally in the order of the compression index Cc . For all othermodels the ck -value should be left to its default value of 1015.

4.1.4 INTERFACES TABSHEET

The properties of interface elements are related to the soil model parameters of thesurrounding soil. The required parameters to derive the interface properties are defined

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in the Interfaces tabsheet of the Soil window. These parameters depend on the materialmodel selected to represent the behaviour of the surrounding soil. In case the LinearElastic model, the Mohr-Coulomb model, the Hardening Soil model, the HS small model,the Soft Soil model, the Soft Soil Creep model, the Jointed Rock model, the Hoek-Brownmodel or the NGI-ADP model has been selected as the Material model, the strengthreduction factor Rinter is the main interface parameter (see Figure 4.26). In case of theModified Cam-Clay model, the interface parameters required are the effective cohesionc’ref , the effective friction angle ϕ’ and the dilatancy angle ψ’. In case of the User-definedsoil models, the tangent stiffness for primary oedometer loading E ref

oed , the effectivecohesion c’ref , the effective friction angle ϕ’, the dilatancy angle ψ’ and the parametersUD-Power and UD-Pref are required as interface parameters. For more information on theinterface parameters required for the User-defined soil models, see Section 14.3 inMaterial Models Manual.

Figure 4.26 Interfaces tabsheet of the Soil window

Interface strength

In case of the Linear Elastic model, the Mohr-Coulomb model, the Hardening Soil model,the HS small model, the Soft Soil model, the Soft Soil Creep model, the Jointed Rockmodel, the Hoek-Brown model or the NGI-ADP model, the interface strength is defined bythe parameter Rinter . The interface strength can be set using the following options:

Rigid: This option is used when the interface should not have a reduced strength withrespect to the strength in the surrounding soil. For example, extended interfaces aroundcorners of structural objects (Figure 3.20) are not intended for soil-structure interactionand should not have reduced strength properties. The strength of these interfaces shouldbe assigned as Rigid (which corresponds to Rinter = 1.0). As a result, the interfaceproperties, including the dilatancy angle ψi , are the same as the soil properties in thedata set, except for Poisson’s ratio νi (see further).

Manual: The value of Rinter can be entered manually if the interface strength is set toManual. In general, for real soil-structure interaction the interface is weaker and moreflexible than the surrounding soil, which means that the value of Rinter should be less than1. Suitable values for Rinter for the case of the interaction between various types of soil

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and structures in the soil can be found in the literature. In the absence of detailedinformation it may be assumed that Rinter is of the order of 2/3. A value of Rinter greaterthan 1 would not normally be used.

When the interface is elastic then both slipping (relative movement parallel to theinterface) and gapping or overlapping (i.e. relative displacements perpendicular to theinterface) could be expected to occur. The magnitudes of the interface displacementsare:

Elastic gap displacement =σ

KN=

σ tiEoed ,i

Elastic slip displacement =τ

Ks=τ tiGi

where Gi is the shear modulus of the interface, Eoed ,i is the one-dimensionalcompression modulus of the interface, ti is the virtual thickness of the interface generatedduring the creation of interfaces in the geometry model (Section 3.4.5), KN is the elasticinterface normal stiffness and KS is the elastic interface shear stiffness.

The shear and compression moduli are related by the expressions:

Eoed ,i = 2 Gi1− νi

1− 2 νi

Gi = R2inter Gsoil ≤ Gsoil

νi = 0.45

Hint: Note that a reduced value of Rinter not only reduces the interface strength,but also the interface stiffness.

It is clear from these equations that, if the elastic parameters are set to low values, theelastic displacements may be excessively large. If the values of the elastic parametersare too large, however, this can result in numerical ill-conditioning of the stiffness matrix.The key factor in the stiffness is the virtual thickness. This value is automatically chosensuch that an adequate stiffness is obtained. The user may change the virtual thickness.This can be done in the Interface window that appears after double clicking an interfacein the geometry model (Section 3.4.5).

Manual with residual strength: When the limit value of the interface strength asdefined by Rinter is reached, the interface strength may soften down to a reduced valueas defined by Rinter ,residual . Definition of the Rinter ,residual is possible when the Manual withresidual strength option is selected for the interface strength.

Interface strength (Rinter ): An elastic-plastic model is used to describe the behaviour ofinterfaces for the modelling of soil-structure interaction. The Coulomb criterion is used todistinguish between elastic behaviour, where small displacements can occur within theinterface, and plastic interface behaviour when permanent slip may occur. For theinterface to remain elastic the shear stress τ is given by:

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|τ |< −σn tanϕi + ci

where σn is the effective normal stress.

For plastic behaviour τ is given by:

|τ |= −σn tanϕi + ci

where ϕi and ci are the friction angle and cohesion (adhesion) of the interface. Thestrength properties of interfaces are linked to the strength properties of a soil layer. Eachdata set has an associated strength reduction factor for interfaces Rinter . The interfaceproperties are calculated from the soil properties in the associated data set and thestrength reduction factor by applying the following rules:

ci = Rinter csoil

tanϕi = Rinter tanϕsoil ≤ tanϕsoil

ψi = 0° for Rinter < 1, otherwise ψi = ψsoil

In addition to Coulomb’s shear stress criterion, the tension cut-off criterion, as describedbefore (see Section 4.1.2), also applies to interfaces (if not deactivated):

σn < σt ,i = Rinterσt ,soil

where σt ,soil is the tensile strength of the soil.

Residual interface strength (Rinter ,residual ): When the Manual with residual strengthoption is selected the parameter Rinter ,residual can be specified. The interface strength willreduce to the residual strength as defined by (Rinter ,residual ) and the strength properties ofthe soil, as soon as the interface strength is reached.

Hint: Note that the same values of the Design Approach factors are applied to bothinterface strength Rinter and residual interface strength Rinter ,residual .

Consider gap closure: When the interface tensile strength is reached a gap may occurbetween the structure and the soil. When the load is reversed, the contact between thestructure and the soil needs to be restored before a compressive stress can developed.This is achieved by selecting the Consider gap closure option in the Interfaces tabsheetof the Soil window. If the option is NOT selected, contact stresses will immediatelydevelop upon load reversal, which may not be realistic.

Interfaces using the Hoek-Brown model: When using the Hoek-Brown model as acontinuum model to describe the behaviour of a rock section in which interface elementsare used, equivalent interface strength properties ϕi , ci and σt ,i are derived from thismodel. The general shear strength criterion for interfaces as well as the tensile strengthcriterion are still used in this case:

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|τ |≤ −σn tanϕi + ci

σn ≤ σt ,i

Starting point for the calculation of the interface strength properties is the minor principaleffective stress σ’3 in the adjacent continuum element. At this value of confining stressthe tangent to the Hoek-Brown contour is calculated and expressed in terms of ϕ and c:

sinϕ =f ‘

2 + f ‘

c =1− sinϕ2 cosϕ

(f +

2σ’3 sinϕ1− sinϕ

)where

f = σci

(mb−σ’3σci

+ c)

a

f ‘ = amb

(mb−σ’3σci

+ s)

a−1

and a, mb, s and ci are the Hoek-Brown model parameters in the corresponding materialdata set. The interface friction angle ϕ’i and adhesion c’i as well as the interface tensilestrength σt ,i are now calculated using the interface strength reduction factor Rinter :

tanϕi = Rinter c

ci = Rinter c

σt ,i = Rinterσt = Rintersσci

mb

For more information about the Hoek-Brown model and an explanation of its parameters,reference is made to Chapter 4 of the Material Models Manual.

Interfaces using the Modified Cam-Clay model: If the Modified Cam-Clay model isselected in the Parameters tabsheet to describe the behaviour of the surrounding soil, thefollowing parameters are required to model the interface behaviour:

cref : Cohesion of the interface [kN/m2]

ϕi : Internal friction angle of the interface [◦]

ψi : Dilatancy angle of the interface [◦]

When the interface is elastic then both slipping (relative movement parallel to theinterface) and gapping or overlapping (i.e. relative displacements perpendicular to theinterface) could be expected to occur.

The magnitudes of these displacements are:

Elastic gap displacement =σ

KN=

σ tiEoed ,i

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Elastic slip displacement =τ

Ks=τ tiGi

where Gi is the shear modulus of the interface, Eoed ,i is the one-dimensionalcompression modulus of the interface and ti is the virtual thickness of the interface,generated during the creation of interfaces in the geometry model (Section 3.4.5). KN isthe elastic interface normal stiffness and KS is the elastic interface shear stiffness. Theshear and compression moduli are related by the expressions:

Eoed ,i =3λ

(1− νi )(1 + νi )

σn

(1 + e0)

Gi =3(1− 2νi )2(1 + νi )

σn

λ(1 + e0)

νi = 0.45

Real interface thickness (δinter )

The real interface thickness δinter is a parameter that represents the real thickness of ashear zone between a structure and the soil. The value of δinter is only of importancewhen interfaces are used in combination with the Hardening Soil model. The realinterface thickness is expressed in the unit of length and is generally of the order of a fewtimes the average grain size. This parameter is used to calculate the change in void ratioin interfaces for the dilatancy cut-off option. The dilatancy cut-off in interfaces can be ofimportance, for example, to calculate the correct bearing capacity of tension piles.

Interfaces below or around corners of structures

When interfaces are extended below or around corners of structures to avoid stressoscillations (Section 3.4.5), these extended interfaces are not meant to modelsoil-structure interaction behaviour, but just to allow for sufficient flexibility. Hence, whenusing Rinter < 1 for these interface elements an unrealistic strength reduction isintroduced in the ground, which may lead to unrealistic soil behaviour or even failure.Therefore it is advised to create a separate data set with Rinter = 1 and to assign this dataset only to these particular interface elements. This can be done by dropping theappropriate data set on the individual interfaces (dashed lines) rather than dropping it onthe associated soil cluster (the dashed lines should blink red; the associated soil clustermay not change colour). Alternatively, you can click the right-hand mouse button onthese particular interface elements and select Properties and subsequently Positiveinterface element or Negative interface element. In the Interface window, select theappropriate material set in the Material set drop-down menu and click the OK button.

Interface permeability

Interfaces do not have a permeability assigned to them, but they are, by default, fullyimpermeable. In this way interfaces may be used to block the flow perpendicular to theinterface in a consolidation analysis or a groundwater flow calculation, for example tosimulate the presence of an impermeable screen. This is achieved by a full separation ofthe pore pressure degrees-of-freedom of the interface node pairs. On the other hand, ifinterfaces are present in the mesh it may be the user’s intension to explicitly avoid any

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influence of the interface on the flow and the distribution of (excess) pore pressures, forexample in interfaces around corner points of structures (Section 3.4.5). In such a casethe interface should be de-activated in the water conditions mode. This can be doneseparately for a consolidation analysis and a groundwater flow calculation. For inactiveinterfaces the pore pressure degrees-of-freedom of the interface node pairs are fullycoupled.

In conclusion:

• An active interface is fully impermeable (separation of pore pressuredegrees-of-freedom of node pairs).

• An inactive interface is fully permeable (coupling of pore pressuredegrees-of-freedom of node pairs).

4.1.5 INITIAL TABSHEET

The Initial tabsheet contains parameters to generate the initial stresses by means of theK0 procedure (Figure 4.27).

Figure 4.27 Soil window (Initial tabsheet of the Mohr-Coulomb model)

The K0-value can be defined automatically by selecting the option Automatic in the K0determination drop-down menu or manually by selecting the option Manual.

K0-values

In general, only one K0-value can be specified:

K0,x = σ’xx/σ’yy K0,z = σ’zz/σ’yy = K0,x

The default K0-value is then in principal based on Jaky’s formula:

K0 = 1− sinϕ

For advanced models (Hardening Soil model, Hardening Soil model with small-strainstiffness, Soft Soil model, Soft Soil Creep model, Modified Cam-Clay model) the defaultvalue is based on the K nc

0 model parameter and is also influenced by the OCR-value and

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POP-value in the following way:

K0,x = K nc0 OCR− νur

1− νur(OCR− 1)+

K nc0 POP− νur

1− νurPOP∣∣σ0

yy

∣∣The POP-value will result in a stress-dependent K0-value within the layers resulting ininvisible K0-values.

Be careful with very low or very high K0-values, since these values might bring the initialstress in a state of failure. For a cohesionless material it can easily be shown that toavoid failure, the value of K0 is bounded by:

1− sinϕ1 + sinϕ

< K0 <1 + sinϕ1− sinϕ

OCR and POP

When using advanced models (Hardening Soil model, Hardening Soil model withsmall-strain stiffness, Soft Soil model, Soft Soil Creep model, Modified Cam-Clay model,Sekiguchi-Ohta model) an initial pre-consolidation stress has to be determined. In theengineering practice it is common to use a vertical pre-consolidation stress, σp, butPLAXIS needs an equivalent isotropic pre-consolidation stress, peq

p to determine theinitial position of a cap-type yield surface. If a material is over-consolidated, information isrequired about the Over-Consolidation Ratio (OCR), i.e. the ratio of the greatest effectivevertical stress previously reached, σp (see Figure 4.28), and the in-situ effective verticalstress, σ’0yy .

OCR =σp

σ’0yy(4.6)

=

σ’0yy

σ’0yy

σp

σpOCR

a. Using OCR

σ’0yy σp

POP

b. Using POP

Figure 4.28 Illustration of vertical pre-consolidation stress in relation to the in-situ vertical effectivestress

It is also possible to specify the initial stress state using the Pre-Overburden Pressure(POP) as an alternative to prescribing the over-consolidation ratio. The Pre-OverburdenPressure is defined by:

POP = |σp − σ’0yy | (4.7)

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These two ways of specifying the vertical pre-consolidation stress are illustrated in Figure4.28.

The pre-consolidation stress σp is used to compute peqp which determines the initial

position of a cap-type yield surface in the advanced soil models. The calculation of peqp is

based on the stress state:

σ’1 = σp and: σ’2 = σ’3 = K nc0 σp (4.8)

where K nc0 is the K0-value associated with normally consolidated states of stress, which

is based on Jaky’s formula, K nc0 ≈ 1− sinϕ, or it is a direct input parameter for the

advanced soil models.

4.2 MODELLING UNDRAINED BEHAVIOUR

In undrained conditions, no water movement takes place. As a result, excess porepressures are built up. Undrained analysis is appropriate when:

• Permeability is low or rate of loading is high.

• Short term behaviour has to be asses

Different modelling schemes are possible in PLAXIS to model undrained soil behaviour.These methods are described here briefly. More details about these methods are give inSection 2.4 to 2.7 of the Material Models Manual.

Hint: The modelling of undrained soil behaviour is even more complicated than themodelling of drained behaviour. Therefore, the user is advised to take theutmost care with the modelling of undrained soil behaviour.

Undrained effective stress analysis with effective stiffness parameters

A change in total mean stress in an undrained material during a Plastic calculation phasegives rise to excess pore pressures. PLAXIS differentiates between steady-state porepressures and excess pore pressures, the latter generated due to small volumetric strainoccurring during plastic calculations and assuming a low (but non zero) compressibility ofthe pore water. This enables the determination of effective stresses during undrainedplastic calculations and allows undrained calculations to be performed with effectivestiffness parameters. This option to model undrained material behaviour based oneffective stiffness parameters is available for all material models in the PLAXIS. Theundrained calculations can be executed with effective stiffness parameters, with explicitdistinction between effective stresses and (excess) pore pressures.

Undrained effective stress analysis with effective strength parameters

Undrained effective stress analysis can be used in combination with effective strengthparameters ϕ’ and c’ to model the material’s undrained shear strength. In this case, thedevelopment of the pore pressure plays a crucial role in providing the right effectivestress path that leads to failure at a realistic value of undrained shear strength (cu or su).

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However, note that most soil models are not capable of providing the right effective stresspath in undrained loading. As a result, they will produce the wrong undrained shearstrength if the material strength has been specified on the basis of effective strengthparameters. Another problem is that for undrained materials effective strengthparameters are usually not available from soil investigation data.

The advantage of using effective strength parameters in undrained loading conditions isthat after consolidation a qualitatively increased shear strength is obtained, although thisincreased shear strength could also be quantitatively wrong, for the same reason asexplained before.

Undrained effective stress analysis with undrained strength parameters

Especially for soft soils, effective strength parameters are not always available, and onehas to deal with measured undrained shear strength (cu or su) as obtained fromundrained tests. Undrained shear strength, however, cannot easily be used to determinethe effective strength parameters ϕ’ and c’. Moreover, even if one would have propereffective strength parameters, care has to be taken as to whether these effective strengthparameters will provide the correct undrained shear strength in the analysis. This isbecause the effective stress path that is followed in an undrained analysis may not be thesame as in reality, due to the limitations of the applied soil model.

In order to enable a direct control on the shear strength, PLAXIS allows for an undrainedeffective stress analysis with direct input of the undrained shear strength (Undrained (B)).

4.2.1 UNDRAINED (A)

The Drainage type Undrained (A) enables modelling undrained behaviour using effectiveparameters for stiffness and strength. The characteristic features of method Undrained(A) are:

• The undrained calculation is performed as an effective stress analysis. Effectivestiffness and effective strength parameters are used.

• Pore pressures are generated, but may be inaccurate, depending on the selectedmodel and parameters.

• Undrained shear strength su is not an input parameter but an outcome of theconstitutive model. The resulting shear strength must be checked against knowndata.

• Consolidation analysis can be performed after the undrained calculation, whichaffect the shear strength.

Undrained (A) drainage type is available for the following models: Linear Elastic model,Mohr-Coulomb model, Hardening Soil model, Hardening Soil model with small-strainstiffness, Soft Soil model, Soft Soil Creep model, Modified Cam-Clay model andUser-defined soil models.

4.2.2 UNDRAINED (B)

The Drainage type Undrained (B) enables modelling undrained behaviour using effectiveparameters for stiffness and undrained strength parameters. The characteristic featuresof method Undrained (B) are:

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• The undrained calculation is performed as an effective stress analysis.

• Effective stiffness parameters and undrained strength parameters are used.

• Pore pressures are generated, but may be highly inaccurate.

• Undrained shear strength su is an input parameter.

• Consolidation analysis should not be performed after the undrained calculation. Ifconsolidation analysis is performed anyway, su must be updated.

Undrained (B) drainage type is available for the following models: Mohr-Coulomb model,Hardening Soil model, Hardening Soil model with small-strain stiffness and NGI-ADPmodel. Note that when using Undrained (B) in the Hardening Soil model or HardeningSoil model with small-strain stiffness, the stiffness moduli in the model are no longerstress-dependent and the model exhibits no compression hardening.

4.2.3 UNDRAINED (C)

The Drainage type Undrained (C) enables simulation of undrained behaviour using a totalstress analysis with undrained parameters. In that case, stiffness is modelled using anundrained Young’s modulus Eu and an undrained Poisson ratio νu , and strength ismodelled using an undrained shear strength cu (su) and ϕ = ϕu = 0°. Typically, for theundrained Poisson ratio a value close to 0.5 is selected (between 0.495 and 0.499). Avalue of exactly 0.5 is not possible, since this would lead to singularity of the stiffnessmatrix. The disadvantage of this approach is that no distinction is made between effectivestresses and pore pressures. Hence, all output referring to effective stresses should nowbe interpreted as total stresses and all pore pressures are equal to zero. Note that adirect input of undrained shear strength does not automatically give the increase of shearstrength with consolidation. The characteristic features of method Undrained (C) are:

• The undrained calculation is performed as a total stress analysis.

• Undrained stiffness parameters and undrained strength parameters are used.

• Pore pressures are not generated.

• Undrained shear strength su is an input parameter.

• Consolidation analysis has no effect and should not be performed. If consolidationanalysis is performed anyway, su must be updated.

Undrained (C) drainage type is available for the following models: Linear Elastic model,Mohr-Coulomb model and NGI-ADP model.

Hint: For Undrained (B) and Undrained (C) an increased shear strength with depthcan be modelled using the advanced parameter su,inc .

4.3 SIMULATION OF SOIL TESTS

The SoilTest option is a quick and convenient procedure to simulate basic soil tests onthe basis of a single point algorithm, i.e. without the need to create a complete finite

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element model. This option can be used to compare the behaviour as defined by the soilmodel and the parameters of a soil data set with the results of laboratory test dataobtained from a site investigation. It also offers the possibility to optimise modelparameters such that a best fit is obtained between the model results and the lab testdata. The SoilTest facility works for any soil model, both standard soil models as well asuser-defined models.

The SoilTest option is available from the Material sets window if a soil data set is selected(see Figure 4.29). Alternatively, the SoilTest option can be reached from the Soil dialog.

Figure 4.29 Material sets window showing the project and the global database

Once the SoilTest option has been selected, a separate window will open (Figure 4.30).This window contains a menu, a toolbar and several smaller sections. The various itemsare described in more detail below.

Figure 4.30 SoilTest window showing drained triaxial test input

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Main menu

The menus available in the menu bar are:

File To open, save and close a soil test data file (*.vlt).

Test To select the test that will be simulated. The options availableare Triaxial, Oedometer, CRS, DSS (Simple Shear) and General.

Results To select the configuration of diagrams to display.

Toolbar

The toolbar allows for loading, saving and running of soil test results and opening thePLAXIS SoilTest — Settings window to set the configuration of the results. It also containsthe parameter optimisation feature (Section 4.3.7).

Material properties

The Material properties box displays the name, material model and parameters of thecurrently selected data set. Transferring of material parameters to and from the materialdatabase is possible. To copy the modified parameters to the material database:

Click the Copy material button in the Material properties box.

• In the program open the Material sets window and either select the correspondingmaterial set or click New.

In the Soil window click Paste material button. The parameters will be copied in thematerial database. In the same way it is also possible to copy material from materialdatabase to soil test.

Test area

The type of test and the testing conditions are defined in the test area. The test optionsavailable are Triaxial, Oedometer, CRS, DSS and General. As one of these options isselected by clicking the corresponding tab, the testing conditions can be defined in thetabsheet. A more detailed description of the tests is given in the following sections.

Run

The Run button starts the currently selected test∗. Once the calculation has finished, theresults will be shown in the Results window.

Test configurations

The Test configurations button can be used to add and manage different soilconfigurations. A test configuration contains information about the test type and thevalues of test input parameters. To save a test configuration select the Save option in themenu displayed as the Test configuration button is clicked. The Manage option can beused to manage the test configurations available. When the Manage option is selected,the Manage configuration window pops up. Note that the name of the window indicatesthe test to which the configuration belongs (Figure 4.31).

∗ Although the soil test calculation kernel is a reduced version of the finite element calculation kernel, theimplementation of the soil models is identical.

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Figure 4.31 Manage configurations window for triaxial tests

The name and the location of the configuration file is indicated in the Filename and Pathrespectively in the Manage configurations window.

Set as default

The Set as default button saves the current input parameters as the default parameters.These will be initialised as such the next time the SoilTest window is opened.

Loaded tests

When previously saved tests of the current type have been opened from the File menu,the Loaded tests window lists all these tests within each tabsheet. The results of allloaded tests are shown together with the results of the current test. The Delete buttoncan be used to remove the selected test from the list of loaded tests. It does not removethe soil test file (*.vlt) from disk.

Results

The results of the test are displayed in the predefined diagrams in the results area.

4.3.1 TRIAXIAL TEST

The Triaxial tabsheet contains facilities to define different types of triaxial tests. Beforespecifying the test conditions, a selection can be made between different triaxial testsoptions.

Triaxial test — Options

Drained / undrained triaxial testIn the latter case, undrained soil conditions and zero drainageare assumed (similar as when the Drainage type has been set toUndrained (A) or Undrained (B), see Section 4.2), irrespective ofthe drainage type setting in the material data set.

Triaxial compression / triaxial extension testIn the former case the axial load is increased; in the latter casethe axial load is decreased.

Isotropically consolidated / K0-consolidated testIn the latter case the K0-value (ratio of lateral stress over axial

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stress) can be specified to set the initial stress state.

Triaxial test — Conditions

The following test conditions can be defined:

Initial effective stress |σ’3|The absolute value of the isotropic cell pressure at which thesample is consolidated, entered in units of stress. This sets theinitial stress state. In the case of a K0-consolidated test, thisvalue represents the initial lateral stress, σ3; the initial verticalstress, σ1, is defined as σ3/K0.

Hint: During a laboratory consolidated undrained triaxial test (CU test) abackpressure is applied to make sure that the sample is fully saturated. Thenthe sample is consolidated by using a constant cell pressure and backpressure. Note that the value assigned to the Initial effective stress in theSoilTest should be the effective stress at the start of the test, which is equalto the cell pressure minus the back pressure at the start of the test.

Maximum strain |ε1| The absolute value of the axial strain that will be reached in thelast calculation step.

Time ∆t Time increment (only relevant for time-dependent models;consolidation is not considered).

Number of steps The number of steps that will be used in the calculation.

|vertical precons. stress|The vertical pre-consolidation pressure to which the soil hasbeen subjected. If the soil is normally consolidated this valueshould be set equal to the initial stress state, i.e. zero. From thevertical pre-consolidation stress the program calculates theisotropic pre-consolidation stress based on the K nc

0 loading path(see Section 2.8 of the Material Models Manual). This option isonly available for the advanced soil models.

Mobilized relative shear strengthThis option is only available for the Hardening Soil model and HSsmall model to set the initial shear hardening contour. This valuemust be between 0 (isotropic stress state) and 1 (failure state).

4.3.2 OEDOMETER

The Oedometer tabsheet contains facilities to define a one-dimensional compression(oedometer) test. The following settings can be defined:

|vertical precons. stress|The vertical pre-consolidation pressure to which the soil hasbeen subjected. If the soil is normally consolidated this valueshould be set equal to the initial stress state, i.e. zero. From the

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vertical pre-consolidation stress the program calculates theisotropic pre-consolidation stress based on the K nc

0 loading path(see Section 2.8 of the Material Models Manual). This option isonly available for the advanced soil models.

Mobilized relative shear strengthThis option is only available for the Hardening Soil model and HSsmall model to set the initial shear hardening contour. This valuemust be between 0 (isotropic stress state) and 1 (failure state).

Phases Lists the different phases of the oedometer test. Each phase isdefined by a Duration (in units of time), a vertical Stressincrement (in units of stress) and a Number of steps. The initialstate is always assumed to be stress free. The given stressincrement will be reached at the end of the given duration in thegiven number of steps. The input values can be changed byclicking in the table. A negative stress increment impliesadditional compression, whereas a positive stress incrementimplies unloading or tension. If a period of constant load isdesired, enter the desired duration with a zero stress increment.

Add Adds a new phase to the end of the Phases list.

Insert Inserts a new phase before the currently selected phase.

Remove Removes the currently selected phase from the Phases list.

4.3.3 CRS

The CRS tabsheet contains facilities to define a constant rate-of-strain compression test.The following settings can be defined:

|vertical precons. stress|The vertical pre-consolidation pressure to which the soil hasbeen subjected. If the soil is normally consolidated this valueshould be set equal to the initial stress state, i.e. zero. From thevertical pre-consolidation stress the program calculates theisotropic pre-consolidation stress based on the K nc

0 loading path(see Section 2.8 of the Material Models Manual). This option isonly available for the advanced soil models.

Mobilized relative shear strengthThis option is only available for the Hardening Soil model and HSsmall model models to set the initial shear hardening contour.This value must be between 0 (isotropic stress state) and 1(failure state).

Phases Lists the different phases of the CRS test. Each phase is definedby a Duration (in units of time), a vertical Strain increment (in %)and a Number of steps. The initial state is always assumed to bestress free. The given strain increment will be reached at the endof the given duration in the given number of steps. The inputvalues can be changed by clicking in the table. A negative strainincrement implies additional compression, whereas a positive

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strain increment implies unloading or tension. If a period of zerostrain is desired, enter the desired duration with a zero strainincrement.

Add Adds a new phase to the end of the Phases list.

Insert Inserts a new phase before the currently selected phase.

Remove Removes the currently selected phase from the Phases list.

4.3.4 DSS

The DSS tabsheet contains facilities to define a direct simple-shear test. Beforespecifying the test conditions, a selection can be made between different test options.

DSS — Options

Drained / undrained DSS testIn the latter case, undrained soil conditions and zero drainageare assumed (similar as when the Drainage type has been set toUndrained (A) or Undrained (B), see Section 4.2), irrespective ofthe drainage type setting in the material data set.

Isotropically consolidated / K0-consolidated testIn the latter case the K0-value (ratio of lateral stress over axialstress) can be specified to set the initial stress state.

DSS — Conditions

The following settings can be defined:

|vertical precons. stress|The vertical pre-consolidation pressure to which the soil hasbeen subjected. If the soil is normally consolidated this valueshould be set equal to the initial stress state or kept zero. Fromthe vertical pre-consolidation stress the program calculates theisotropic pre-consolidation stress based on the K nc

0 loading path(see Section 2.8 of the Material Models Manual). This option isonly available for the advanced soil models.

Mobilized relative shear strengthThis option is only available for the Hardening Soil model and HSsmall model to set the initial shear hardening contour. This valuemust be between 0 (isotropic stress state) and 1 (failure state).

Initial stress |σyy | The absolute value of the initial vertical stress at which thesample is consolidated, entered in units of stress. In the case ofan isotropically consolidated test, the initial lateral stress is equalto the initial vertical stress. In the case of a K0-consolidated test,the initial lateral stress is equal to K0σyy .

Time ∆t Time increment (only relevant for time-dependent models;consolidation is not considered).

Number of steps The number of steps that will be used in the calculation.

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Maximum shear strain |γxy |The maximum value of shear strain (entered in %) that will bereached in the last calculation step.

4.3.5 GENERAL

The General tabsheet contains facilities to define arbitrary stress and strain conditions.The following settings can be defined:

Type of test The type of the test, whether Drained or Undrained can bespecified.

|vertical precons. stress|The vertical pre-consolidation pressure to which the soil hasbeen subjected. If the soil is normally consolidated this valueshould be set equal to the initial stress state or kept zero. Fromthe vertical pre-consolidation stress the program calculates theisotropic pre-consolidation stress based on the K nc

0 loading path(see Section 2.8 of the Material Models Manual). This option isonly available for the advanced soil models.

Mobilized relative shear strengthThis option is only available for the Hardening Soil model and HSsmall model to set the initial shear hardening contour. This valuemust be between 0 (isotropic stress state) and 1 (failure state).

Phases Lists the initial stress conditions and the stress/strain conditionsin the subsequent phases of the test. In the initial phase it shouldbe indicated for each direction whether a stress increment or astrain increment is defined for that direction (applies to allphases). Each phase is defined by a Duration (in units of time)and a Number of steps, followed by the applied stress or strainincrements. The given stress or strain increment will be reachedat the end of the given duration in the given number of steps.The input values can be changed by clicking in the table. Anegative stress or strain increment implies additionalcompression, whereas a positive stress or strain incrementimplies unloading or tension.

Add Adds a new phase to the end of the Phases list.

Insert Inserts a new phase before the currently selected phase.

Remove Removes the currently selected phase from the Phases list.

4.3.6 RESULTS

The Results window shows several predefined typical diagrams to display the results ofthe current test. Double-clicking one of the graphs opens the selected diagram in a largerwindow (Figure 4.32). This window shows the selected diagram, the table of the datapoints that are used to plot this diagram as well as the tangent and the secant values ofthe plot. Note that the point to be taken into consideration for the calculation of thetangent and the secant values can be determined by clicking on the plot. Both the

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diagram and the data can be copied to the clipboard using the Copy button on the toolbar.

Figure 4.32 Results diagram

The diagram can be zoomed in or out using the mouse by first clicking and holding theleft mouse button in the diagram area and then moving the mouse to a second locationand releasing the mouse button. Moving the mouse from the left upper corner to the rightlower corner zooms the diagram to the selected area, whereas moving the mouse fromthe right lower corner to the left upper corner resets the view. The zoom action can alsobe undone using the Zoom out option on the toolbar.

The wheel button of the mouse can be used for panning: click and hold the mouse wheeldown and move the diagram to the desired position. When clicking the left mouse buttonon a curve in the diagram, the corresponding secant and tangent line through theselected point are indicated by dashed lines. The corresponding secant and tangentvalues are indicated below the table.

Hint: The failure line is indicated by a dashed line in the plot.» In plots where deviatoric stress q is considered, the failure line is always

shown for the compression point.

4.3.7 PARAMETER OPTIMISATION

The soil test facility can be used to optimise model parameters such that a best fit isobtained between the model results and the results of real soil lab tests. This option canbe selected from the toolbar.

Click the Parameter optimisation button in the toolbar. The Parameter optimisationwindow will appear, showing different colour tabs according to the various steps to

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follow in the parameter optimisation process (Figure 4.33). The first tab (Selectparameters) is active.

Figure 4.33 Parameter optimisation window

Select parameters

The Select parameters tab shows the parameters of the selected material data set thatcould participate in the optimisation process. Click on the square in front of theparameter(s) that need(s) to be optimised (Figure 4.34). The more parameters areselected, the more time the optimisation process will take. For the selected parameters,minimum and maximum values need to be specified. The optimisation algorithm willsearch for optimum values within this range. If the optimised value turns out to be equalto the minimum or maximum value, it might be that the best value lies outside thespecified range.

Note that parameters may influence only specific parts of a test. For example, whenconsidering a triaxial test, the initial part of the test curve is dominated by stiffnessparameters (such as E50), whereas the last part of the curve is dominated by strengthparameters (such as ϕ’). In order to obtain a best fit the optimisation should beperformed in separate runs; one for the stiffness parameter using the initial part of thecurve and one for the strength parameter using the last part of the curve, while fixing thestiffness as the previously optimised value.

Figure 4.34 Selection of the parameters in the Select parameters tabsheet

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Select curves

The Select curves tab enables selection and uploading of real soil lab test data andcorresponding test conditions. Alternatively, synthetic test data may be used in the formof other PLAXIS soil test results. In this way it is possible to optimise, for example,parameters of the Mohr-Coulomb model against simulated tests using the Hardening Soilmodel.

Initially, the window shows a tree with the five standard test types (Triaxial, Oedometer,CRS, DSS and General). For each test type, different test conditions can be defined,which can be taken into account in the optimisation process. By default, the Currentmodel test is available as test conditions for each test type. The Current model testcontains the test conditions as previously defined for that test (Figure 4.35).

Figure 4.35 Selection of the test curves in the Select curves tabsheet

New test conditions can be defined by selecting the New test configuration optionfrom the tool bar. This will introduce Custom # under the selected test, for which the

test conditions can be defined in the right-hand panel (Figure 4.36).

Figure 4.36 Custom test definition in the Select curves tabsheet

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In both cases (Current model test and Custom test) corresponding test data needto be selected and uploaded using the Import curve option. Another possibility is to

upload test conditions together with the test data in case it is stored in the format of aPLAXIS soil test project (<test>.vlt).

Hence, there are different ways to define test conditions and to select the external testdata. The possibilities are summarized below:

• If the test data corresponds to one of the Current model test conditions, thecorresponding line should be selected in the tree and the Import curve option shouldbe used to upload the test data (Figure 4.37). The test data are assumed to bestored in a text file (<data>.txt) and should contain two columns, separated by aSpace, Tab, Comma, Colon (:), Semicolon (;) or arbitrary character. The separator isto be indicated at the top of the Import test data window. The meaning of the valuesin each column has to be selected from the drop down list below the column. Here,a selection can be made amongst various stress and strain quantities. Moreover, thebasic units of the test data quantities need to be selected from the drop down lists inthe Units group. By pressing OK the data is read and visualised in a diagram, andthe curve is listed in the tree under the Current model (test) conditions.

Figure 4.37 Import test data window

• If the test data corresponds to other than one of the current model test conditions,first new Custom test conditions need to be defined. Select the appropriate test typeand click the New test configuration button. The test conditions of the data to beuploaded can be defined in the right-hand panel. Subsequently, the Import curveoption should be used to upload the test data. The test data are assumed to bestored in a text file (<data>.txt) and should contain two columns (see explanationbefore). The meaning of the values in each column has to be selected from the dropdown list below the column. Moreover, the basic units of the test quantities need tobe selected from the drop down lists in the Units group. By pressing OK the data isread and a visualised in a diagram, and the curve is listed in the tree under theCustom (test) conditions (Figure 4.38).

• If the test data together with the test conditions are stored in the format of a PLAXIS

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Figure 4.38 Display of the imported test curves

soil test project (<test>.vlt), the Open file option should be used. After selection of avalid PLAXIS soil test project, the test conditions are listed under the correspondingtest type in the tree, and the available test data curves are listed under the testconditions (Figure 4.39). This option should typically be used to fit current modelparameters to synthetic data previously produced in the PLAXIS soil test facility andstored in <test>.vlt format.

Figure 4.39 Importing data from SoilTest

All test data to be used in the optimisation process need to be selected in the tree byclicking the square in front of the corresponding line (if not already selected). Thecorresponding test conditions are automatically selected.

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Hint: When a line representing test conditions is selected in the tree, thecorresponding test conditions are shown on the panel at the right-hand side.

» When a line representing test data is selected in the tree, the correspondingcurve is visualised in the diagram, and a table of corresponding data points isshown at the right-hand side of the diagram.

» A sub-set of test data to be used in the optimisation process can be selectedin the table at the right-hand side by clicking on the corresponding cells,using the standard multi-select convention (using <Shift> for ranges and<Ctrl> for individual values). The selected values are indicated as ‘thick’ linesin the curve whereas non-selected values are indicated as ‘thin’ lines.

» A line in the tree (either test conditions or test data) can be removed byselecting that line and clicking the red cross in the toolbar.

Multiple phases

In the case of an Oedometer, CRS or General test, the SoilTest facility allows for multiplephases. However, the parameter optimisation facility can only deal with one phase at atime. Therefore, after importing the test data, the desired calculation phase needs to beselected from the drop down list above the test data curve, together with thecorresponding part of the test data in the column at the right-hand side. In this way it ispossible, for example, to optimise a primary loading stiffness against the first (loading)phase in an oedometer test and the unloading stiffness against the second (unloading)phase. Note that this has to be done in two separate optimisation runs.

Settings

The Settings tab enables the accuracy selection of the optimisation process (Figure4.40). Three levels of search intensity are available: Coarse and quick, Moderate,Thorough. In addition, the relative tolerance of the search algorithm can be selected. Thedefault value is 1E-3. Note that a more rigorous optimisation may give more accurateresults, but also requires more calculation time. The calculation time also depends on thenumber of parameters to be optimised, as selected in the first tab.

Figure 4.40 Settings window

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Resulting parameters

The Resulting parameters tab shows the optimum values of the parameters used toobtain the best fit to the selected test data in addition to the minimum and maximumvalues and the reference values in the material data set (Figure 4.41). If the optimumvalue is equal to the minimum or maximum value, it might be that the best value liesoutside the specified range. Finally, the table shows the sensitivity of the selectedparameters. A sensitivity of 100% means that the parameter has a high influence on thesimulated test results, whereas a low sensitivity means that the parameter has a lowinfluence on the simulated test results. Note that a low sensitivity also means that the testmay not be suitable to optimise that parameter and, as a result, the suggested optimumvalue may not be accurate. Therefore it is better to do separate optimisations for differentparameters based on relevant sections of test data curves rather than one optimisationwith multiple parameters based on the full data curves.

Figure 4.41 Resulting parameters window

A button is available to copy the optimised parameters to the material dataset. This should only be done after it has been properly validated that the optimised

parameters are indeed better than the original parameters, considering the use of thematerial data set in the finite element model.

Note that the parameters optimised for soil lab tests may not be the best parameters forthe practical application as considered in the finite element model.

Resulting charts

The Resulting charts tab shows the results of the selected tests (Figure 4.42).

For each test, three curves are visible:

Optimisation target This curve represents the uploaded test data.

Optimisation results This curve represents the simulated test with optimisedparameters.

Reference simulation This curve represents the simulated test with originalparameters. It has no meaning in the optimisation process, butjust shows how good or bad the existing material data set wouldfit the uploaded test data for the selected test conditions withoutoptimisation.

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Figure 4.42 Resulting charts window

Limitations

The Parameter optimisation facility should be used with care. Note that parametersoptimised for soil lab tests may not be the best parameters for the practical application asconsidered in the finite element model. This is because the application may involvestress levels, stress paths and strain levels which might be significantly different from theones that occur in the soil lab tests.

Furthermore, the parameter optimisation facility has the following limitations:

• It is not possible to automatically optimise test data curves that consist of multiplephases (for example loading and unloading phases). Such curves may be uploadedat once, but then individual parts of the curves (phases) need to be selected in orderto perform the optimisation phase by phase.

• The optimisation process itself is a numerical procedure which may involvenumerical errors. The user remains responsible for validating the outcome of theoptimisation process and the use of optimised model parameters in applications.

4.4 MATERIAL DATA SETS FOR PLATES

In addition to material data sets for soil and interfaces, the material properties and modelparameters for plates are also entered in separate material data sets. Plates are used tomodel the behaviour of slender walls, plates or thin shells. Distinction can be madebetween elastic and elastoplastic behaviour. A data set for plates generally represents acertain type of plate material, and can be assigned to the corresponding (group of) plateelements in the geometry model.

4.4.1 MATERIAL SET

Several data sets may be created to distinguish between different types of plates. Figure4.43 shows the Plate window. The material data set is defined by:

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Figure 4.43 Plate window

Identification:A user may specify any identification title for a data set. It is advisable to use ameaningful name since the data set will appear in the database tree view by itsidentification.

Comments:A user may write down comments related to the material data set.

Colour : Colour can be used as a distinction tool in the model.

Material type:There are two available options, describing the material type of a plate. Theseoptions are Elastic and Elastoplastic. The availability of the parameters definedin the Properties box depends on the selected material type.

4.4.2 PROPERTIES

The properties required for plates can be grouped into general properties, stiffnessproperties, strength properties in case of elastoplastic behaviour and dynamic properties.

Isotropic

Different stiffnesses in-plane and out-of-plane may be considered. The latter is mostrelevant for axisymmetric models when modelling sheet pile profiles (which have a lowstiffness in the out-of-plane direction). If this is not the case, the Isotropic option may beselected to ensure that both stiffness are equal.

End bearing of plates

In reality vertical loads on structures, such as walls, are sustained by the shaft frictionand the tip resistance. A certain amount of resistance is offered by the soil under the tip,

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depending on the thickness or the cross section area of the tip.

Slender structures are often modelled as plates. Due to the zero thickness of the plateelements vertical plates (walls) have no end bearing. The effects of the end bearing canstill be considered in the calculation when the corresponding option is selected in thematerial data set. In order to consider the bearing capacity at the bottom of plates, a zonein the soil volume elements surrounding the bottom of the plate is identified where anykind of soil plasticity is excluded (elastic zone). The size of this zone is determined asDeq =

√12EI/EA.

General properties

A plate has two general properties:

d : The (equivalent) thickness (in the unit of length) is automatically calculated fromthe ratio of the axial stiffness EA and flexural rigidity EI (see Stiffness properties).

w : In a material set for plates a specific weight can be specified, which is entered asa force per unit of length per unit width in the out-of-plane direction.

For relatively massive structures the weight of a plate is, in principle, obtained bymultiplying the unit weight of the plate material by the thickness of the plate. Note that ina finite element model, plates are superimposed on a continuum and therefore ‘overlap’the soil. To calculate accurately the total weight of soil and structures in the model, theunit weight of the soil should be subtracted from the unit weight of the plate material. Forsheet-pile walls the weight (force per unit area) is generally provided by the manufacturer.This value can be adopted directly since sheet-pile walls usually occupy relatively littlevolume.

The weight of plates is activated together with the soil weight by means of the ΣMweightparameter.

Stiffness properties

For elastic behaviour, several parameters should be specified as material properties.PLAXIS 2D allows for orthotropic material behaviour in plates, which is defined by thefollowing parameters:

EA: For elastic behaviour an in-plane axial stiffness EA should be specified. For bothaxisymmetric and plane strain models the value relates to a stiffness per unitwidth in the out-of-plane direction.

EA2: For orthotropic elastic behaviour an axial stiffness EA2 should be specifiedwhere 2 indicates the direction out of plane.

EI: For elastic behaviour a flexural rigidity EI should be specified. For bothaxisymmetric and plane strain models the value relates to a stiffness per unitwidth in the out-of-plane direction.

ν (nu): Poisson’s ratio.

From the ratio of EI and EA an equivalent thickness for an equivalent plate (deq) isautomatically calculated from the equation:

deq =√

12EIEA

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For the modelling of plates, PLAXIS uses the Mindlin beam theory as described in Bathe(1982). This means that, in addition to bending, shear deformation is taken into account.The shear stiffness of the plate is determined from:

Shear stiffness =5EA

12(1 + ν)=

5E(deq ·1m

)12(1 + ν)

This implies that the shear stiffness is determined from the assumption that the plate hasa rectangular cross section. In the case of modelling a solid wall, this will give the correctshear deformation. However, in the case of steel profile elements, like sheet-pile walls,the computed shear deformation may be too large. You can check this by judging thevalue of deq . For steel profile elements, deq should be at least of the order of a factor 10times smaller than the length of the plate to ensure negligible shear deformations.

More information about the behaviour and structural forces in plates can be found inSection 15.5 of the Material Models Manual.

In addition to the above stiffness parameters, a Poisson’s ratio, ν, is required. For thinstructures with a certain profile or structures that are relatively flexible in the out-of-planedirection (like sheet-pile walls), it is advisable to set Poisson’s ratio to zero. For realmassive structures (like concrete walls) it is more realistic to enter a true Poisson’s ratioof the order of 0.15.

Since PLAXIS considers plates (extending in the out-of-plane direction) rather thanbeams (one-dimensional structures), the value of Poisson’s ratio will influence the flexuralrigidity of the isotropic plate as follows:

Input value of flexural rigidity: EI

Observed value of flexural rigidity:EI

1− ν2

The stiffening effect of Poisson’s ratio is caused by the stresses in the out-of-planedirection (σzz ) and the fact that strains are prevented in this direction. Note that thePoisson’s ration (ν) is assumed to be zero in anisotropic case.

Strength properties (plasticity)

Strength parameters are required in case of plasticity:

Mp: Maximum bending moment.

Np,1: The maximum force in 1-direction.

Np,2: The maximum force in 2-direction (anisotropic behaviour).

Plasticity may be taken into account by specifying a maximum bending moment, Mp. Themaximum bending moment is given in units of force times length per unit width. Inaddition to the maximum bending moment, the axial force is limited to Np. The maximumaxial force, Np, is specified in units of force per unit width. When the combination of abending moment and an axial force occur in a plate, then the actual bending moment oraxial force at which plasticity occurs is lower than respectively Mp or Np. Moreinformation is given in Section 15.5 of the Material Models Manual.

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The relationship between Mp and Np is visualised in Figure 4.44. The diamond shaperepresents the ultimate combination of forces for which plasticity will occur. Forcecombinations inside the diamond will result in elastic deformations only. The ScientificManual describes in more detail how PLAXIS deals with plasticity in plates.

Bending moments and axial forces are calculated at the stress points of the beamelements (Figure 3.15). If Mp or Np is exceeded, stresses are redistributed according tothe theory of plasticity, so that the maxima are complied with. This will result inirreversible deformations. Output of bending moments and axial forces is given in thenodes, which requires extrapolation of the values at the stress points. Due to the positionof the stress points in a beam element, it is possible that the nodal values of the bendingmoment may slightly exceed Mp. If the Isotropic option is checked the input is limited toNp,1 where as Np,1 =Np,2.

N

M

Np

Np

MpMp

Figure 4.44 Combinations of maximum bending moment and axial force

It is possible to change the material data set of a plate in the framework of stagedconstruction. However, it is very important that the ratio of EI / EA is not changed, sincethis will introduce an out-of-balance force (see Section 3.4.2).

Dynamic properties

For dynamic behaviour, two additional parameters can be specified as materialproperties:

Rayleigh α:Rayleigh damping parameter determining the influence of mass in the dampingof the system.

Rayleigh β:Rayleigh damping parameter determining the influence of the stiffness in thedamping of the system.

For more information on Rayleigh damping, see Page 71.

4.5 MATERIAL DATA SETS FOR GEOGRIDS

In addition to material data sets for soil and interfaces, the material properties and modelparameters for geogrids are also entered in separate material data sets. Geogrids areflexible elastic elements that represent a grid or sheet of fabric. Geogrids cannot sustain

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compressive forces. A data set for geogrids generally represents a certain type ofgeogrid material, and can be assigned to the corresponding (group of) geogrid elementsin the geometry model.

Figure 4.45 Geogrid window

4.5.1 MATERIAL SET

Several data sets may be created to distinguish between different types of geogrids.Figure 4.45 shows the Geogrid window. The material data set is defined by:

Identification:A user may specify any identification title for a data set. It is advisable to use ameaningful name since the data set will appear in the database tree view by itsidentification.

Comments:A user may write down comments related to the material data set.

Colour : Colour can be used as a distinction tool in the model.

Material type:There are two available options, describing the material type of a plate. Theseoptions are Elastic and Elastoplastic. The availability of the parameters definedin the Properties box depends on the selected material type.

4.5.2 PROPERTIES

The properties required for geogrids can be grouped into stiffness properties andstrength properties in case of elastoplastic behaviour.

Isotropic

Different stiffnesses in-plane and out-of-plane may be considered. The latter is mostrelevant for axisymmetric models when modelling geogrids with an anisotropic pattern. If

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this is not the case, the Isotropic option may be selected to ensure that both stiffness areequal.

Stiffness properties

For elastic behaviour, the axial stiffness EA should be specified. PLAXIS 2D allows fororthotropic material behaviour in geogrids, which is defined by the following parameters:

EA1: The normal elastic stiffness in 1-direction (in plane).

EA2: The normal elastic stiffness in 2-direction (out of plane, anisotropic behaviour).

The axial stiffness EA is usually provided by the geogrid manufacturer and can bedetermined from diagrams in which the elongation of the geogrid is plotted against theapplied force in a longitudinal direction. The axial stiffness is the ratio of the axial forceper unit width and the axial strain (∆l/l where ∆l is the elongation and l is the length):

EA =F

∆l/l

If the Isotropic option is checked the input is limited to EA1 where as EA1 =EA2.

Hint: When a material dataset is imported from PLAXIS 2D to PLAXIS 3D thevalue of GA is defined as GA = min (EA1, EA2) / 2.

Strength properties (plasticity)

Strength parameters are required in case of plasticity:

Np,1: The maximum force in 1-direction (in-plane).

Np,2: The maximum force in 2-direction (out of plane, anisotropic behaviour).

The maximum axial tension force Np is specified in units of force per unit width. If Np isexceeded, stresses are redistributed according to the theory of plasticity, so that themaxima are complied with. This will result in irreversible deformations. Output of axialforces is given in the nodes, which requires extrapolation of the values at the stresspoints. Due to the position of the stress points in a geogrid element, it is possible that thenodal values of the axial force may slightly exceed Np.

If the Isotropic option is checked the input is limited to Np, 1 where as Np, 1 =Np, 2.

4.6 MATERIAL DATA SETS FOR EMBEDDED PILE ROWS

Properties and model parameters for embedded pile rows are entered in separatematerial data sets. A data set for embedded piles generally represents a certain type ofpile, including the pile material and geometric properties, the interaction properties withthe surrounding soil (pile bearing capacity) as well as the out of plane spacing of thepiles.

Note that the embedded pile material data set does not contain so-called ‘p-y curves’, norequivalent spring constants. In fact, the stiffness response of an embedded pile

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Figure 4.46 Embedded pile row window

subjected to loading is the result of the specified pile length, equivalent radius, spacing,stiffness, bearing capacity, the stiffness of the interface as well as the stiffness of thesurrounding soil.

Hint: In contrast to what is common in the Finite Element Method, the bearingcapacity of an embedded pile is considered to be an input parameter ratherthan the result of the finite element calculation. The user should realise theimportance of this input parameter. Preferably, the input value of thisparameter should be based on representative pile load test data. Moreover, itis advised to perform a calibration in which the behaviour of the embeddedpile is compared with the behaviour as measured from the pile load test.Since embedded piles are used in a row, the group action must be taken intoaccount when defining the pile bearing capacity.

4.6.1 MATERIAL SET

Several data sets may be created to distinguish between different types of embeddedpiles or pile spacings. Figure 4.46 shows the Embedded pile row window.

The material data set is defined by:

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Identification:A user may specify any identification title for a data set. It is advisable to use ameaningful name since the data set will appear in the database tree view by itsidentification.

Comments:A user may write down comments related to the material data set.

Colour : Colour can be used as a distinction tool in the model.

4.6.2 PROPERTIES

The material properties are defined for a single pile, but the use of PLAXIS 2D impliesthat a row of piles in the out-of-plane direction is considered. The properties required forembedded piles are:

E : Young’s modulus.

γ: Unit weight of the pile material.

Geometric properties

An embedded pile requires several geometric parameters used to calculate additionalproperties:

Pile type:Either a Predefined or a User defined type can be selected.

Predefined pile type:A list of predefined types (Massive circular pile, Circular tube, Massive squarepile).

Diameter :The pile diameter is to be defined for Massive circular pile and Circular tubepredefined pile types. The pile diameter determines the size of the elastic zonein the soil under the pile in which plastic soil behaviour is excluded. It alsoinfluences the default values of the interface stiffness factors (Section 4.6.4).

Width: The pile width is to be defined for a Massive square pile predefined pile type.The pile width is recalculated into an equivalent diameter, Deq =

√12EI/EA.

This diameter determines the size of the elastic zone in the soil under the pile inwhich plastic soil behaviour is excluded. It also influences the default values ofthe interface stiffness factors.

Thickness:The wall thickness needs to be defined for a Circular tube predefined pile type.

Alternatively, a user-defined type may be defined by means of the pile cross section area,A, and its respective moment of inertia I:A: The cross section area is the actual area (in the unit of length squared)

perpendicular to the pile axis where pile material is present. For piles that havea certain profile (such as steel beams), the cross section area can be found intables that are provided by steel factories.

I: Moment of inertia against bending around the pile axis.

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I =1

64πD4 Massive circular pile

I =14π[(

D4

)4 − (D2− t)4] Circular tube

I =1

12h4 Massive square pile

where D is the pile diameter, t is the wall thickness and h is the pile width.

Lspacing :Spacing of the piles in the out-of-plane direction

Dynamic properties

For dynamic behaviour, two additional parameters can be specified as materialproperties:

Rayleigh α:Rayleigh damping parameter determining the influence of mass in the dampingof the system.

Rayleigh β:Rayleigh damping parameter determining the influence of the stiffness in thedamping of the system.

For more information on Rayleigh damping, see Page 71.

4.6.3 INTERACTION PROPERTIES (PILE BEARING CAPACITY)

The interaction between the pile (embedded pile element) and the surrounding soil (soilvolume element) is modelled by means of a special interface element. An elastic-plasticmodel is used to describe the behaviour of the interface. The elastic behaviour of theinterface should account for the difference in pile displacements and average soildisplacements in the out-of-plane direction. This depends on the out-of-plane pilespacing in relation to the pile diameter. Regarding the plastic behaviour distinction ismade in the material data set between the Skin resistance (in the unit of force per unitpile length) and the Base resistance (in the unit of force). In a plane strain analysis, thesevalues are automatically recalculated per unit of width in the out-of-plane direction. Forthe skin resistance as well as the base resistance a failure criterion is used to distinguishbetween elastic interface behaviour and plastic interface behaviour. For elastic behaviourrelatively small displacement differences occur within the interface (i.e. between the pileand the average soil displacement), and for plastic behaviour permanent slip may occur.

For the interface to remain elastic the shear force ts at a particular point is given by:

|ts|< Tmax

where Tmax is the equivalent local skin resistance at that point.

For plastic behaviour the shear force ts is given by:

|ts|= Tmax

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The input for the shaft resistance is defined by means of the skin resistance at the piletop, Ttop,max (in force per unit pile length) and the skin resistance at the pile bottom,Tbot ,max (in force per unit pile length). This way of defining the pile skin resistance ismostly applicable to piles in a homogeneous soil layer. Using this approach the total pilebearing capacity, Npile, is given by:

Npile = Fmax +12

Lpile(Ttop,max + Tbot ,max

)where Lpile is the pile length.

Hint: Note that the length of the embedded pile and the magnitude of the skinresistance increments are inversely proportional.

In addition to the shaft resistance, the embedded pile has extra bearing capacity at thebase. The base resistance Fmax can be entered directly (in the unit of force) in theembedded pile material data set window.

Hint: The base resistance is only mobilized when the pile body moves in thedirection of the base (example: with a load on top).

The pile bearing capacities are automatically divided by the pile spacing in order to obtainthe equivalent bearing capacity per unit of width in the out-of-plane direction.

4.6.4 INTERFACE STIFFNESS FACTOR

The interface stiffnesses are related to the shear stiffness of the surrounding soil (Gsoil )according to:

RS = ISFRSGsoil

Lspacing

RN = ISFRNGsoil

Lspacing

KF = ISFKFGsoilReq

Lspacing

The interface stiffness factors to be defined are:

• Axial skin stiffness factor, ISFRS

• Lateral skin stiffness factor, ISFRN

• Pile base stiffness factor, ISFKF

where the default values of the interface stiffness are calculated according to:

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Figure 4.47 Modelling of soil-pile interaction

ISFRS = 2.5

(Lspacing

Deq

)−0.75

ISFRN = 2.5

(Lspacing

Deq

)−0.75

ISFKF = 25

(Lspacing

Deq

)−0.75

where

Deq =√

12EIEA

In order to ensure that a realistic pile bearing capacity as specified can actually bereached, a zone in the soil volume elements surrounding the bottom of the pile isidentified where any kind of soil plasticity is excluded (elastic zone). The size of this zoneis determined by the embedded pile’s diameter Deq or equivalent radius Req (= Deq/2)(Figure 4.48).

Figure 4.48 Elastic zone surrounding the bottom of the pile (after Sluis (2012))

In addition to displacement differences and shear forces in axial direction along the pile,the pile can undergo transverse forces, t⊥, due to lateral displacements. Thesetransverse forces are not limited in the special interface element that connects the pile

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with the soil, but, in general, they are limited due to failure conditions in the surroundingsoil itself. However, embedded piles are not meant to be used as laterally loaded pilesand will therefore not show accurate failure loads when subjected to transverse forces.

Note that the default values of the interface stiffness factors are valid for bored pileswhich are loaded statically in the axial direction and behaviour of the surrounding soil ismodelled using the HS small model. The phreatic level is assumed to be located at theground surface. These values should be modified if the conditions in the model aredifferent from the ones assumed to derive the default values.

4.7 MATERIAL DATA SETS FOR ANCHORS

In addition to material data sets for soil and interfaces, the material properties and modelparameters for anchors are also entered in separate material data sets. A material dataset for anchors may contain the properties of node-to-node anchors as well as fixed-endanchors. In both cases the anchor is just a spring element. A data set for anchorsgenerally represents a certain type of anchor material, and can be assigned to thecorresponding (group of) anchor elements in the geometry model.

Figure 4.49 Anchor window

4.7.1 MATERIAL SET

Several data sets may be created to distinguish between different types of anchors.Figure 4.49 shows the Anchor window. The material data set is defined by:

Identification:A user may specify any identification title for a data set. It is advisable to use ameaningful name since the data set will appear in the database tree view by itsidentification.

Comments:A user may write down comments related to the material data set.

Colour : Colour can be used as a distinction tool in the model.

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Material type:There are three available options, describing the material type of an anchor.These options are Elastic, Elastoplastic and Elastoplastic with residual strength.The availability of the parameters defined in the Properties box depends on theselected material type.

4.7.2 PROPERTIES

The properties required for anchors can be grouped into stiffness properties and strengthproperties in case of elastoplastic behaviour.

Stiffness properties

An anchor requires only one stiffness parameter:

EA: Axial stiffness, entered per anchor in the unit of force and not per unit width in theout-of-plane direction

To calculate an equivalent stiffness per unit width, the out-of-plane spacing, Ls, must beentered.

Strength parameters (plasticity)

If the material type is selected as Elastoplastic, two maximum anchor forces can beentered:Fmax ,tens:

Maximum tension force

Fmax ,comp:Maximum compression force

The Force-displacement diagram displaying the elastoplastic behaviour of the anchors isgiven in Figure 4.50.

Figure 4.50 The force-displacement diagram displaying the elastoplastic behaviour of anchors

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In the same way as the stiffness, the maximum anchor forces are divided by theout-of-plane spacing in order to obtain the proper maximum force in a plane strainanalysis.

The Elastoplastic with residual strength option can be used to model anchor failure orsoftening behaviour (e.g. buckling of struts). When this option is selected two residualanchor forces can be specified:

Fresidual ,tens:Residual tension force

Fresidual ,comp:Residual compression force

The Force-displacement diagram displaying the elastoplastic behaviour with residualstrength of the anchors is given in Figure 4.51.

Figure 4.51 The force-displacement diagram displaying the elastoplastic behaviour with residualstrength of the anchors

If, during a calculation, the maximum anchor force is reached, the maximum force willimmediately reduce to the residual force. From that point on the anchor force will notexceed the residual force anymore. Even if the anchor force would intermediately reduceto lower values, the defined residual force will be its maximum limit.

Note that if the anchor has failed (in tension, compression or both) the residual force willbe valid in the following calculation phases where the anchor is active. If the anchor isdeactivated in a phase and reactivated in the next phase, the maximum anchor force willbe restored, assuming that the anchor is a completely a new one.

Anchors can be prestressed in a Staged construction calculation. In such a calculationthe prestress force for a certain calculation phase can directly be given in the Anchorwindow. The prestress force is not considered to be a material property and is thereforenot included in an anchor data set.

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4.8 ASSIGNING DATA SETS TO GEOMETRY COMPONENTS

After creating all material data sets for the various soil layers and structures, the data setsmust be assigned to the corresponding components. This can be done in different ways.

The first method is based on an opened Material sets window, showing the createdmaterial sets in the project data base tree view. The desired material set can be dragged(select it and keep the left mouse button down) to the draw area and dropped on thedesired component. It can be seen from the shape of the cursor whether or not it is validto drop the material set. Note that material sets cannot be dragged directly from theglobal data base tree view.

The second method is to double click the desired component. As a result, the Propertieswindow appears on which the material set is indicated. If no material set has beenassigned, the Material set box displays <Unassigned>. When clicking on the Changebutton the Material sets window appears from which the required material set can beselected. The material set can be dragged from the project data base tree view anddropped on the Properties window. Alternatively, after the selection of the requiredmaterial set it can be assigned to the selected geometry component by clicking on theOK button in the Material sets window. In this case, the Material sets window issubsequently closed.

The third method is to move the cursor to a geometry component and to click the righthand mouse button. Through the cursor menu (Properties) one can select the desiredgeometry component. As a result, the Properties window appears. From here theselection of the proper material set is the same as for the second method.

After assigning a material data set to a soil cluster, the cluster obtains the colour of thecorresponding data set. By default, the colours of data sets have a low intensity. Toincrease the intensity of all data set colours, the user may press <Ctrl><Alt><C>simultaneously on the keyboard. There are five levels of colour intensity that can beselected in this way.

When data sets are assigned to structural objects, these objects will blink red for abouthalf a second to confirm the correct data set assignment.

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5 CALCULATIONS

After the generation of a finite element model, the actual finite element calculations canbe executed. Therefore it is necessary to define which types of calculations are to beperformed and which types of loadings or construction stages are to be activated duringthe calculations. This is done in the Calculations program.

PLAXIS 2D allows for different types of finite element calculations. The calculationprocess can be defined in three different modes, the Classical mode, the Advanced modeand the Flow mode (see Section 5.3).

In the engineering practice, a project is divided into project phases. Similarly, acalculation process in PLAXIS is also divided into calculation phases. Examples ofcalculation phases are the activation of a particular loading at a certain time, thesimulation of a construction stage, the introduction of a consolidation period, thecalculation of a safety factor, etc. Each calculation phase is generally divided into anumber of calculation steps. This is necessary because the non-linear behaviour of thesoil requires loadings to be applied in small proportions (called load steps). In mostcases, however, it is sufficient to specify the situation that has to be reached at the end ofa calculation phase. Robust and automatic procedures in PLAXIS will take care of thesub-division into appropriate load steps.

Distinction is made between Plastic, Consolidation, Safety (phi/c reduction), Dynamic,Free vibration, Groundwater flow (steady-state) or Groundwater flow (transient). TheDynamic and Free vibration options require the presence of the PLAXIS Dynamicsmodule, whereas the latter two options require the presence of the PLAXIS PlaxFlowmodule. Both modules are available as extensions to PLAXIS 2D. The first three types ofcalculations (Plastic, Consolidation and Safety) optionally allow for the effects of largedisplacements being taken into account. This is termed Updated mesh, which is availableas an advanced option. The different types of calculations are explained in Section5.5.The first calculation phase (Initial phase) is always a calculation of the initial stressfield for the initial geometry configuration by means of Gravity loading or K0 procedure.After this initial phase, subsequent calculation phases may be defined by the user. Ineach phase, the type of calculation must be selected.

5.1 LAYOUT OF THE CALCULATIONS PROGRAM

This icon represents the Calculations program. The Calculationsprogram contains all facilities to define and start up finite element calculations.

The calculation process can be activated in the Input program by selecting theCalculations mode tab sheet. In this case, the current project is automatically selected inthe Calculations program. Alternatively, the Calculations program can be run by clickingthe program icon. As a result, the general file requester appears which enables the userto browse through all available directories and to select the desired PLAXIS project file(*.P2D). In this case, the user has to select the project for which calculations are to bedefined. The selection window allows for a quick selection of one of the fifteen mostrecent projects. If a project that does not appear in the list is to be selected, the optionOpen an existing project can be used.

After the selection of a project, the main window of the Calculations program appears,

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which contains the following items (Figure 5.1).

Figure 5.1 Main window of the Calculations program

Title bar

The name of the program and the title of the project is displayed in the title bar. Unsavedmodifications in the project are indicated by a ‘∗’ in the project name.

Menu bar

The menus in the menu bar contain all operation facilities of the Calculations program.Most options are also available as buttons in the toolbar.

Toolbar

The toolbar contains buttons that may be used as a shortcut to menu facilities. Themeaning of a particular button is presented after the pointer is positioned above thebutton.

Open project.

Save project.

Print the information displayed in the phases list.

Select points for curves.

Calculate the phases market for calculation.

Display the results of the selected phase.

Indication of the current calculation mode. Clicking the button activates the Selectcalculation mode window.

Tabsheets

The tabsheets are used to define and preview a calculation phase (see Section 5.4 andfurther). Switching between tabsheets can be done by clicking the corresponding tab.

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Phases list

This list gives an overview of all calculation phases of a project. Each line corresponds toa separate phase.

Identification ID of the phase as defined in the General tabsheet.

Phase no. Number of the calculation phase. Phases are numberedsuccessively by the program.

Start from Number of the parent phase the current phase starts from.

Calculation The calculation type of the phase as defined in the Generaltabsheet.

Loading input The loading input as defined in the Parameters tabsheet.

Pore pressure The pore pressure generation option as defined in the Waterconditions tabsheet in the Staged construction.

Time Time interval of the calculation phase.

Stage Indication of the binary file extension where stage information isstored.

Water Indication of the binary file extension where the informationabout the water conditions of the calculation phase is stored.

First The number of the first calculation step of the phase.

Last The number of the last calculation step of the phase.

Design approach The design approach considered when the phase is calculated.

Hint: If the phase has not yet been executed, the step numbers will be blank.

The status of the calculation phases is indicated by a mark at the left of the phase ID.

The phase is to be calculated.

The phase is not to be calculated.

The phase was calculated. No error occurred during calculation.

Calculation failed. Information is provided in the Log info box in the Generaltabsheet of the Phases window.

Calculation failed however the calculation of the child phases is possible.Information is provided in the Log info box in the General tabsheet of the Phaseswindow. Note that the calculation of the child phase will not start automatically.

Calculation is correct but there are additional non-crucial modifications required.The next calculation must be a Staged construction calculation.

5.2 MENUS IN THE MENU BAR

The menu bar of the Calculations program contains pull-down menus covering mostoptions for handling files, defining calculation phases and executing calculations. The

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Calculations menu consists of the menus File, Edit, Tools, Calculate and Help.

File menu

Open To open a project for which calculation phases have to bedefined. The file requester is presented.

Save To save the current status of the calculations list.

Save as To save the current status of the calculations list under a differentname.

Print To print the list of calculations phases.

Pack project To compress the current project.

Recent projects To quickly open one of the fifteen most recent projects.

Exit To leave the program.

Edit menu

Next phase To focus on the next phase in the calculations list. If the nextphase does not exist, a new calculation phase is introduced.

Insert phase To insert a new calculation phase at the position of the currentlyfocused phase.

Delete phase (s) To erase the selected calculation phase or phases.

Copy to clipboard To copy the list of calculation phases to the clipboard.

Select all To select all calculation phases.

Tools menu

Select points for curves To select nodes and stress points for the generation ofload-displacement curves and stress paths.

Calculation mode To select the calculation mode in which the calculation processwill be defined (Section 5.3).

Calculate menu

Current project To start up the calculation process of the current project.

Multiple projects To select a project for which the calculation process has to bestarted. The file requester is presented. After selection of aproject, the project is added to the calculation manager window.

Sensitivity To perform Sensitivity analysis.

Parameter variation To perform Parameter variation analysis.

Help menu

Manuals To display the manuals.

Update license To update the PLAXIS 2D license via e-mail.

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http://www.plaxis.nl/ To reach the PLAXIS website.

Disclaimer The complete disclaimer text is displayed.

About Information about the program version and license are displayed.

5.3 CALCULATION MODES

The calculation process definition depends on the selected calculation mode. When aproject is opened in the Calculation program for the first time, the Select calculation modewindow will automatically be shown (see Figure 5.2). In this window one of the threemodes Classical mode, Advanced mode or Flow mode can be selected and a shortdescription of each calculation mode is given. In addition, the Select calculation modewindow can be opened by selecting the option Calculation mode in the Tools menu or byclicking the corresponding button in the toolbar. A description of all three modes is givennext.

Figure 5.2 Select calculation mode window

5.3.1 CLASSICAL MODE

This is the default mode which uses Terzaghi’s definition of stress and is very similar tothe old PLAXIS 2D versions. Old projects can be modelled in this mode.

In this mode, pore pressures are divided into steady-state pore pressures and excesspore pressures. Steady-state pore pressures are input data, i.e. generated based onphreatic levels or groundwater flow. Excess pore pressures are generated in undrainedmaterial during plastic calculations or consolidation analyses. The weight of the soil iscalculated according to its position compared to the phreatic level: the saturated weight ofthe soil, γsat , is used in case the soil is below the phreatic level and the unsaturatedweight of the soil, γunsat , is used in case the soil is above the phreatic level.

The types of calculations which can be performed in this mode are:

• Plastic

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• Consolidation based on excess pore pressure

• Safety

• Dynamic (available in Dynamics module of PLAXIS 2D )

• Free vibration (available in Dynamics module of PLAXIS 2D )

5.3.2 ADVANCED MODE

This mode uses Bishop’s definition of stress instead of Terzaghi’s stress and is suitablefor calculating unsaturated response of soils and for performing fully coupledhydro-mechanical behaviour of soils. Bishop’s stress is defined by:

σ = σ’ + Se · σw

in which Se is the effective degree of saturation. The effective degree of saturationdepends on the suction pore pressure and this relationship is known as the Soil WaterCharacteristic Curve (SWCC). The options Van Genuchten, Approximated VanGenuchten and User defined are available in PLAXIS 2D to describe the Soil WaterCharacteristic Curve. Note that in the partially saturated zone, effective stresses maychange by changing SWCC parameters. This causes a difference in the results obtainedin the Advanced mode compared to the results obtained in the Classical mode whencalculating the same project. Therefore, it is strongly recommended to select propervalues for SWCC.

The weight of the soil is defined as:

γ = (1− Se) · γunsat + Se · γsat

where γsat and γunsat are the saturated and unsaturated weight of the soil, respectively.

The types of calculations which can be done in this mode are:

• Plastic

• Consolidation based on total pore pressure

• Safety

• Dynamic (available in Dynamics module of PLAXIS 2D )

• Free vibration (available in Dynamics module of PLAXIS 2D )

5.3.3 FLOW MODE

In this calculation mode pure groundwater flow calculations under saturated andunsaturated conditions can be performed.

The types of calculations in this mode are:

• Groundwater flow (steady-state)

• Groundwater flow (transient)

The first calculation phase is always a steady-state calculation. Subsequent phases are,by default, transient calculations, but they may also be steady-state. For furtherinformation about the Groundwater flow calculations, Consolidation, undrained behaviour

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and unsaturated modelling, see Galavi (2010).

5.4 DEFINING CALCULATION PHASES

Finite element calculations can be divided into several sequential calculation phases.Each calculation phase corresponds to a particular loading or construction stage.Consider a new project for which no calculation phase has yet been defined. In this case,the calculations list contains only one line, indicated as ‘Initial phase’ with phase number0. This line represents the initial situation of the project. The ‘Initial phase’ is the startingpoint for further calculations.

To introduce the first calculation phase for the current project, the Next button just abovethe calculations list should be clicked after which a new line appears. Alternatively, theNext phase option may be selected from the Edit menu. After the introduction of the newcalculation phase, the phase has to be defined. This should be done using the General,Parameters and Multipliers tabsheets. On pressing the <Enter> or <Tab> key after eachinput parameter, the user is guided through all parameters. Most parameters have adefault setting, which simplifies the input. In general, only a few parameters have to beconsidered to define a calculation phase. More details on the various parameters aregiven in the following sections.

When all parameters have been set, the user can choose to define another calculationphase or to start the calculation process. Introducing and defining another calculationphase can be done in the same way as described above.

The calculation process can be started by clicking the Calculate button in the toolbar or, alternatively, by selecting the Current project option in the Calculate menu. It

is not necessary to define all calculation phases before starting the calculation processsince the program allows for defining new calculation phases after previous phases havebeen calculated.

5.4.1 CALCULATION TABSHEETS

The Calculation program consists of four tabsheets to define and preview a calculationphase. These tabsheets are listed below.

General tabsheet

The General tabsheet is used to define the general settings of a particular calculationphase (Figure 5.1).

Phase: The items in the Phase group box can be used to identify the calculation phaseand, more importantly, to determine the ordering of calculation phases by selecting thecalculation phase that is used as a starting point for the current calculation (Section5.4.3).

Calculation type: The selections made in the Calculation type group determine the typeof calculation that is used (Section 5.5); the options in the drop-down menu depend onthe active calculation mode (Section 5.3). Clicking the Comments button will open theComments window in which any information related to a particular calculation phase canbe stored.

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Log info: The Log info box displays messages generated during the finite elementcalculation and is used for logging purposes.

Remarks: The Remarks box displays messages that give information about the selectedcalculation type.

Parameters tabsheet

The Parameters tabsheet is used to define the control parameters of a particular phaseand the corresponding solution procedure (see Section 5.7).

Multipliers tabsheet

The Multipliers tabsheet is used to define the multipliers of a particular phase. The valuesin this tabsheet can only be modified when either the option Incremental multipliers orTotal multipliers is selected as Loading input (see Section 5.11).

Preview tabsheet

The Preview tabsheet is used to take a look at the preview of a particular phase.

5.4.2 INSERTING AND DELETING CALCULATION PHASES

In general, a new calculation phase is defined at the end of the calculation list using theNext button. It is possible, however, to insert a new phase between two existing phases.This is done by clicking the Insert button while the line where the new phase is to beinserted is focused. By default, the new phase will start from the results of the previousphase in the list, as indicated by the Start from phase value. This means that the statusof active clusters, structural objects, loads, water conditions and multipliers is adoptedfrom the previous phase.

Hint: When inserting and deleting calculation phases note that the start conditionsfor the subsequent phases will change and must again be specified manually.

The user has to define the settings for the inserted phase in a similar way as defining anew phase at the end of the calculations list.

The next phase, which originally started from a previous phase, will keep the existingStart from phase value and will thus not start automatically from the inserted phase. If itis desired that the next phase starts from the inserted phase then this should be specifiedmanually by changing the Start from phase parameter. In this case it is required that thenext phase is fully redefined, since the start conditions have changed. This may alsohave consequences for the phases thereafter.

Besides inserting calculation phases it is also possible to delete phases. This is done byselecting the phase to be deleted and clicking on the Delete button. Before deleting aphase it should be checked which of the subsequent phases refer to the phase to bedeleted in the Start from column. After confirmation of the delete operation, all phases ofwhich the Start from phase value referred to the deleted phase will be modifiedautomatically such that they now refer to the predecessor of the deleted phase.

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Nevertheless, it is required that the modified phases are redefined, since the startconditions have changed.

5.4.3 PHASE IDENTIFICATION AND ORDENING

The Phase group in the General tabsheet shows the phase number and an identificationstring of the current calculation phase. PLAXIS automatically assigns a number to eachcalculation phase which cannot be changed by the user. The identification string is, bydefault, set to <Phase #>, where # is the phase number, but this string may be changedby the user to give it a more appropriate name. The identification string and phasenumber appear in the list of calculation phases at the lower part of the window.

In addition, the Start from phase parameter must be selected from the drop-down menuin the Phase group. This parameter refers to the phase from which the current calculationphase should start (this is termed the reference phase). By default, the previous phase isselected here, but, if more calculation phases have already been defined, the referencephase may also be an earlier phase. A phase that appears later in the calculation listcannot be selected.

Special cases

In some special cases, the order of calculation phases is not straightforward. Examplesof some cases are:

• The Initial phase may be selected as reference if different loadings or loadingsequences are to be considered separately for the same project.

• For a certain situation, a load is increased until failure to determine the safetymargin. When continuing the construction process, the next phase should start fromthe previous construction stage rather than from the failure situation.

• A third example where the phase ordering is not straightforward is in calculationswhere safety analysis for intermediate construction stages is considered. Thecalculation type in this case is Safety. In general, such a phase results in a state offailure. When continuing the construction process, the next stage should start fromthe previous phase rather than from the results of the safety analysis. Alternatively,safety analyses for the various construction stages can be performed at the end ofthe calculation process. In that case, the reference phase selected in the Start fromphase drop-down menu should refer to the corresponding construction stage.

In the Phases window, users need to select at least the Calculation type and the Loadingtype for each new phase. PLAXIS provides convenient default values for most calculationcontrol parameters, but the user can change these values. A description of thecalculation types and control parameters is given in the next section.

5.5 TYPES OF ANALYSIS

The first step in a PLAXIS analysis is defining a calculation type of a phase in theCalculation type drop-down menu in the Phases window. The options available are K0procedure and Gravity loading for the initial phase, and Plastic, Consolidation, Safety andDynamic for other phases.

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The calculation types available depend on the program modules available and on theselected calculation mode. For the sake of completeness, all possible calculation typesavailable in PLAXIS will be discussed.

5.5.1 INITIAL STRESS GENERATION

Many analysis problems in geotechnical engineering require the specification of a set ofinitial stresses. The initial stresses in a soil body are influenced by the weight of thematerial and the history of its formation. This stress state is usually characterised by aninitial vertical effective stress (σ’v ,0). The initial horizontal effective stress σ’h,0 is relatedto the initial vertical effective stress by the coefficient of lateral earth pressure K0(σ’h,0 = K0 · σ’v ,0).

In PLAXIS, initial stresses may be generated by using the K0 procedure or by usingGravity loading. Note that these options are available in the Calculation type drop-downmenu only for the Initial phase. It is recommended to generate and inspect results frominitial stresses first before defining and executing other calculation phases.

Hint: As a rule, one should use the K0 procedure only in cases with a horizontalsurface and with all soil layers and phreatic levels parallel to the surface. Forall other cases, Gravity loading should be used.

Examples of non-horizontal surfaces, and non-horizontal weight stratifications are:

K0 procedure

K0 procedure is a special calculation method available in PLAXIS to define the initialstresses for the model, taking into account the loading history of the soil. The parametersrequired in the initial stresses development procedures are defined in the Initial tabsheetof material data sets for soil and interfaces (Section 4.1.5).

Only one K0 value can be specified:

K0,x = σ’xx/σ’yy K0,z = σ’zz/σ’yy = K0,x

In practice, the value of K0 for a normally consolidated soil is often assumed to be relatedto the friction angle by Jaky’s empirical expression:

K0 = 1− sinϕ

In an over-consolidated soil, K0 would be expected to be larger than the value given bythis expression.

For the Mohr-Coulomb model, the default value K0-value is based on Jaky’s formula. Forthe advanced models, (Hardening Soil model, Hardening Soil model with small-strainstiffness, Soft Soil model, Soft Soil Creep model, Modified Cam-Clay model,

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Sekiguchi-Ohta model), the default value is based on the K nc0 parameter and is also

influenced by the overconsolidation ratio (OCR) or the pre-overburden pressure (POP)(see Section 4.1.5 and the Material Models Manual for more information):

K0,x = K nc0 OCR− νur

1− νur(OCR− 1)+

K nc0 POP− νur

1− νurPOP∣∣σ0

yy

∣∣Using very low or very high K0-values in the K0 procedure may lead to stresses thatviolate the Mohr-Coulomb failure condition. In this case PLAXIS automatically reducesthe lateral stresses such that the failure condition is obeyed. Hence, these stress pointsare in a plastic state and are thus indicated as plastic points. Although the correctedstress state obeys the failure condition, it may result in a stress field which is not inequilibrium. It is generally preferable to generate an initial stress field that does notcontain Mohr-Coulomb plastic points.

Hint: The plot of plastic points may be viewed after the presentation of the initialeffective stresses in the Output program by selecting the Plastic points optionfrom the Stresses menu (see Section 7.3.8).

For a cohesionless material it can easily be shown that to avoid Mohr-Coulomb plasticity,the value of K0 is bounded by:

1− sinϕ1 + sinϕ

< K0 <1 + sinϕ1− sinϕ

When the K0 procedure is adopted, PLAXIS will generate vertical stresses that are inequilibrium with the self-weight of the soil. Horizontal stresses, however, are calculatedfrom the specified value of K0. Even if the value of K0 is chosen such that plasticity doesnot occur, the K0 procedure does not ensure that the complete stress field is inequilibrium. Full equilibrium is only obtained for a horizontal soil surface with any soillayers parallel to this surface and a horizontal phreatic level. If the stress field requiresonly small equilibrium corrections, then these may be carried out using the calculationprocedures described below. If the stresses are substantially out of equilibrium, then theK0 procedure should be abandoned in favor of the Gravity loading procedure.

At the end of the K0 procedure, the full soil is weight activated. The soil weight can not bechanged in any other calculation phase.

Gravity loading

Gravity loading is a type of Plastic calculation (Section 5.5.2), in which initial stresses aregenerated based on the volumetric weight of the soil. If Gravity loading is adopted, thenthe initial stresses are set up by applying the soil self-weight in the first calculation phase.In this case, when using an elastic perfectly-plastic soil model such as the Mohr-Coulombmodel, the ratio of horizontal effective stress over vertical effective stress, K0, dependsstrongly on the assumed values of Poisson’s ratio. It is important to choose values ofPoisson’s ratio that give realistic values of K0. If necessary, separate material data setsmay be used with Poisson’s ratio adjusted to provide the proper K0-value during gravity

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loading. These sets may be changed by other material sets in subsequent calculations(Section 5.8.5). For one-dimensional compression an elastic computation will give:

K0 =ν

(1− ν)

If a value of K0 of 0.5 is required, for example, then it is necessary to specify a value ofPoisson’s ratio of 0.333. As Poisson’s ratio must be lower than 0.5, it is notstraightforward to generate K0 values larger than 1 using Gravity loading. If K0 valueslarger than 1 are desired, it is necessary to simulate the loading history and use differentPoisson’s ratio for loading and unloading or use the K0 procedure.

When advanced soil models are used, the resulting K0-value after gravity loadingcorresponds to the K nc

0 in the material data set.

Hint: To make sure that Gravity loading results in initial effective stresses insituations where undrained materials are used, the parameter Ignoreundrained behaviour should be selected.

» Once the initial stresses have been set up using Gravity loading, thedisplacements should be reset to zero at the start of the next calculationphase. This removes the effect of the initial stress generation procedure onthe displacements developed during subsequent calculations, whereas thestresses remain.

In some cases plastic points will be generated during the Gravity loading procedure. Forcohesionless soils in one-dimensional compression, for example, plastic Mohr-Coulombpoints will be generated unless the following inequality is satisfied:

1− sinϕ1 + sinϕ

<ν

1− ν< 1

Results of initial stress generation

After the generation of initial stresses the plot of the initial effective stresses can beinspected (Section 6.3.1). It is also useful to view the plot of plastic points.

Using K0 values that differ substantially from unity may sometimes lead to an initial stressstate that violates the Mohr-Coulomb criterion. If the plot of the plastic points shows manyred plastic points (Mohr-Coulomb points), the value of K0 should be chosen closer to 1.0.

If there are a small number of plastic points, it is advisable to perform a plastic nil-step.When using the Hardening Soil model and defining a normally consolidated initial stressstate (OCR = 1.0 and POP = 0.0), the plot of plastic points shows many hardening points.Users need not be concerned about these plastic points as they just indicate a normallyconsolidated stress state.

Plastic nil-step

If the K0 procedure generates an initial stress field that is not in equilibrium or whereMohr-Coulomb plastic points occur, then a plastic nil-step should be adopted. A plasticnil-step is a plastic calculation step in which no additional load is applied (Section 5.5.10).

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After this step has been completed, the stress field will be in equilibrium and all stresseswill obey the failure condition.

If the original K0 procedure generates a stress field that is far from equilibrium, then theplastic nil-step may fail to converge. This happens, for example, when the K0 procedureis applied to problems with very steep slopes. For these problems, the Gravity loadingprocedure should be adopted.

It is important to ensure that displacements calculated during a plastic nil-step (if it isapplied immediately after generating the initial stresses) do not affect later calculations.This is achieved by selecting the Reset displacements to zero parameter in thesubsequent calculation phase (Section 5.7.4).

5.5.2 PLASTIC CALCULATION

A Plastic calculation is used to carry out an elastic-plastic deformation analysis in which itis not necessary to take the decay of excess pore pressure with time into account. If theUpdated mesh parameter has not been selected, the calculation is performed accordingto the small deformation theory. The stiffness matrix in a normal plastic calculation isbased on the original undeformed geometry. This type of calculation is appropriate inmost practical geotechnical applications.

Although a time interval can be specified, a plastic calculation does not take time effectsinto account, except when the Soft Soil Creep model is used (see Material ModelsManual). Considering the quick loading of saturated clay-type soils, a Plastic calculationmay be used for the limiting case of fully undrained behaviour using the Undrained (A),Undrained (B) or Undrained (C) option in the material data sets. On the other hand,performing a fully drained analysis can assess the settlements on the long term. This willgive a reasonably accurate prediction of the final situation, although the precise loadinghistory is not followed and the process of consolidation is not dealt with explicitly.

An elastic-plastic deformation analysis where undrained behaviour (Undrained (A) orUndrained (B)) is temporarily ignored can be defined by checking the Ignore undr.behaviour (A, B) parameter. In this case the stiffness of water is not taken into account.

Note that Ignore undrained behaviour does not affect materials of which the drainagetype is set to Undrained (C).

When changing the geometry configuration (Section 5.8) it is also possible (for eachcalculation phase) to redefine the water boundary conditions and recalculate the porepressures (Section 5.9). For more details on theoretical formulations of a plasticcalculation reference should be made to the Scientific Manual.

5.5.3 CONSOLIDATION CALCULATION IN CLASSICAL MODE

A Consolidation calculation in the Classical mode is usually conducted when it isnecessary to analyse the development and dissipation of excess pore pressures in asaturated clay-type soil as a function of time. PLAXIS allows for true elastic-plasticconsolidation analysis. In general, consolidation analysis without additional loading isperformed after an undrained plastic calculation. It is also possible to apply loads duringa consolidation analysis. However, care should be taken when a failure situation isapproached, since the iteration process may not converge in such a situation.

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A consolidation analysis requires additional boundary conditions on excess porepressures (Section 5.9).

Hint: In PLAXIS, total pore pressures are divided into steady-state pore pressuresand excess pore pressures. Steady state pore pressures are generatedaccording to the water conditions assigned to the soil layers for each phase,whereas excess pore pressures are calculated as a result of undrained soilbehaviour (Undrained (A) or Undrained (B)) or consolidation. A Consolidationcalculation in Classical mode in PLAXIS only affects the excess porepressures.

» A Consolidation calculation in Classical mode does not affect Undrained (C)materials.

5.5.4 CONSOLIDATION CALCULATION IN ADVANCED MODE

A Consolidation analysis in Advanced mode is a more general formulation of theConsolidation analysis in Classical mode, based on Biot’s theory of consolidation whichenables the user to simultaneously calculate deformation and groundwater flow withtime-dependent boundary conditions in saturated and partially saturated soils. In thistype of calculation, no distinction between the steady-state and the excess porepressures is made and the resulting pore pressure is the active pore pressure. In caseswhere the stationary pore pressure is unknown at the beginning of the calculation stage(e.g. undrained excavation with dewatering or simulation of wave loading in off-shoreconditions), this type of calculation can be used. For more details see Galavi (2010).

5.5.5 SAFETY CALCULATION (PHI/C REDUCTION)

The Safety calculation type is an option available in PLAXIS to compute global safetyfactors. This option can be selected as a separate Calculation type in the Generaltabsheet.

In the Safety approach the strength parameters tan ϕ and c of the soil are successivelyreduced until failure of the structure occurs. The dilatancy angle ψ is, in principle, notaffected by the phi/c reduction procedure. However, the dilatancy angle can never belarger than the friction angle. When the friction angle ϕ has reduced so much that itbecomes equal to the (given) dilatancy angle, any further reduction of the friction anglewill lead to the same reduction of the dilatancy angle. The strength of interfaces, if used,is reduced in the same way. The strength of structural objects like plates and anchors isnot influenced by a Safety (phi/c reduction) calculation.

The total multiplier ΣMsf is used to define the value of the soil strength parameters at agiven stage in the analysis:

ΣMsf =tanϕinput

tanϕreduced=

cinput

creduced=

su,input

su,reduced

where the strength parameters with the subscript ‘input’ refer to the properties entered inthe material sets and parameters with the subscript ‘reduced’ refer to the reduced valuesused in the analysis. ΣMsf is set to 1.0 at the start of a calculation to set all material

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strengths to their input values.

A Safety calculation is performed using the Load advancement number of stepsprocedure (Section 5.6.3). The incremental multiplier Msf is used to specify the incrementof the strength reduction of the first calculation step. This increment is by default set to0.1, which is generally found to be a good starting value. The strength parameters aresuccessively reduced automatically until all Additional steps have been performed. Bydefault, the number of additional steps is set to 100, but a larger value up to 10000 maybe given here, if necessary. It must always be checked whether the final step has resultedin a fully developed failure mechanism. If that is the case, the factor of safety is given by:

SF =available strengthstrength at failure

= value of ΣMsf at failure

The ΣMsf -value of a particular calculation step can be found in the Calculationinformation window displayed as the corresponding option is selected in the Projectmenu of the Output program. It is also recommended to view the development of ΣMsffor the whole calculation using the Curves option (Chapter 8.2). In this way it can bechecked whether a constant value is obtained while the deformation is continuing; inother words: whether a failure mechanism has fully developed. If a failure mechanismhas not fully developed, then the calculation must be repeated with a larger number ofadditional steps.

To capture the failure of the structure accurately, the use of Arc-length control parameteris required. The use of a Tolerated error of no more than 1% is also required. Bothrequirements are complied with when using the default iteration parameters (Section5.7.1.)

Hint: When performing Safety calculation without Arc-length control, the reductionfactor ΣMsf cannot go down and an overestimation of safety factor can occur.

When using Safety calculation in combination with advanced soil models, these modelswill actually behave as a standard Mohr-Coulomb model, since stress-dependentstiffness behaviour and hardening effects are excluded from the analysis. In that case,the stiffness is calculated at the beginning of the calculation phase based on the startingstresses and kept constant until the calculation phase is completed. Note that when usingthe Modified Cam-Clay model and Sekiguchi-Ohta model, the strength is not reduced atall since these models do not have a cohesion or friction angle as model parameter.

Hint: In case of the Jointed Rock model the strength on all the planes will bereduced by ΣMsf.

» In the case of the NGI-ADP model all undrained parameters are reduced bythe ΣMsf .

» Strength in the Modified Cam-Clay model and Sekiguchi-Ohta model is notreduced in Safety analysis.

» When using Safety analysis in combination with user-defined soil models,none of the parameters of these models will be reduced.

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The Safety approach resembles the method of calculating safety factors asconventionally adopted in slip-circle analysis. For a more detailed description of themethod of Safety you are referred to Brinkgreve & Bakker (1991).

Hint: Due to the use of suction in the Advanced mode, a more realistic value of thesafety factor will be obtained. This value is generally higher than aconventional safety factor ignoring suction. Therefore, care should be takenwhen interpreting this value. It is possible to ignore suction in the Advancedmode by performing a plastic nil-step and using the Pore pressure tensioncut-off before running the Safety analysis.

Strength factorization in the Hoek-Brown model

When using the Hoek-Brown model to describe the behaviour of a rock section, theSafety analysis procedure is slightly modified, since the failure contour is not describedby the Mohr-Coulomb criterion anymore. In order to have an equivalent definition of asafety factor as for the Mohr-Coulomb model, the Hoek-Brown yield function isreformulated to include the strength reduction factor ΣMsf for safety analyses:

fHB = σ’1 − σ’3 + f red (σ’3)

with

f red =fη

=σci

η

(mb−σ’3σci

+ s)

a

and

η =12

∑

Msf(

2− f ‘)√√√√√√√√1 +

1∑Msf 2

− 1

f ‘2

(2− f ‘

)2

+ f ‘

where

f ‘ =∂f∂σ’3

= −amb

(mb−σ’3σci

+ s)

a−1

More details and a derivation of the above equations can be found in Benz, Schwab,Vermeer & Kauther (2007).

Updated mesh

The geometry of the model considered in a Safety calculation depends on whether theUpdated mesh option is selected or not in the parent phase. If the mesh is updated, theresulting geometry at the end of the parent phase will be considered in the safety

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calculations.

During a safety calculation the mesh is not updated at the beginning of each load stepeven if the Updated mesh option is selected for the Safety phase.

5.5.6 DYNAMIC CALCULATION

The Dynamic option should be selected when it is necessary to consider stress wavesand vibrations in the soil. With PLAXIS 2D it is possible to perform a dynamic analysisafter a series of plastic calculations.

Hint: It is not possible to use updated mesh in a dynamic analysis.» It is not possible to use staged construction type of loading for a dynamic

calculation.

In the Calculation program, dynamic loads are treated in a different way than static loads.The input value of a dynamic load is usually set to a unit value, whereas dynamicmultipliers in the Calculation program are used to scale the loads to their actualmagnitudes (Section 5.7.3). The applied dynamic load is the product of the input valueand the corresponding dynamic load multiplier. This principle is valid for both static anddynamic loads. However, static loads are applied generally in Staged Construction byactivating the load or changing the input value (whilst the corresponding load multiplier isusually equal to 1), whereas dynamic loads are applied in the Dynamic load multiplierinput window by specifying the variation of the corresponding load multiplier with time(whilst the input value of the load is a unit value and the load is active).

The procedure to apply dynamic loads is summarised below:

• Create loads in the Input program (point loads, distributed loads in load system A orB, and/or prescribed displacements).

• Set the appropriate load system as a dynamic load system in the Loads menu of theInput program.

• Activate the dynamic loads by entering the dynamic load multipliers in the Dynamicload multipliers input window of the Calculation program.

5.5.7 FREE VIBRATION

Free vibration is a type of dynamic calculation in which a previously activated externalload is released, as a result of which the system starts to vibrate. This type of calculationis only available after a plastic or consolidation type of calculation in which a staticexternal load was applied. The external load should be released via the Loading type inthe Parameter tabsheet of the Calculation program.

5.5.8 GROUNDWATER FLOW (STEADY-STATE)

Groundwater flow (steady-state) is an analysis in which the pore water pressure at anypoint in the geometry remains constant with time. A Groundwater flow (steady-state)calculation can be considered to set up an situation of groundwater flow or to evaluatesteady-state conditions where time tends to go to infinity. Note that this option is only

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available in the Flow calculation mode.

5.5.9 GROUNDWATER FLOW (TRANSIENT)

In contrast to a steady-state groundwater flow calculation, the pore pressures and waterconditions may change with time during Groundwater flow (transient) analyses. Timedependent boundary conditions are available for this type of calculation. Note that thisoption is only available in the Flow calculation mode.

5.5.10 PLASTIC NIL-STEP

A plastic calculation may also be used to carry out a so-called plastic nil-step. A plasticnil-step is a plastic calculation phase in which no additional loading is applied. Each newphase introduced in the Phases explorer is initially a plastic nil-step, until the calculationtype, geometry or load configuration is changed. It may sometimes be required to solvelarge out-of-balance forces and to restore equilibrium. Such a situation can occur after acalculation phase in which large loadings were activated (for example gravity loading) or ifthe K0 procedure generates an initial stress field that is not in equilibrium or where plasticpoints occur. After this step has been completed, the stress field will be in equilibrium andall stresses will obey the failure condition. In this case no changes should be made to thegeometry configuration or to the water conditions. If necessary, such a calculation can beperformed with a reduced Tolerated error to increase the accuracy of the equilibriumstress field.

If the original K0 procedure generates a stress field that is far from equilibrium, then theplastic nil-step may fail to converge. This happens, for example, when the K0 procedureis applied to problems with very steep slopes. For these problems the Gravity loadingprocedure should be adopted instead.

It is important to ensure that displacements calculated during a plastic nil-step (if it isused applied immediately after generating the initial stresses) do not affect latercalculations. This may be achieved by using the Reset displacements to zero option inthe subsequent calculation phase (Section 5.7.4).

The Staged construction loading type is used to perform plastic nil-stepsto solve existing out-of-balance forces. No changes in the geometry, load level, load

configuration and water pressure distribution should be made.

5.5.11 UPDATED MESH ANALYSIS

In conventional finite element analysis, the influence of the geometry change of the meshon the equilibrium conditions is neglected. This is usually a good approximation when thedeformations are relatively small as is the case for most engineering structures. However,there are circumstances under which it is necessary to take this influence into account.Typical applications where updated mesh analyses may be necessary include theanalysis of reinforced soil structures, the analysis of large offshore footing collapseproblems and the study of problems where soils are soft and large deformations occur.

When large deformation theory is included in a finite element program some specialfeatures need to be considered. Firstly it is necessary to include additional terms in thestructure stiffness matrix to model the effects of large structural distortions on the finiteelement equations.

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Secondly, it is necessary to include a procedure to model correctly the stress changesthat occur when finite material rotations occur. This particular feature of largedisplacement theory is usually dealt with by adopting a definition of stress rate thatincludes rotation rate terms. Several stress rate definitions have been proposed byresearchers working in this field although none of these are wholly satisfactory. InPLAXIS the co-rotational rate of Kirchhoff stress (otherwise known as the Hill stress rate)is adopted. This stress rate would be expected to give accurate results provided that theshear strains do not become excessive.

Thirdly, it is necessary to update the finite element mesh as the calculation proceeds.This is done automatically within PLAXIS when the Updated mesh option is selected.

It should be clear from the descriptions given above that the updated mesh proceduresused in PLAXIS involve considerably more than simply updating nodal coordinates as thecalculation proceeds. These calculation procedures are in fact based on an approachknown as an Updated Lagrangian formulation (Bathe, 1982). Implementation of thisformulation within PLAXIS is based on the use of various advanced techniques that arebeyond the scope of this manual (van Langen, 1991).

The three basic types of calculations (Plastic, Consolidation and Safety) can optionallybe performed as an Updated mesh analysis, taking into account the effects of largedeformations. Therefore, the Updated mesh parameter should be selected. It can also beselected whether water pressures should be continuously recalculated according to theupdated position of the stress points. This option is termed Updated water pressures andis meant to take into account the effects of soil settling (partly) below a constant phreaticlevel.

Please note that an updated mesh calculation cannot be followed by a ‘normal’calculation. Reversely, a normal calculation can be followed by an updated meshcalculation, provided that the option Reset displacements to zero is used (Section 5.7.4).

It should be noted that an updated mesh analysis takes much more time and is lessrobust than a normal calculation. Hence, this option should only be used in special cases.

Distributed loads

Distributed loads on deformed boundaries are taken into account as if those boundarieswere not deformed. This is to avoid that the total force involved does not change whenthe boundary stretches or shrinks. This also applies to axisymmetric applications wherethe radius changes as a result of deformation.

Calculation procedures

In order to carry out an updated mesh analysis the Advanced button should be clicked inthe Calculation type box of the General tabsheet. As a result, the Advanced generalsettings window appears in which the Updated mesh option can be selected.

Updated mesh calculations are carried out using iteration procedures similar to theconventional calculation options (Plastic or Consolidation) as described in precedingsections. Therefore an updated mesh analysis uses the same parameters. However,because of the large deformation effect, the stiffness matrix is always updated at thebeginning of a load step. Due to this procedure and to the additional terms and morecomplex formulations, the iterative procedure in an updated mesh analysis is

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considerably slower than that for conventional calculations.

Safety calculations

The geometry of the model considered in a Safety calculation depends on whether theUpdated mesh option is selected or not in the parent phase. If the mesh is updated, theresulting geometry at the end of the parent phase will be considered in the safetycalculations.

During a safety calculation the mesh is not updated at the beginning of each load stepeven if the Updated mesh option is selected for the Safety phase.

Practical considerations

Updated mesh analysis tends to require more computer time than an equivalent,conventional calculation. It is recommended, therefore, that when a new project is understudy a conventional calculation is carried out before an updated mesh analysis isattempted.

It is not possible to give simple guidelines that may be used to indicate when an updatedmesh analysis is necessary and where a conventional analysis is sufficient. One simpleapproach would be to inspect the deformed mesh at the end of a conventional calculationusing the Deformed mesh option in the Output program. If the geometry changes arelarge (on a real scale!) then significant importance of geometric effects might besuspected. In this case the calculation should be repeated using the updated meshoption. It cannot definitely be decided from the general magnitudes of the deformationsobtained from a conventional plasticity calculation whether geometric effects areimportant or not. If the user is in any doubt about whether updated mesh analysis isnecessary then the issue can only be resolved by carrying out the updated mesh analysisand comparing the results with the equivalent conventional analysis.

In general, it is not appropriate to use an updated mesh calculation for gravity loading toset up the initial stress field. Displacements resulting from gravity loading are physicallymeaningless and should therefore be reset to zero. Resetting displacements to zero isnot possible after an updated mesh analysis. Hence, gravity loading should be applied ina normal plastic calculation.

Changing from a ‘normal’ plastic calculation or consolidation analysis to an updated meshanalysis is only valid when displacements are reset to zero, because a series of updatedmesh analyses must start from an undeformed geometry. Changing from an updatedmesh calculation to a ‘normal’ plastic calculation or consolidation analysis is not valid,because then all large deformation effects will be disregarded.

By default, the loading type of most types of calculation is set to Staged construction. Inthis PLAXIS specific feature it is possible to change the geometry and load configurationby deactivating or reactivating loads, structural objects or soil volumes. An overview ofthe available options is given below.

Updated water pressures

After the selection of Updated mesh option in the Advanced window of the Generaltabsheet, a further selection of Updated water pressures may be selected. When thisoption is selected, pore pressures in stress points and external water pressures at model

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boundaries are updated during the calculation according to the deformed modelboundaries and the displaced position of stress points. Basis for the update of waterpressures is the general phreatic level and the cluster phreatic levels. In this way, thebuoyancy effect of soil that is submerged below the phreatic level is taken into account.

Note that the pore pressures in clusters that have user-defined pore pressures are notupdated. Also, pore pressures that are calculated from groundwater flow calculations arenot updated.

5.6 LOAD STEPPING PROCEDURES

When soil plasticity is involved in a finite element calculation the equations becomenon-linear, which means that the problem needs to be solved in a series of calculationsteps. An important part of the non-linear solution procedure is the choice of step sizeand the solution algorithm to be used.

During each calculation step, the equilibrium errors in the solution are successivelyreduced using a series of iterations. The iteration procedure is based on an acceleratedinitial stress method. If the calculation step is of a suitable size then the number ofiterations required for equilibrium will be relatively small, usually around ten.

If the step size is too small, then many steps are required to reach the desired load leveland computer time will be excessive. On the other hand, if the step size is too large thenthe number of iterations required for equilibrium may become excessive or the solutionprocedure may even diverge.

In PLAXIS there are various procedures available for the solution of non-linear plasticityproblems. All procedures are based on an automatic step size selection. The followingprocedures are available: Load advancement ultimate level, Load advancement numberof steps and Automatic time stepping. Users do not need to worry about the properselection of these procedures, since PLAXIS will automatically use the most appropriateprocedure by itself to guarantee optimum performance.

The automatic load stepping procedure is controlled by a number of calculation controlparameters (Section 5.7). There is a convenient default setting for most controlparameters, which strikes a balance between robustness, accuracy and efficiency. Foreach calculation phase, the user can influence the automatic solution procedures bymanually adjusting the control parameters in the Numerical control parameters subtreein the the Phases window. In this way it is possible to have a stricter control over stepsizes and accuracy. Before proceeding to the description of the calculation controlparameters, a detailed description is given of the solution procedures themselves.

5.6.1 AUTOMATIC STEP SIZE PROCEDURE

Both of the Load advancement procedures (Ultimate level and Number of steps) makeuse of an automatic step size algorithm (van Langen & Vermeer, 1990). The size of thefirst load step is either chosen automatically (Section 5.6.2) or manually by the user(Section 5.6.3), depending on the applied algorithm. The automatic step size procedurefor subsequent computations is described below.

When a new load step is applied, a series of iterations are carried out to reachequilibrium. The following three outcomes of this process are possible:

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Case 1: The solution reaches equilibrium within a number of iterations that is less thanthe Desired minimum control parameter. By default, the Desired minimum number ofiterations is 6, but this value may be changed in the Manual settings window of theIterative procedure group box of the Numerical control parameters subtree in the Phaseswindow(Section 5.7.1). If fewer iterations than the desired minimum are required to reachthe equilibrium state then the calculation step is assumed to be too small. In this case,the size of the load increment is multiplied by two and further iterations are applied toreach equilibrium.

Case 2: The solution fails to converge within a Desired maximum number of iterations.By default, the Desired maximum number of iterations is 15, but this value may bechanged in the Manual settings window of the Iterative procedure group box of theNumerical control parameters subtree in the Phases window. (Section 5.7.1). If thesolution fails to converge within the desired maximum number of iterations then thecalculation step is assumed to be too large. In this case, the size of the load increment isreduced by a factor of two and the iteration procedure is continued.

Case 3: The number of required iterations lies between the Desired minimum number ofiterations and the Desired maximum number of iterations in which case the size of theload increment is assumed to be satisfactory. After the iterations are complete, the nextcalculation step begins. The initial size of this calculation step is made equal to the sizeof the previous successful step.

If the outcome corresponds to either case 1 or case 2 then the process of increasing orreducing the step size continues until case 3 is achieved.

5.6.2 LOAD ADVANCEMENT — ULTIMATE LEVEL

This automatic step size procedure is used for calculation phases where a certain ‘state’or load level (the ‘ultimate state’ or ‘ultimate level’) has to be reached, as in the case for aPlastic calculation where the Undrained A and Undrained B behaviours are ignored. Theprocedure terminates the calculation when the specified state or load level is reached orwhen soil failure is detected. By default, the Max steps parameter is set to 250, but thisparameter does not play an important role, since in most cases the calculation stopsbefore the maximum number of steps is reached.

An important property of this calculation procedure is that the user specifies the state orthe values of the total load that is to be applied. A Plastic calculation where the Loadinginput is set to Staged construction or Total multipliers uses this Load advancementultimate level procedure. The size of the first load step is obtained automatically usingone of the two following methods:

• PLAXIS performs a trial calculation step and determines a suitable step size on thebasis of this trial.

• PLAXIS sets the initial load step size to be equal to the final load step size of anyprevious calculation.

The first method is generally adopted. The second method would only be used if theloading applied during the current load step is similar to that applied during the previousload step, for example if the number of load steps applied in the previous calculationproved to be insufficient.

In subsequent steps, the automatic load stepping procedures are adopted (Section

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5.6.1). If at the end of the calculation, the defined state or load level has been reached,the calculation is considered to be successful. A successful calculation is indicated by acheck mark in a green circle in the Phases window.

If the defined state or load level has NOT been reached, the calculation is considered tohave failed. A failed calculation is indicated by a cross mark in a red circle in the Phaseswindow. A message describing the error is given in the Log info for the last calculationbox in the Phases window:

Prescribed ultimate state not reached; Soil body collapses: A collapse load hasbeen reached. In this case, the total specified load has not been applied. Collapse isassumed when the applied load reduces in magnitude in a number successivecalculation steps as defined by the Additional steps parameter and the current stiffnessparameter CSP is less than 0.015 (see Section 5.13.9 for the definition of CSP). It is alsopossible that the problem is failing but due to switched-off arc-length control, the programis not allowed to take negative step sizes. The user should check the output of the laststep and judge whether the project is failing or not. In case of failure, recalculating theproject with a higher Additional steps parameter is useless.

Prescribed ultimate state not reached; load advancement procedure fails. Trymanual control: The load advancement procedure is unable to further increase theapplied load, but the current stiffness parameter CSP is larger than 0.015. In this casethe total load specified has not been applied. The user can now attempt to rerun thecalculation with slight changes to the iterative parameters in Numerical controlparameters subtree in the the Phases window, in particular turning off the Arc-lengthcontrol type parameter.

Prescribed ultimate state not reached; Not enough load steps: The maximumspecified number of additional load steps have been applied. In this case, it is likely thatthe calculation stops before the total specified load has been applied. It is advised torecalculate the phase with an increased value of Max steps.

Cancelled by user: This occurs when the calculation process is terminated by clickingStop in the Active tasks window.

Prescribed ultimate state not reached; Numerical error: A numerical error hasoccurred. In this case, the total specified load has not been applied. There may bedifferent causes for a numerical error. Most likely, it is related to an input error. Carefulinspection of the input data, the finite element mesh and the defined calculation phase issuggested.

Severe divergence: This is detected when the global error is increasing and hasreached huge values. This error, for example, can be caused by very small time steps ina consolidation phase. The program scales down the step size when the tolerated errorcannot be reached, resulting in small time steps. One of the reasons can be that a failuresituation is reached. As for consolidation the arc-length procedure is not used, theprogram cannot really detect failure.

File xxxx not found: Such a message appears when a file that ought to exist does notexist.

Messages may indicate errors related to the iterative solution algorithm or the matrixcondition. In the case of ‘floating’ elements (insufficient boundary conditions), one couldget a message indicating that the matrix is nearly singular. Checking and improving the

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defined calculation phase usually solves the problem.

5.6.3 LOAD ADVANCEMENT — NUMBER OF STEPS

This automatic step size procedure always performs the number of steps specified inAdditional steps and is, in general, used for calculation phases where a complete failuremechanism should be developed during the analysis. This algorithm is therefore usedduring a Safety analysis or a Plastic calculation where the Loading input is set toIncremental multipliers.

The size of the first step is determined by the incremental multiplier as defined for theparticular calculation phase. For Safety calculations the Loading type parameter isIncremental multipliers and the default increment is Msf = 0.1. This value may bechanged in the General subtree of the Phases window. In subsequent steps, theautomatic load stepping procedures are adopted (Section 5.6.1).

If at the end of the calculation the value assigned to the Additional steps parameter hasbeen reached, the calculation is considered to be successful. A successful calculation isindicated by a tick mark in a green circle in the Phases window.

If the value assigned to the Additional steps parameter has NOT been reached, thecalculation is considered to have failed. A failed calculation is indicated by a cross markin a red circle in the Phases window. A message describing the error is given in the Loginfo for last calculation box in the Phases window.

Cancelled by user: This occurs when the calculation process is terminated by clickingStop in the Active tasks window.

Apart from cancellation by the user, a load advancement calculation will proceed until thenumber of additional steps defined in the Additional steps parameter have been applied.In contrast to the Ultimate level procedure the calculation will not stop when failure isreached.

5.6.4 AUTOMATIC TIME STEPPING (CONSOLIDATION)

When the Calculation type is set to Consolidation, the Automatic time stepping procedureis used. This procedure will automatically choose appropriate time steps for aconsolidation analysis. When the calculation runs smoothly, resulting in very fewiterations per step, then the program will choose a larger time step. When the calculationuses many iterations due to an increasing amount of plasticity, then the program will takesmaller time steps.

The first time step in a consolidation analysis is generally based on the First time stepparameter. This parameter is, by default, based on the advised minimum time step(overall critical time step) as described in Section 5.7. The First time step parameter canbe changed in the Manual settings window appearing after clicking the Define buttonwhen Manual settings has been selected in the Iterative procedure group box. However,care should be taken with time steps that are smaller than the advised minimum timestep.

In a consolidation analysis where the Loading input is set to Incremental multipliers, theapplied first time step is based on the Time increment parameter rather than on the Firsttime step parameter. In this case, the specified number of Additional steps is always

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performed. In a consolidation analysis where the Loading input is set to Stagedconstruction or Minimum pore pressure, the specified number of Additional steps is justan upper bound. In that case, the calculation is generally stopped earlier, when otherconditions are met.

During a Consolidation calculation, arc-length control is always inactive.

5.6.5 AUTOMATIC TIME STEPPING (DYNAMICS)

When the Calculation type is set to Dynamic, the Newmark time integration scheme isused in which the time step is constant and equal to the critical time step during the wholeanalysis. The proper critical time step for dynamic analyses is calculated based onmaterial property, element size and time history functions (see Section 5.7.1 for moreinformation). The critical time steps is calculated based on the values assigned toAdditional steps, Number of sub-steps and Dynamic time interval. To be able to changethe critical time step, the user needs to change the number of sub-steps.

During a dynamic calculation, arc-length control is always inactive.

5.7 CALCULATION CONTROL PARAMETERS

The Parameters tabsheet is used to define the control parameters of a particularcalculation phase and the corresponding solution procedure (Figure 5.3).

Figure 5.3 Parameters tabsheet of the Calculations window

5.7.1 ITERATIVE PROCEDURE CONTROL PARAMETERS

The iterative procedures, in particular the load advancement procedures, are influencedby some control parameters. These parameters can be set in the Iterative proceduregroup. PLAXIS has an option to adopt a Standard setting for these parameters, which in

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most cases leads to good performance of the iterative procedures. Users who are notfamiliar with the influence of the control parameters on the iterative procedures areadvised to select the Standard setting.

Figure 5.4 Manual settings window of the Iterative procedure group

In some situations, however, it might be desired or even necessary to change thestandard setting. In this case the user should select the Manual setting option and clickon the Define button in the Iterative procedure group. As a result, a window is opened inwhich the control parameters are displayed with their current values (Figure 5.4).

Tolerated error

In any non-linear analysis where a finite number of calculation steps are used there willbe some drift from the exact solution, as shown in Figure 5.5. The purpose of a solutionalgorithm is to ensure that the equilibrium errors, both locally and globally, remain withinacceptable bounds (Section 5.13.9). The error limits adopted in PLAXIS are linkedclosely to the specified value of the Tolerated error.

Within each step, the calculation program continues to carry out iterations until thecalculated errors are smaller than the specified value. If the tolerated error is set to a highvalue then the calculation will be relatively quick but may be inaccurate. If a low toleratederror is adopted then computer time may become excessive. In general, the standardsetting of 0.01 is suitable for most calculations. For preliminary calculations an increasedvalue of 0.03 or even 0.05 may be used.

Hint: A warning appears when a value higher than 0.05 is assigned to theTolerated error parameter.

If a plastic calculation gives failure loads that tend to reduce unexpectedly with increasingdisplacement, then this is a possible indication of excessive drift of the finite elementresults from the exact solution. In these cases the calculation should be repeated using alower value of the tolerated error. For further details of the error checking proceduresused in PLAXIS see Section 5.13.9.

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load

exact solution

numerical solution

displacement

Figure 5.5 Computed solution versus exact solution

Tolerated error (flow)

In the case of performing a flow calculation (steady-state or transient) or a Consolidationanalysis based on total pore pressure, it is possible to define the tolerated error for flowas a separate parameter to ensure that the equilibrium errors in a flow calculation remainwithin acceptable bounds. For more information about the use of a tolerated error, seeabove.

Over-relaxation

To reduce the number of iterations needed for convergence, PLAXIS makes use of anover-relaxation procedure as indicated in Figure 5.6. The parameter that controls thedegree of over-relaxation is the over-relaxation factor. The theoretical upper bound valueis 2.0, but this value should never be used. For low soil friction angles, for example ϕ <20◦, an over-relaxation factor of about 1.5 tends to optimise the iterative procedure. If theproblem contains soil with higher friction angles, however, then a lower value may berequired. The standard setting of 1.2 is acceptable in most calculations.

load

load

over relaxation = 1

displacement displacement

over relaxation > 1

Figure 5.6 Iteration process

Maximum iterations

This value represents the maximum allowable number of iterations within any individualcalculation step. In general, the solution procedure will restrict the number of iterations

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that take place. This parameter is required only to ensure that computer time does notbecome excessive due to errors in the specification of the calculation. The standard valueof Maximum iterations is 60, but this number may be changed within the range 1 to 100.

If the maximum allowable number of iterations is reached in the final step of a calculationphase, then the final result may be inaccurate. If this is the case then the message’Maximum iterations reached in final step’ is displayed in the Log info box of the Generaltabsheet. Such a situation occasionally occurs when the solution process does notconverge. This may have various causes, but it mostly indicates an input error. It mayalso happen at the end of a Safety analysis when very large deformations have occurred.

Desired minimum and desired maximum

If Plastic or Safety is selected as calculation type then PLAXIS makes use of anautomatic step size algorithm (Load advancement ultimate level or Number of steps).This procedure is controlled by the two parameters Desired minimum and Desiredmaximum, specifying the desired minimum and maximum number of iterations per steprespectively. The standard values of these parameters are 6 and 15 respectively, butthese numbers may be changed within the range 1 to 100. For details on the automaticstep size procedures see Section 5.6.

It is occasionally necessary for the user to adjust the values of the desired minimum andmaximum from their standard values. It is sometimes the case, for example, that theautomatic step size procedure generates steps that are too large to give a smoothload-displacement curve. This is often the case where soils with very low friction anglesare modelled. To generate a smoother load-displacement response in these cases, thecalculations should be repeated with smaller values for these parameters, for example:

Desired minimum =3 Desired maximum = 7

If the soil friction angles are relatively high, or if high-order soil models are used, then itmay be appropriate to increase the desired minimum and maximum from their standardvalues to obtain a solution without the use of excessive computer time. In these casesthe following values are suggested:

Desired minimum = 8 Desired maximum = 20

In this case it is recommended to increase the Maximum iterations to 80.

Arc-length control

The Arc-length control procedure is a method that is by default selected in a Plasticcalculation or a Safety analysis to obtain reliable collapse loads for load-controlledcalculations (Rheinholdt & Riks, 1986). Arc-length control is not available forConsolidation analyses.

The iterative procedure adopted when arc-length control is not used is shown in Figure5.7a for the case where a collapse load is being approached. In the case shown, thealgorithm will not converge. If arc-length control is adopted, however, the program willautomatically evaluate the portion of the external load that must be applied for collapseas shown in Figure 5.7b.

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load

displacement

step 1

step 2

step 3

load control

a. Normal load control

load

displacement

step 1

step 2

step 3 arc

arc-length control

olb. Arc-length control

Figure 5.7 Iterative procedure

Arc-length control is activated by selecting the corresponding check box in the Manualsettings window, which is displayed as the Manual settings option is selected and Defineis clicked in the Iterative procedure box in the Parameters tabsheet. The arc-lengthcontrol procedure should be used for load-controlled calculations, but it may bedeactivated, if desired, for displacement-controlled calculations. When using Incrementalmultipliers as loading input, arc-length control will influence the resulting load increments.As a result, the load increments applied during the calculation will generally be smallerthan prescribed at the start of the analysis.

Hint: The use of arc-length control occasionally causes spontaneous unloading tooccur (i.e. sudden changes in sign of the displacement and load increments)when the soil body is far from collapse. If this occurs, then the user isadvised to de-select Arc-length control and restart the calculation. Note thatif arc-length control is deselected and failure is approached, convergenceproblems may occur.

First time step

The First time step is the increment of time used in the first step of a consolidationanalysis, except when using Incremental multipliers as Loading input. By default, the firsttime step is equal to the overall critical time step, as described below.

Care should be taken with time steps that are smaller than the advised minimum timestep. For most numerical integration procedures, accuracy increases when the time stepis reduced, but for consolidation there is a threshold value. Below a particular timeincrement (critical time step) the accuracy rapidly decreases and stress oscillations mayoccur. For one-dimensional consolidation (vertical flow) this critical time step is calculatedas:

∆tcritical =H2γw (1− 2ν)(1 + ν)

80ky E(1− ν)(15− node triangles)

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∆tcritical =H2γw (1− 2ν)(1 + ν)

40ky E(1− ν)(6− node triangles)

Where γw is the unit weight of the pore fluid, ν is Poisson’s ratio, ky is the verticalpermeability, E is the elastic Young’s modulus, and H is the height of the element used.Fine meshes allow for smaller time steps than coarse meshes. For unstructured mesheswith different element sizes or when dealing with different soil layers and thus differentvalues of k , E and ν, the above formula yields different values for the critical time step. Tobe on the safe side, the time step should not be smaller than the maximum value of thecritical time steps of all individual elements. This overall critical time step is automaticallyadopted as the First time step in a consolidation analysis. For an introduction to thecritical time step concept, the reader is referred to Vermeer & Verruijt (1981). Detailedinformation about various types of finite elements is given by Song (1990).

Extrapolation

Extrapolation is a numerical procedure, which is automatically used in PLAXIS ifapplicable, when a certain loading that was applied in the previous calculation step iscontinued in the next step. In this case, the displacement solution to the previous loadincrement can be used as a first estimate of the solution to the new load increment.Although this first estimate is generally not exact (because of the non-linear soilbehaviour), the solution is usually better than the solution according to the initial stressmethod (based on the use of the elastic stiffness matrix) (Figure 5.8). After the firstiteration, subsequent iterations are based on the elastic stiffness matrix, as in the initialstress method (Zienkiewicz, 1977). Nevertheless, using Extrapolation the total number ofiterations needed to reach equilibrium is less than without extrapolation. Theextrapolation procedure is particularly useful when the soil is highly plastic. Note thatthere is no possibility to activate or de-activate this option by the user.

load

without extrapolation

displacementapolation

a. Elastic prediction

load

displacement

with extrapolation

b. Extrapolation

Figure 5.8 Difference between elastic prediction and extrapolation from previous step

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Dynamic sub steps

The time step used in a dynamic calculation is constant and equal to δt = ∆t / (m · n),where ∆t is the duration of the dynamic loading (Time interval), m is the number ofAdditional steps and n is the number of Dynamic sub steps. The result of themultiplication of the Additional step number (m) and the Dynamic sub steps number (n)gives the total number of steps to be used in the time discretization. It is important todefine a proper number of steps such that the dynamic signal used in dynamic loading isproperly covered.

The number of the additional steps specifies the number of the steps which can be usedin plots in the Output program. A higher number of Additional steps provides moredetailed plots, however the processing time required by the Output program is increasedas well.

For each given number of additional time step, PLAXIS estimates the number of substeps on the basis of the generated mesh and the calculated δtcritical (see theory oncritical time, Section 7.2.1 of the Scientific Manual). If the wave velocities (functions ofmaterial stiffness) in a model exhibit remarkable differences and/or the model containsvery small elements, the standard number of sub steps can be very large. In suchsituations it may not always be vital to follow the automatic time stepping with thestandard number of dynamic sub-steps.

It is possible to change the calculated number of Dynamic sub steps in the Manualsettings window in the Iterative procedure box of the Parameters tabsheet. Changing thenumber of sub steps will also influence the time step (δt) used in a dynamic calculation.In general it is a good habit to check the number of dynamic sub-steps by selecting theManual settings option and clicking the Define button.

Newmark alpha and beta

The Newmark alpha and beta parameters in the Manual settings of the Iterativeprocedure group determine the numeric time-integration according to the implicitNewmark scheme. In order to obtain an unconditionally stable solution, these parametersmust satisfy the following conditions:

Newmark β ≥ 0.5 and Newmark α ≥ 0.25(0.5 + β)2

For an average acceleration scheme you can use the standard settings (α = 0.25 andβ = 0.5). Using a higher β-value and corresponding α-value results in a dampedNewmark scheme (e.g. α = 0.3025 and β = 0.6).

Hint: Newmark alpha and beta should not be confused with Rayleigh α and β. Formore information about Rayleigh α and β see Section 4.1.1.

Boundary C1 and Boundary C2

Boundary C1 and Boundary C2 are relaxation coefficients used to improve the waveabsorption on the absorbent boundaries. C1 corrects the dissipation in the direction

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normal to the boundary and C2 does this in the tangential direction. If the boundaries aresubjected only to waves that come in perpendicular to the boundary, relaxation is notnecessary (C1 = C2 = 1). When there are waves in arbitrary direction (which is normallythe case), C2 has to be adjusted to improve the absorption. The standard values areC1 = 1 and C2 = 1.

5.7.2 PORE PRESSURE LIMITS

Limitations to the pore pressures can be defined in the Pore pressure limits group.

Cavitation cut-off

In case of unloading of undrained materials tensile excess pore pressures may begenerated. These excess pore pressures might give rise to tensile active pore pressures.In case the cavitation cut-off option is activated, excess pore pressures are limited so thatthe tensile active pore pressure is never larger than the cavitation cut-off stress. Bydefault, the cavitation cut-off option is not activated. If it is activated, the default cavitationcut-off stress is set to 100 kN/m2.

Pore pressure tension cut-off

When the pore pressures are generated by the phreatic level option or by groundwaterflow calculations, tensile pore water stresses will be generated above the phreatic level.

In the Classical mode in which Terzaghi stress is used, the use of these tensile porestresses in a deformation analysis will lead to an overestimation of the shear strengthwhen effective strength parameters are used for the soil. In order to avoid such asituation, tensile pore stresses can be cut off by selecting the Pore pressure tensioncut-off option. Subsequently, the Max. tensile stress parameter can be set to themaximum allowable tensile stress (in the unit of stress). When using the Classical mode,the Pore pressure tension cut-off option is selected by default and the Max.tensile stressparameter is set to 0.001 kPa.

In the Advanced mode, in which Bishop stress is used, this option is not selected and themaximum tensile pore water pressure, by default, is not limited. In this mode, the strengthof material is mainly governed by the selection of the Soil Water Characteristic Curve(SWCC) used for unsaturated area (see Section 5.3.2). It is strongly suggested toactivate the Pore pressure tension cut-off in a Plastic analysis before performing a Safetyanalysis.

5.7.3 LOADING INPUT

The Loading input group box is used to specify which type of loading is considered in aparticular calculation phase. Only one of the described loading types can be activated inany single calculation phase.

In Plastic calculations, distinction is made between the following types of Loading input :

• Loading in the sense of changing the load combination, stress state, weight,strength or stiffness of elements, activated by changing the load and geometryconfiguration or pore pressure distribution by means of Staged construction. In thiscase, the total load level that is to be reached at the end of the calculation phase is

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defined by specifying a new geometry and load configuration, and/or pore pressuredistribution, in the Staged construction mode (Section 5.8).

• Loading in the sense of increasing or decreasing a predefined combination ofexternal forces, activated by changing Total multipliers. In this case, the total loadlevel that is to be reached at the end of the calculation phase is defined by enteringvalues for the Total multipliers in the Multipliers tabsheet.

• Loading in the sense of increasing or decreasing a predefined combination ofexternal forces, activated by changing Incremental multipliers. In this case, the firstincrement of load is defined by entering values for the Incremental multipliers in theMultipliers tabsheet, and this loading is continued in subsequent steps.

When selecting Safety distinction is made between the following types of Loading input :

• Reduction of the soil and interface strength parameters towards a target value of thetotal multiplier ΣMsf . The program first performs a full safety analysis until failureand then it recalculates the last step before the target value of ΣMsf in order toreach the target exactly. Note that the ΣMsf parameter is available in the Multiplierstabsheet as well.

• Reduction of the soil and interface strength parameters by using the Incrementalmultipliers option. In this case, the increment of the strength reduction of the firstcalculation step, Msf , is defined. Note that the Msf parameter is available in theMultipliers tabsheet as well.

In a Consolidation analysis based on excess pore pressure, the following options areavailable:

• Consolidation and simultaneous loading in the sense of changing the loadcombination, stress state, weight, strength or stiffness of elements, activated bychanging the load and geometry configuration or pore pressure distribution bymeans of Staged construction. It is necessary to specify a value for the Time intervalparameter, which has in this case the meaning of the total consolidation periodapplied in the current calculation phase. The applied first time increment is based onthe First time step parameter in the Manual settings window of the Iterativeprocedure group. The Staged construction option should also be selected if it isdesired to allow for a certain consolidation period without additional loading.

• Consolidation without additional loading, until all excess pore pressures havedecreased below a certain minimum value, specified by the Minimum porepressures parameter. By default, Minimum pore pressures is set to 1 stress unit, butthis value may be changed by the user. Please note that the Minimum porepressures parameter is an absolute value, which applies to pressure as well astensile stress. The input of a Time interval is not applicable in this case, since itcannot be determined beforehand how much time is needed to fulfill the minimumpore pressure requirement. The applied first time increment is based on the Firsttime step parameter in the Manual settings window of the Iterative procedure group.

• Consolidation and simultaneous loading in the sense of increasing or decreasing apredefined combination of external forces, activated by changing Incrementalmultipliers. It is necessary to specify a value for the Time increment parameter inthe unit of time. The Time increment sets in this case the applied first time step anddetermines the loading rate, together with the current configuration of external loads

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and the incremental multipliers in the Multipliers tabsheet.

• Consolidation without additional loading, until a desired degree of consolidation,specified by the Degree of consolidation parameter, is reached. By default, Degreeof consolidation is set to 90.0 %, but this value may be changed by the user. Theinput of a Time interval is not applicable in this case, since it cannot be determinedbeforehand how much time is needed to fulfill the degree of consolidationrequirement. The applied first time increment is based on the First time stepparameter in the Manual settings window of the Iterative procedure group.

In a Consolidation analysis based on total pore pressure, the following options areavailable:

• Consolidation and simultaneous loading in the sense of changing the loadcombination, stress state, weight, strength or stiffness of elements, activated bychanging the load and geometry configuration or pore pressure distribution bymeans of Staged construction. It is necessary to specify a value for the Time intervalparameter, which has in this case the meaning of the total consolidation periodapplied in the current calculation phase. The applied first time increment is based onthe First time step parameter in the Manual settings window of the Iterativeprocedure group. The Staged construction option should also be selected if it isdesired to allow for a certain consolidation period without additional loading.

• Consolidation and simultaneous loading in the sense of increasing or decreasing apredefined combination of external forces, activated by changing Incrementalmultipliers. It is necessary to specify a value for the Time increment parameter inthe unit of time. The Time increment sets in this case the applied first time step anddetermines the loading rate, together with the current configuration of external loadsand the incremental multipliers in the Multipliers tabsheet.

In a Dynamics analysis, the following options are available:

• Dynamic loading in the sense of increasing or decreasing a predefined combinationof external dynamic forces, activated by changing Total multipliers. In this case, thetotal load level that is to be reached at the end of each calculation step is specifiedas a (harmonic) function or is imported from a file which contains values for the Totalmultipliers, in the Multipliers tabsheet.

In a Free vibration analysis, the following options are available:

• Dynamic analysis by releasing external static load system A.

• Dynamic analysis by releasing external static load system B.

• Dynamic analysis by releasing all external static load systems (A and B).

In a Groundwater flow (steady-state), the following options are available:

• Steady state groundwater flow calculation in the sense of changing (or defining) flowboundary conditions or defining a new geometry configuration by means of Stagedconstruction.

In a Groundwater flow (transient), the following options are available:

• Transient groundwater flow calculation in the sense of changing (or defining)time-dependent flow boundary conditions or defining a new geometry configurationby means of Staged construction.

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Staged construction

If Staged construction is selected from the Loading input box, then the user can specify anew state that is to be reached at the end of the calculation phase. This new stage can bedefined by pressing the Define button and changing the water pressure distribution, thegeometry, the input values of loads and the load configuration in the Water conditions andStaged construction mode. The Staged construction option may also be used to performplastic nil-steps to solve existing out-of-balance forces. In this case, no changes in thegeometry, load level, load configuration and water pressure distribution should be made.

Before specifying the construction stage, the Time interval of the calculation phaseshould be considered. The Time interval is expressed in the unit of time. A non-zerovalue is only relevant in the case of a Consolidation analysis or if a time-dependent soilmodel (such as Soft Soil Creep model) is used. The appropriate value can be entered inthe Loading input group of the Parameters tabsheet.

Since staged construction is performed using the Load advancement ultimate levelprocedure (Section 5.6.2), it is controlled by a total multiplier (ΣMstage). This multiplieralways starts at zero and is expected to reach the ultimate level of 1.0 at the end of thecalculation phase. In some special situations, however, it might be necessary to split thestaged construction process into more than one calculation phase and to specify anintermediate value of ΣMstage. This can be done by clicking on the Advanced button inthe Loading input group, which is only available for a Plastic calculation. As a result, awindow appears in which the desired ultimate level of ΣMstage can be specified.However, care must be taken with an ultimate level smaller than 1.0, since this isassociated with a resulting out-of-balance force. Such calculations must always befollowed by another staged construction calculation.Without specifying a value forΣMstage, the program always assumes an ultimate level of ΣMstage = 1.0. Beforestarting any other type of calculation the ΣMstage parameter must first have reached thevalue 1.0. This can be verified after a calculation by selecting the Reached values optionin the Multipliers tabsheet (Section 5.11.2).

Total multipliers

If the Total multipliers option is selected in the Loading input box, then the user mayspecify the multipliers that are applied to current configuration of the external loads. Theactual applied load at the end of the calculation phase is the product of the input value ofthe load and the corresponding load multiplier, provided a collapse mechanism orunloading does not occur earlier.

Before specifying the external loads, the Time interval of the calculation may be specifiedin the Loading input box of the Parameters tabsheet. The time interval is the timeinvolved in the current calculation phase, expressed in the unit of time as specified in theProject properties window of the Input program. A non-zero value is only relevant if atime-dependent soil model (such as the Soft Soil Creep model) is used. The combinationof the total multipliers and the time interval determine the loading rate that is applied inthe calculation.

In addition to the time interval, an estimate is given of the total time at the end of thecalculation phase (Estimated end time), which is a summation of all time intervals ofpreceding calculation phases including the current one. If the calculation phase has beenexecuted, the Realised end time is given instead, which is the total time that has actually

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been reached at the end of the calculation phase. In addition the reached values of themultipliers can be viewed by selecting the corresponding radio button in the Multiplierstabsheet.

Incremental multipliers

Selecting Incremental multipliers in the Loading input box enables the user to specifyincremental load multipliers that are applied to current configuration of the external loads.The initially applied load increment in the first step of the calculation phase is the productof the input value of the load and the corresponding incremental multiplier. Note that theresulting increments of load in the first calculation step will be influenced by theArc-length control procedure if it is active.

Before entering an increment of external load, a Time increment can be entered in theLoading input box of the Parameters tabsheet. This is only relevant for a Consolidationanalysis or if a time dependent soil models (such as the Soft Soil Creep model) is used.The combination of the incremental multipliers and the time increment determine theloading rate that is applied in the calculation. The time increment is expressed in the unitof time as entered in the Project properties window of the Input program.

Minimum pore pressure (consolidation)

The Minimum pore pressure option in the Loading input box is a criterion for terminatinga consolidation analysis. The calculation stops when the maximum absolute excess porepressure is below the prescribed value of Minimum pore pressure. Note that the numberof Additional steps is a maximum number and will not be reached if the Minimum porepressure criterion is met before. For example, when the maximum excess pore pressurehas reached a certain value during the application of load, the user can make sure thatthe consolidation process is continued until all nodal values of excess pore pressure areless than Minimum pore pressure, provided the number of Additional steps is sufficient.

Degree of consolidation

The option Degree of consolidation is an alternative criterion for terminating aconsolidation analysis. The calculation stops when the degree of consolidation, asdefines herein, is below the value of Degree of consolidation. The degree ofconsolidation is an important indication of the consolidation state. Strictly, the degree ofconsolidation, U, is defined in terms of the proportion of the final settlement although theterm is often used to describe the proportion of pore pressures that have dissipated to atleast (100-U)% of their values immediately after loading. The Degree of consolidationoption may be used to specify the final degree of consolidation in any analysis.

In this case the Minimum pore pressure parameter (see above) is set to a value asdefined by the maximum excess pore pressure in the previous phase and the definedDegree of consolidation (U):

Minimum pore pressure = (100− U)Pmax

where Pmax is the maximum excess pore pressure reached in the previous phase whichcan be found in the Multipliers tabsheet of the previous calculation phase when selectingthe Reached values option (Section 5.11.2). The calculation steps when the maximumabsolute excess pore pressure is below this calculated value of Minimum pore pressure.

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Releasing a load system (free vibration)

An applied external static load (system A, B or both) can be released in a dynamic Freevibration analysis to evaluate the eigen frequencies of a structure.

Before entering which load system should be released, a Time interval can be entered inthe Loading input box of the Parameters tabsheet. A dynamic analysis is preformedbased on the time interval and the out of balance force generated by the released load.The time interval is expressed in seconds similar to all dynamic calculations.

Time increment, Time interval, Realised end time, Estimated end time

These time parameters control the progress of time in the calculations. All timeparameters are expressed in the unit of time as defined in the Model tabsheet of theProject properties window. A non-zero value for the Time increment or Time intervalparameters is only relevant when a consolidation analysis is performed, when transientgroundwater flow is considered or when using time-dependent material models (such asthe Soft Soil Creep model). The meaning of the various time parameters is describedbelow:

• Time increment is the increment of time considered in a single step (first step) in thecurrent calculation phase.

• Time interval is the total time period considered in the current calculation phase.

• Realised end time is the actual accumulated time at the end of a finished calculationphase.

• Estimated end time is an estimation of the accumulated time at the end of a phasethat is to be calculated. This parameter is estimated from the Time interval of thecurrent phase and the Realised or Estimated end time of the previous phase.

5.7.4 CONTROL PARAMETERS

In addition to the parameters defining the solution procedure and the loading input, someadditional control parameters can be defined.

Additional steps

This parameter specifies the maximum number of calculation steps (load steps) that areperformed in a particular calculation phase.

If Plastic or Consolidation analysis is selected as the calculation type and the loadinginput is set to Incremental multipliers, then the number of additional steps should be setto an integer number representing the required number of steps for this calculationphase. In this case the number of additional steps is an upper bound to the actualnumber of steps that will be executed. By default, the Additional steps parameter is set to250, but this number can be changed within the range 1 to 10000.

If Safety, Dynamic or Free vibration is selected as the calculation type and the loadinginput is set to Staged construction, Total multipliers, Minimum pore pressure or Degree ofconsolidation, then the number of additional steps is always exactly executed. In general,it is desired that such a calculation is completed within the number of additional steps and

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stops when either the prescribed ultimate state is reached or the soil body collapses. Ifsuch a calculation reaches the maximum number of additional steps, it usually meansthat the ultimate level has not been reached. By default, the Additional steps parameter isset to 100, which is generally sufficient to complete the calculation phase. However, thisnumber may be changed within the range 1 to 10000.

In the case of a dynamic calculation, it is suggested to check the number of dynamicsub-steps by selecting the Manual settings and click the Define button. If the number ofdynamic sub-steps is high (e.g. > 10) it is suggested to increase the number of Additionalsteps such that the number of sub-steps is not larger than 10.

Max number of steps stored

This parameter defines the number of steps to be saved in a calculation phase. Ingeneral the final output step contains the most relevant result of the calculation phase,whereas intermediate steps are less important. The final step of a calculation phase isalways saved.

When Max. steps saved is larger than one, then also the first step is saved plus (when>2) a selection of available intermediate steps, such that the intervals between the stepnumbers are more or less equally divided.

If a calculation phase does not finish successfully then all calculation steps are retained,regardless of the defined value. This enables a stepwise evaluation of the cause of theproblem.

Reset displacements to zero

This option should be selected when irrelevant displacements of previous calculationsteps are to be disregarded at the beginning of the current calculation phase, so that thenew calculation starts from a zero displacement field. For example, deformations due togravity loading are physically meaningless. Hence, this option may be chosen aftergravity loading to remove these displacements. If the option is not selected thenincremental displacements occurring in the current calculation phase will be added tothose of the previous phase. The selection of the Reset displacements to zero optiondoes not influence the stress field.

The use of the Reset displacements to zero option may not be used in a sequence ofcalculations where the Updated Mesh option is used. However, if an Updated meshcalculation starts from a calculation where the Updated mesh option is not used, then theReset displacements to zero option must be used in this Updated mesh calculation.

Ignore undrained behaviour

Ignore undrained behaviour excludes temporarily the effects of undrained behaviour insituations where undrained material data sets (Undrained (A) or Undrained (B)) are used.The selection of this option is associated with the selection of the Plastic and Plasticdrained calculation types. In the latter case, the option Ignore undrained behaviour isselected whereas in the former case it is not selected. When the option is selected, thestiffness of water is not taken into account. As a result, all undrained material clusters(except for Undrained (C) materials) become temporarily drained. Existing excess porepressures that were previously generated will remain, but no new excess pore pressureswill be generated in that particular calculation phase.

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Gravity loading of undrained materials will result in unrealistic excess pore pressures.Stresses due to the self-weight of the soil, for example, are based on a long-term processin which the development of excess pore pressures is irrelevant. The Ignore undrainedbehaviour option enables the user to specify the material type from the beginning asundrained for the main loading stages and to ignore the undrained behaviour during theGravity loading stage, at least for data sets defined as Undrained A or Undrained B.

Hint: The Ignore undrained behaviour option is not available for Consolidationanalyses, since a consolidation analysis does not consider the Drainage typeas specified in the material data sets, but uses the material permeabilityinstead.

Note that Ignore undrained behaviour does not affect materials of which the drainagetype is set to Undrained (C).

5.8 STAGED CONSTRUCTION — GEOMETRY DEFINITION

Staged construction is the most important type of Loading input. In this special PLAXISfeature it is possible to change the geometry and load configuration by deactivating orreactivating loads, volume clusters or structural objects as created in the geometry input.Staged construction enables an accurate and realistic simulation of various loading,construction and excavation processes. The option can also be used to reassign materialdata sets or to change the water pressure distribution in the geometry. To carry out astaged construction calculation, it is first necessary to create a geometry model thatincludes all of the objects that are to be used during the calculation.

A staged construction analysis can be executed in a Plastic calculation as well as aConsolidation analysis or flow calculation. In the Parameters tabsheet, the Stagedconstruction option can be selected in the Loading input box (except for a flowcalculation). On subsequently clicking on the Define button, the Input program is startedin the staged construction window.

The staged construction window consists of two different modes:

The Staged construction mode and the Water conditions mode. The Staged constructionmode can be used to activate or deactivate loadings, soil clusters and structural objectsand to reassign material data sets to clusters and structural objects. In addition to thesefacilities, staged construction allows for the prestressing of anchors. The Waterconditions mode can be used to generate a new water pressure distribution based on theinput of a new set of phreatic levels or on a groundwater flow calculation using a new setof boundary conditions.

Switching between the Staged construction mode and the Water conditions mode can beachieved by clicking the appropriate blue button in the toolbar. After the new situation hasbeen defined, the Update button should be clicked to store the information and return tothe Calculations program. In addition, the next calculation phase may be defined or thecalculation process may be started.

Changes to the geometry configuration or the water conditions generally causesubstantial out-of-balance forces. These out-of-balance forces are stepwise applied to

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the finite element mesh using a Load advancement ultimate level procedure. During astaged construction calculation, a multiplier that controls the staged construction process(ΣMstage) is increased from zero to the ultimate level (generally 1.0). In addition, aparameter representing the active proportion of the geometry (ΣMarea) is updated.

5.8.1 CHANGING GEOMETRY CONFIGURATION

Clusters or structural objects may be reactivated or deactivated to simulate a process ofconstruction or excavation. This can be done by clicking on the object in the geometrymodel. When clicking once on an object, the object will change from active to inactive,and vice versa. If more than one object is present on a geometry line (for example platesand distributed loads), a selection window appears from which the desired object can beselected.

Active soil clusters are drawn in the material data set colour whereas deactivated clustersare drawn in the background colour (white). Active structural objects are drawn in theiroriginal colour, whereas deactivated structures are drawn in grey.

When double clicking a structural object, the corresponding properties window appearsand the properties can be changed.

In the Select window that appears after double clicking a soil cluster, you can eitherchange the material properties (Section 5.8.5) or apply a volume strain to the selectedcluster (Section 5.8.6).

Interfaces can be activated or deactivated individually. Deactivation of interfaces may beconsidered in the following situations:

• To avoid soil-structure interaction (slipping and gapping) e.g. before a sheet pile wallor tunnel is installed in the soil (when corresponding plate elements are inactive).

• To avoid blocking of flow before a structure composed of plate elements is active.

In any case, interface elements are present in the finite element mesh from the verybeginning. However, the following special conditions are applied to inactive interfaces:

• Purely elastic behaviour (no slipping or gapping).

• Fully coupled pore pressure degrees-of-freedom in node pairs (no influence on flowin consolidation or groundwater calculations).

5.8.2 ACTIVATING AND DEACTIVATING CLUSTERS OR STRUCTURAL OBJECTS

Soil clusters and structural objects can be activated or deactivated by clicking once onthe cluster or structural object in the geometry model in the Staged construction mode.Anchors may only be active if at least one of the soil clusters or plates to which they areconnected is also active; otherwise the calculations program deactivates themautomatically.

At the start of a staged construction calculation the information about active and inactiveobjects in the geometry model is transformed into information on an element level.Hence, deactivating a soil cluster results in ‘switching off’ the corresponding soil elementsduring the calculation.

The following rules apply for elements that have been switched off:

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• Properties, such as weight, stiffness and strength, are not taken into account.

• All stresses are set to zero.

• All inactive nodes will have zero displacements.

• Boundaries that arise from the removal of elements are automatically taken to befree and permeable. In the case of groundwater flow or consolidation, theseboundaries allow for free outflow of water if not specified otherwise.

• Steady-state pore pressures (not excess pore pressures) are always taken intoaccount, even for inactive elements. This means that PLAXIS will automaticallygenerate suitable water pressures on submerged boundaries caused by the removalof elements. This may be checked when entering the Water conditions mode. On’excavating’ (i.e. deactivating) clusters below the general phreatic level, theexcavation remains filled with water. If, on the other hand, it is desired to remove thewater from the excavated part of the soil, then a new water pressure distributionshould be defined in the Water conditions mode. This feature is demonstrated in theTutorial Manual.

• External loads or prescribed displacements that act on a part of the geometry that isinactive will not be taken into account.

For elements that have been inactive and that are (re)activated in a particular calculation,the following rules apply:

• Stiffness and strength will be fully taken into account from the beginning (i.e. the firststep) of the calculation phase.

• Weight will, in principle, be fully taken into account from the beginning of thecalculation phase. However, in general, a large out-of-balance force will occur at thebeginning of a staged construction calculation. This out-of-balance force is stepwisesolved in subsequent calculation steps.

• The stresses will develop from zero.

• When a node becomes active, an initial displacement is estimated by stresslesspredeforming the newly activated elements such that they fit within the deformedmesh as obtained from the previous step. Further increments of displacement areadded to this initial value. As an example, one may consider the construction of ablock in several layers, allowing only for vertical displacements (one-dimensionalcompression). Starting with a single layer and adding one layer on top of the first willgive settlements of the top surface. If a third layer is subsequently added to thesecond layer, it will be given an initial deformation corresponding to the settlementsof the surface.

• If an element is (re)activated and the Material type of the corresponding materialdata set has been set to Undrained (A) or Undrained (B), then the element willtemporarily behave «drained» in the phase where the element was activated. This isto allow for the development of effective stresses due to the self weight in the newlyactivated soil. If the element remains active in later calculation phases, then theoriginal type of material behaviour is retained in those phases.

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5.8.3 ACTIVATING OR CHANGING LOADS

By default, all loads will be inactive in the initial phase, but they can be reactivated usinga staged construction process. As in the case of structural objects, loads can beactivated or deactivated by clicking once on the load in the geometry model. Active loadsare drawn in their original colour, whereas deactivated loads are drawn in grey.

When activating loads, the actual value of the load that is applied during a calculation isdetermined by the input value of the load and the corresponding load multiplier(ΣMloadA or ΣMloadB).

Input value of a load

By default, the input value of a load is the value as given during the geometry creation.The input value of the load may be changed in each calculation phase in the frameworkof Staged construction. This can be done by double clicking the load in the geometry.After double clicking a point load the Point load window appears in which the x- andy -components can be entered directly (Figure 5.9).

Figure 5.9 Input window for a point load

After double clicking a distributed load the Distributed load window appears in which thex- and y -components can be entered directly at the two respective geometry points(Figure 5.10). The Perpendicular button may be used to make sure that the distributedload is perpendicular to the corresponding geometry line.

Load labels

When an ULS phase is defined and a design approach is selected in the Stagedconstruction window, the predefined labels (Section 3.6.2) can be assigned to loads byusing the options available in the Load window. The predefined labels are listed in theLabel drop-down menu. The defined value of the selected partial factor is displayed inthe Factor cell. Note that the reference values of the load are displayed when the Showreference values option is selected at the bottom of the window.

Load multiplier

The actual value of the load that is applied during a calculation is determined by theproduct of the input value of the load and the corresponding load multiplier (ΣMloadA orΣMloadB). The multiplier ΣMloadA is used to globally increase (or decrease) all loads ofload system A (point loads and distributed loads), whereas ΣMloadB is used to changeall loads of load system B (Section 5.11.1). However, in general it is not necessary to

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Figure 5.10 Input window for a distributed load

change the load multipliers when applying or changing loads by means of stagedconstruction since the program will initially set the corresponding multiplier to unity.

5.8.4 APPLYING PRESCRIBED DISPLACEMENTS

Prescribed displacements that were created in the geometry input are not automaticallyapplied during calculations, but they can be activated by means of a staged constructionprocess. As long as prescribed displacements are not active, they do not impose anycondition on the model. Hence, at parts of the model where prescribed displacementshave been defined that are currently inactive, the nodes are fully free. Similar as forloads, prescribed displacements can be activated or deactivated by selecting and clickingonce on the prescribed displacement in the geometry. Active prescribed displacementsare drawn in their original colour, whereas inactive prescribed displacements are drawn ingrey.

If it is desired to temporarily ‘fix’ the nodes where prescribed displacements are created,the input value of the prescribed displacement should be set to 0.0 rather thandeactivating the prescribed displacement. In the former case a prescribed displacementof zero is applied to the nodes, whereas if the prescribed displacement is deactivated thenodes are free.

When activating prescribed displacements, the actual value of the prescribeddisplacement that is applied during a calculation is determined by the input value of theprescribed displacement and the corresponding load multiplier (ΣMdisp).

Input value of prescribed displacement

By default, the input value of a prescribed displacement is the value given during thegeometry creation. The input value of the load may be changed in each calculationphase using a staged construction procedure. This can be done by double clicking theprescribed displacement in the geometry. As a result, a prescribed displacement windowappears in which the input values of the prescribed displacement can be changed.

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Figure 5.11 Input window for a prescribed displacement

Prescribed displacement labels

When an ULS phase is defined and a design approach is selected in the Stagedconstruction window, the predefined labels (Section 3.6.2) can be assigned to prescribeddisplacements by using the options available in the Prescribed displacement window.The predefined labels are listed in the Label drop-down menu. The defined value of theselected partial factor is displayed in the Factor cell. Note that the reference values of theprescribed displacement are displayed when the Show reference values option isselected at the bottom of the window.

Corresponding multiplier

The actual value of the prescribed displacement that is applied during a calculation isdetermined by the product of the input value of the prescribed displacement and thecorresponding load multiplier (ΣMdisp). The multiplier ΣMdisp is used to globallyincrease (or decrease) all prescribed displacements (Section 5.11.1). However, ingeneral it is not necessary to change the multiplier when applying or changing prescribeddisplacements by means of a staged construction process since the program will initiallyset the corresponding multiplier to unity.

5.8.5 REASSIGNING MATERIAL DATA SETS

The option to reassign material data sets may be used to simulate the change of materialwith time during the various stages of construction. The option may also be used tosimulate soil improvement processes, e.g. removing poor quality soil and replacing it withsoil of a better quality.

On double clicking a soil cluster or structural object in the geometry model, the propertieswindow appears (Figure 5.12) in which the material data set of that object can bechanged.

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Figure 5.12 Soil properties window

The material data set of the cluster can be changed by clicking the Change button. As aresult, the material data base is presented with all existing material data sets. It is eitherpossible to change the data in the material data set itself or to assign another (alreadyexisting or newly created) data set to the cluster or object (see also Chapter 4). However,it is not possible to delete a material data set. At the start of the calculations, the data inthe material data sets are stored for each calculation phase separately, so that the Outputprogram can always show the data used during the calculations. However, changing thedata of a material data set in one calculation phase will also change the data of thismaterial data set in all other calculation phases calculated after this change.

After selecting the appropriate material data set from the data base tree view and clickingthe OK button the data set is assigned to the soil cluster or structural object.

In addition, it is possible to change the material data set of a cluster or object by firstopening the material database by clicking the Materials button in the toolbar, select

the appropriate material data set and then using the drag-and-drop procedure (seeSection 4.8).

The change of certain properties, for example when replacing peat by dense sand, canintroduce substantial out-of-balance forces. These out-of-balance forces are solvedduring the staged construction calculation. This is the most important reason why thereassignment of material data sets is considered to be a part of a staged constructionprocess.

If a change in the data set of a plate is considered it is important to note that a change inthe ratio EI/EA will change the equivalent thickness deq and thus the distance separatingthe stress points. If this is done when existing forces are present in the beam element, itwould change the distribution of bending moments, which is unacceptable. For thisreason, if material properties of a plate are changed during an analysis it should be notedthat the ratio EI/EA must remain unchanged.

5.8.6 APPLYING A VOLUMETRIC STRAIN IN VOLUME CLUSTERS

In PLAXIS you can impose an internal volumetric strain in soil clusters. This option maybe used to simulate mechanical processes that result in volumetric strains in the soil,such as grouting or thermal expansion. In the properties window that appears afterdouble clicking a soil cluster, you can click the Volume strain button.

In the Volume strain window that appears you can specify the volumetric strain. Inaddition, an estimation of the total volume change is given in the unit of volume per unit of

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Figure 5.13 Volume strain window

width in the out-of-plane direction.

An Anisotropic volumetric strain can be assigned to a soil cluster by selecting the Applyanisotropic volumetric stain option in the window. The components of the volumetricstrain in x, y and z direction (εx , εy , εz ) can be defined.

In contrast to other types of loading, volume strains are not activated with a separatemultiplier. Note that the imposed volume strain is not always fully applied, depending onthe stiffness of the surrounding clusters and objects.

A positive value of the volume strain represents a volume increase (expansion), whereasa negative value represents a volume decrease (compaction).

5.8.7 PRESTRESSING OF ANCHORS

Prestressing of anchors can be activated in the Staged construction mode. Therefore thedesired anchor should be double clicked. As a result, the Anchor window appears, whichindicates by default no prestress. On selecting the Adjust prestress check box it ispossible to enter a value for the prestress force in the corresponding edit box. A

prestress force should be given as a force per unit of width in the out-of-plane direction.Note that tension is considered to be positive and compression is considered negative.

To deactivate a previously entered prestress force, the Adjust prestress parameter mustbe deselected rather than setting the prestress force to zero. In the former case theanchor force will further develop based on the changes of stresses and forces in thegeometry. In the latter case the anchor force will remain at zero, which is generally notcorrect. After the input of the prestress force the OK button should be clicked. As aresult, the Anchor window is closed and the geometry configuration mode is presented,where the prestressed anchor is indicated with a ‘p’.

During the staged construction calculation the prestressed anchor is automaticallydeactivated and a force equal to the prestress force is applied instead. At the end of thecalculation the anchor is reactivated and the anchor force is initialised to match theprestress force exactly, provided that failure had not occurred. In subsequent calculationsthe anchor is treated as a spring element with a certain stiffness, unless a new prestress

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force is entered.

5.8.8 APPLYING CONTRACTION OF A TUNNEL LINING

To simulate soil volume loss due to the construction of a shield tunnel, the contractionmethod may be used. In this method a contraction is applied to the tunnel lining tosimulate a reduction of the tunnel cross section area. The contraction is expressed as apercentage, representing the ratio of the area reduction and the original outer tunnelcross section area. Contraction can only be applied to circular tunnels (bored tunnels)with an active continuous homogeneous lining (Section 3.4.8).

Contraction can be activated in the Staged construction mode by double clicking thecentre point of a tunnel for which a contraction is to be specified. As a result, the Tunnelcontraction window appears, in which an input value of the contraction increment can beentered. In contrast to other types of loading, contraction is not activated with a separatemultiplier.

As the contraction is applied to the tunnel lining (shell elements) these must be presentand active during the phase a contraction is applied. Note that no contraction can beapplied to a tunnel lining represented by volume elements.

Note that the entered value of contraction is not always fully applied, depending on thestiffness of the surrounding clusters and objects. The computed contraction can beviewed in the output program (Section 7.4.2)

5.8.9 DEFINITION OF DESIGN CALCULATIONS

A design calculation can be defined by assigning a predefined design approach to thephase in the Staged construction tabsheet. Note that the layout of the project of thephase is already defined in the ULS phase. A drop-down menu where the defineddesigned approaches are listed appears in the Staged construction tabsheet.

Figure 5.14 Assignment of design approach to phases

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By default, the Staged construction tabsheet indicates that Reference values will be usedfor loads and model parameters (drop down list at the top left side of the window),meaning that all partial factors are set to unity. For design calculations, the user mustselect the appropriate design approach from the drop-down menu. The list only showsthe design approaches that are available for this project. Note that it is not possible toassign design approaches defined in other projects or available in the Global designapproaches database that are not imported to the current project. More information onassigning labels to loads and prescribed displacements is given in the Section 5.8.3 andthe Section 5.8.4 respectively.

5.8.10 STAGED CONSTRUCTION WITH ΣMSTAGE < 1

In general, the total multiplier associated with the staged construction process, ΣMstage,goes from zero to unity in each calculation phase where staged construction has beenselected as the loading input. In some very special situations it may be useful to performonly a part of a construction stage. This can be done by clicking on the Advanced buttonin the Parameters tabsheet and specifying an ultimate level of ΣMstage smaller than 1.0.The lowest allowed input value is 0.001. If ΣMstage is lower than this value, the load isconsidered to be negligible and no calculations take place. A value larger than 1.0 is notpossible. By entering the default value of 1.0, the staged construction procedure isperformed in the normal way.

In general, care must be taken with an ultimate level of ΣMstage smaller than 1.0, sincethis leads to a resulting out-of-balance force at the end of the calculation phase. Such acalculation phase must always be followed by another staged construction calculation. IfΣMstage is not specified by the user, the default value of 1.0 is always adopted, even if asmaller value was entered in the previous calculation phase.

Tunnel construction with ΣMstage < 1

In addition to the simulation of the construction of shield tunnels using the contractionmethod (Section 5.8.8), it is possible with PLAXIS to simulate the construction process oftunnels with a sprayed concrete lining (NATM). The major point in such an analysis is toaccount for the three-dimensional arching effect that occurs within the soil and thedeformations that occur around the unsupported tunnel face. A method that takes theseeffects into account is described below.

There are various methods described in the literature for the analysis of tunnelsconstructed according to the New Austrian Tunnelling Method. One of these is theso-called Converge confinement method or β-method (Schikora & Fink, 1982), but othershave presented similar methods under different names. The idea is that the initialstresses pk acting around the location where the tunnel is to be constructed are dividedinto a part (1− β) pk that is applied to the unsupported tunnel and a part βpk that isapplied to the supported tunnel (Figure 5.15). The β-value is an ‘experience value’,which, among other things, depends on the ratio of the unsupported tunnel length andthe equivalent tunnel diameter. Suggestions for this value can be found in literature(Schikora & Fink, 1982).

Instead of entering a β-value in PLAXIS, one can use the staged construction option witha reduced ultimate level of ΣMstage. In fact, when deactivating the tunnel clusters aninitial out-of-balance force occurs that is comparable with pk . In the beginning of the

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staged construction calculation, when ΣMstage is zero, this force is fully applied to theactive mesh and it will be stepwise decreased to zero with the simultaneous increase ofΣMstage towards unity. Hence, the value of ΣMstage can be compared with 1− β. Inorder to allow for the second step in the β-method, the ultimate level of ΣMstage shouldbe limited to a value of 1− β while deactivating the tunnel clusters. This can be done byclicking on the Advanced button while the Staged construction option has been selectedfrom the Loading input group of the Parameters tabsheet. In general, care must be takenwith an ultimate level of ΣMstage smaller than 1.0, since this is associated with aresulting out-of-balance force at the end of the calculation phase. In this case the nextcalculation phase is a staged construction calculation in which the tunnel construction iscompleted by activating the tunnel lining. By default, the ultimate level of ΣMstage is 1.0.Hence, the remaining out-of-balance force will be applied to the geometry including thetunnel lining.

1 Pk 2 (1− β)Pk 3 βPk

Figure 5.15 Schematic representation of the β-method for the analysis of NATM tunnels

The process is summarised below:

1. Generate the initial stress field and apply eventual external loads that are presentbefore the tunnel is constructed.

2. De-activate the tunnel clusters without activation of the tunnel lining and apply anultimate level of ΣMstage equal to 1− β.

3. Activate the tunnel lining.

5.8.11 UNFINISHED STAGED CONSTRUCTION CALCULATION

At the start of a staged construction calculation, the multiplier that controls the stagedconstruction process, ΣMstage, is zero and this multiplier is stepwise increased to theultimate level (generally 1.0). When ΣMstage has reached the ultimate level, the currentphase is finished. However, if a staged construction calculation has not properly finished,i.e. the multiplier ΣMstage is less than the desired ultimate level at the end of a stagedconstruction analysis, then a warning appears in the Log info box. The reached value ofthe ΣMstage multiplier may be viewed by selecting the Reached values option in theShow group on the Multipliers tabsheet (Section 5.11.2).

There are three possible reasons for an unfinished construction stage.

• The ultimate value of ΣMstage was reduced using the Advanced stagedconstruction option (Section 5.8.10). Note that the out-of-balance force is still partlyunresolved. The remain out-of-balance forces must be solved in the next calculationphase.

• Failure of the soil body has occurred during the calculation. This means that it is not

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possible to finish the construction stage. Note that the out-of-balance force is stillpartly unsolved so that further calculations starting from the last calculation phaseare meaningless.

• The maximum number of loading steps was insufficient. In this case theconstruction stage should be continued by performing another staged constructioncalculation that is directly started without changing the geometry configuration orwater pressures. Alternatively, the phase may be recalculated using a larger numberof Additional steps. Note that it is advised against applying any other type of loadingas long as the multiplier ΣMstage has not reached the value 1.0.

In the case of an unfinished staged construction calculation, the load that has actuallybeen applied differs from the defined load configuration. The reached value of theΣMstage multiplier may be used in the following way to estimate the load that hasactually been applied:

fapplied = f0 + ΣMstage(fdefined − f0)

where fapplied is the load that has actually been applied, f0 is the load at the beginning ofthe calculation phase (i.e. the load that has been reached at the end of the previouscalculation phase) and fdefined is the defined load configuration.

A reduced ultimate level of ΣMstage may be reduced repetitively. In the case of multiplesubsequent phases with ΣMstage < 1, it should be realized that ΣMstage starts at 0 inevery phase. For example, if three phases are defined, where in phase 1ΣMstage = 0.5; in phase 2 ΣMstage = 0.5 and phase 3 ΣMstage = 1.0 (withoutadditional changes), it means that:

• At the end of phase 1 50% of the unbalance is solved

• At the end of phase 2 50% of the remainig unbalance (= 75% of the initialunbalance) is solved

• At the end of phase 3 100% of the remaining unbalance (= 100%of the initialunbalance) is solved

5.9 STAGED CONSTRUCTION — WATER CONDITIONS

PLAXIS is generally used for effective stress analyses in which a clear distinction is madebetween active pore pressures, pactive, and effective stresses, σ’. In the active porepressures, a further distinction is made between steady-state pore pressures, psteady , andexcess pore pressures, pexcess:

pactive = psteady + pexcess

Excess pore pressures are pore pressures that occur due to loading of clusters for whichthe type of material behaviour in the material data set is specified as Undrained (A) orUndrained (B). In a Plastic analysis, excess pore pressures can be created only in theseundrained clusters. A Consolidation analysis based on excess pore pressure may beused to calculate the time-dependent generation or dissipation of excess pore pressures.In this type of calculation the development of excess pore pressures is determined by thepermeability parameters rather than by the drainage type as specified in the material data

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set. This type of calculation is suitable for applications that involve a horizontal phreaticsurface for which the governing equations can be simplified by decomposing the activepore pressure into a constant component (steady-state pore pressure) and a timedependent component (excess pore pressure).

Steady-state pore pressures are pore pressures that represent a stable hydraulicsituation. Such a situation is obtained when external water conditions remain constantover a long period. To reach a steady-state, it is not necessary that pore pressures, bythemselves, are in static equilibrium (i.e. a horizontal phreatic surface), since situations inwhich permanent groundwater flow or seepage occur may also lead to a stable state.

Water pressures can be generated in the following way:

• By a phreatic level based on a general phreatic level and cluster pore pressuredistribution.

• By a steady-state groundwater flow calculation based on hydraulic boundaryconditions.

• By a transient groundwater flow transient based on time-dependent hydraulicboundary conditions. Although transient flow does not generally give steady-statepore pressures, the pore pressures obtained from this program are treated in adeformation analysis as if they are steady.

• From the previous calculated step.

In addition to, or instead of, a change in the geometry configuration, the water pressuredistribution in the geometry may be changed. Examples of problems that may beanalysed using this option include the settlement of soft soil layers due to a lowering ofthe water table, the deformation and force development of walls or tunnel linings due toexcavation and dewatering, and the stability of a river embankment after an increase ofthe external water level. However, the Water conditions mode may be skipped in projectsthat do not involve water pressures. In this case, a general phreatic level is taken at thebottom of the geometry model and all pore pressures are zero (by default).

5.9.1 WATER UNIT WEIGHT

The properties of water are defined in the Water window (Figure 5.16) which is activatedwhen the corresponding option is selected in the Geometry menu.

Figure 5.16 Water window

In projects that involve pore pressures, the input of a unit weight of water is required todistinguish between effective stresses and pore pressures. By default, the unit weight ofwater is set to 10 kN/m3 or its equivalent value when other units of force or length havebeen chosen.

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5.9.2 PHREATIC LEVEL

Pore pressures and external water pressures can be generated on the basisof phreatic levels. A phreatic level represents a series of points where the water

pressure is just zero. Using the input of a phreatic level, the water pressure will increaselinearly with depth according to the specified water weight (i.e. the pressure variation isassumed to be hydrostatic). Before entering a phreatic level the user must enter thecorrect water weight. The option to enter phreatic levels can be selected from theGeometry menu or by clicking on the corresponding button in the tool bar. The input of aphreatic level is similar to the creation of a geometry line (Section 3.4.1).

Phreatic levels are defined by two or more points. Points may be entered from ‘left’ to’right’ (increasing x-coordinate) or vice versa (decreasing x-coordinate). The points andlines are superimposed on the geometry model, but they do not interact with the model.Crossings of a phreatic levels and existing geometry lines do not introduce additionalgeometry points.

If a phreatic level does not cover the full x-range of the geometry model, the phreatic levelis considered to extend horizontally from the most left point to minus infinity and from themost right point to plus infinity. Below the phreatic level there will be a hydrostatic porepressure distribution, whereas above the phreatic level the pore pressures will be positive(suction) and will increase according to the hydrostatic distribution. This is the case atleast when the water pressure is generated on the basis of phreatic levels.

The generation of water pressures is actually performed when selecting the Generatewater pressures option (Section 5.9.8). The positive pore pressures generated above thephreatic level are cut off according to the pore pressure tension cut-off in the calculationprogram (Section 5.9.1).

Hint: When a steady state calculation of flow is performed, the phreatic leveldefined in the input specifies the boundary conditions of the flow. Thepressure distribution in the model is calculated by the program. The resultingphreatic level can be displayed by selecting the Phreatic level option in theGeometry menu in the Output program (Section 6.2.4).

General phreatic level

If none of the clusters is selected and a phreatic level is drawn, this phreatic level isconsidered to be the General phreatic level. By default, the general phreatic level islocated at the bottom of the geometry model; on entering a new line the old generalphreatic level is replaced. The general phreatic level can be used to generate a simplehydrostatic pore pressure distribution for the full geometry. The general phreatic level is,by default, assigned to all clusters in the geometry.

If the general phreatic level is outside the geometry model and the correspondingboundary is a free boundary, external water pressures will be generated on the basis ofthis surface. This also applies to free boundaries that arise due to the excavation(de-activation) of soil clusters in the framework of staged construction. The calculationprogram will treat external water pressures as distributed loads and they are taken intoaccount together with the soil weight and the pore pressures as controlled by the

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ΣMweight parameter. The external water pressures are calculated such that equilibriumof water pressures is achieved across the boundary. However, if the phreatic levelcrosses the boundary in a non-existing geometry point, the external water pressurescannot be calculated accurately (Figure 5.17).

inaccurate accurate

Figure 5.17 Inaccurate and accurate modelling of external water pressures

This is because the value of the external water pressure is only defined at the two endpoints of the geometry line and the pressure can only vary linearly along a geometry line.Hence, to calculate external water pressures accurately, the general phreatic level shouldpreferably cross the model boundary at existing geometry points. This condition shouldbe taken into account when creating the geometry model. If necessary, an additionalgeometry point should be introduced for this purpose at the geometry boundary.

The general phreatic level can also be used to create boundary conditions for thegroundwater head in the case that pore pressures are calculated on the basis of agroundwater flow calculation (Section 5.9.6).

If a horizontal general phreatic level is required, the general phreatic level can also bedefined by selecting the Set global phreatic level option in the Geometry menu. The Setglobal phreatic level will pop up in which it is either possible to define the general phreaticlevel below the geometry (option below the geometry) or at a specific y -coordinate(option at specific y-coordinate) (see Figure 5.18).

Figure 5.18 Set global phreatic level window

Cluster phreatic level

To allow for a discontinuous pore pressure distribution, each cluster can be given aseparate Cluster phreatic level. In fact, a cluster phreatic level is not necessarily a truephreatic level. In the case of an aquifer layer, the cluster phreatic level represents thepressure height, i.e. the virtual zero-level of the pore pressures in that layer. It should benoted that Cluster phreatic level is ignored in all groundwater flow calculation types.

A cluster phreatic level can be entered by first selecting the cluster for which a separatephreatic level has to be specified and subsequently selecting the Phreatic level option

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from the tool bar or the Geometry menu and entering the phreatic level while the clusterremains selected. When selecting multiple clusters at the same time (by holding the<Shift> key down) and entering a phreatic level, this line will be assigned to all selectedclusters as a cluster phreatic level. The clusters for which no specific cluster phreatic levelwas entered, retain the general phreatic level. To identify which phreatic level belongs toa particular cluster, one can select the cluster and see which phreatic level is indicated inred. If no phreatic level is indicated in red, then another option was chosen for that cluster.

After double clicking on a cluster in the Water conditions mode the Cluster pore pressuredistribution window appears in which it is indicated by means of radio buttons how thepore pressures will be generated for that soil cluster. If a cluster phreatic level wasassigned to the cluster by mistake, it can be reset to the general phreatic level byselecting General phreatic level in this window. As a result, the cluster phreatic level isdeleted unless other clusters share the same cluster-phreatic level. More informationabout the options in the Cluster pore pressure distribution window are given in Section5.9.5.

Time-dependent water level

In case of a groundwater flow (transient) calculation or a Consolidation analysis based ontotal pore pressure with a non-zero time interval, seasonal or irregular variations in waterlevels can be modelled using linear, harmonic or user-defined time distributions. This canbe done by double clicking the water level in the Water conditions mode. As a result, theTime dependent head window appears (see Figure 5.19). After selecting the option Usetime dependent data, distinction can be made between Linear input, Harmonic input orinput by a Table.

Hint: The external parts of the water level must be horizontal, as shown in Figure5.20

Figure 5.19 Time dependent head window

Linear: For a linear variation of groundwater head, the input of the following parametersare required:

∆t This parameter represents the time interval for the calculation

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Figure 5.20 External parts of the water level must be horizontal

phase, expressed in unit of time. Its value is equal to the Timeinterval parameter as specified in the Parameters tabsheet of thePhase list window. The value is fixed and cannot be changed inthe Time dependent head window.

y0 This parameter represents the actual height of the water level,expressed in unit of length. Its value is taken from the water levelas entered for the current calculation phase and cannot bechanged in the Time dependent head window.

∆y This parameter, specified in unit of length, represents theincrease or decrease of the water level in the time interval for thecurrent calculation phase. Hence, together with the time intervalthis parameter determines the rate of the water level increase ordecrease.

Harmonic: The harmonic variation of the groundwater head is described as:

y (t) = y0 + 0.5H sin(ω0t + φ0), with ω0 = 2π/T

in which H is wave height (in unit of length), T is the wave period (in unit of time) and φ0is the initial phase angle.

Table: In addition to the pre-defined functions for variations with time, PLAXIS providesthe possibility to enter user-defined time series. This option can be useful for aback-analysis when measurements are available. After selection of the Table radiobutton, a table appears at the right hand side of the window, as shown in Figure 5.21.Time series can be either entered manually by direct input in this table or by importing atable. The time value should increase with each new line. It is not necessary to useconstant time intervals.

Clicking the Open .txt file button on the right hand side of the window will open theOpen window where the file can be selected. The file must be an ASCII file that can

be created with any text editor. For every line a pair of values (actual time andcorresponding water level value) must be defined, leaving at least one space betweenthem. Note that PLAXIS only supports the English notation of decimal numbers using adot. The resulting graph of the input data is shown in the Graph tabsheet of the Timedependent head window (see Figure 5.22).

5.9.3 CLOSED BOUNDARY

A closed boundary is a geometry boundary where flow (groundwater flow orconsolidation) across this boundary does not occur. This option can be selected by

clicking the Closed boundary button on the tool bar or by selecting the corresponding

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Figure 5.21 Table input for user-defined time-dependent conditions

Figure 5.22 Graph tabsheet of the Time dependent head window

option from the Conditions submenu. The input of a closed boundary is similar to thecreation of a geometry line. However, a closed boundary can only be placed over existinggeometry lines of the geometry model. Note that a closed boundary is effective only if it islocated at the outer boundaries of the geometry of the phase being calculated.

Hint: In contrast to the previous PLAXIS versions, no distinction is made betweenclosed flow and closed consolidation boundaries.

5.9.4 PRECIPITATION

The Precipitation option can be used to specify a general vertical recharge or infiltration(q) due to weather conditions. This condition is applied at all boundaries that representthe ground surface. This option can be selected from the Geometry menu or by clickingon the Precipitation button on the tool bar.

The parameters used to define precipitation are:

q Recharge (infiltration), specified in the unit of length per unit oftime. Negative values can be used to model evapotranspiration

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Figure 5.23 Precipitation window

Hint: It is not possible to have a combination of infiltration and a phreatic lineconditions on inclined surfaces.If the inclined boundary is divided in twopieces by adding an additional geometry point on the spot where the phreaticlevel and the inclined surface intersect, Precipitation can be assigned to thepart of the boundary above the point of intersection.

(evaporation + transpiration).

ψmax Maximum pore pressure head, relative to the elevation of theboundary, specified in the unit of length (default 0.1 length units).

ψmin Minimum pore pressure head, relative to the elevation of theboundary, specified in the unit of length (default -1.0 lengthunits).

At horizontal ground surface boundaries, the full precipitation as specified by the value ofq is applied as a recharge. At inclined ground surface boundaries (slopes) under anangle α with respect to the horizon, a recharge is applied perpendicular to the inclinedboundary with a magnitude qcos(α).

If the resulting pore pressure head at a certain point of a boundary where a positiveprecipitation has been prescribed is increased such that it reaches the value y + ψmax(i.e. the water level comes above the ground surface at a depth of ψmax ) then the water issupposed to run-off. As a result, a constant head boundary condition equal to y + ψmax isapplied instead.

If the resulting pore pressure head at a certain point of a boundary where a negativeprecipitation (evapotranspiration) has been prescribed is below a value y + ψmin (i.e. theupper part of the ground has become unsaturated), then the evapotranspiration issupposed to stop. As a result, a constant head boundary condition equal to y + ψmin isapplied instead.

For transient groundwater flow calculations, a variation of the precipitation in time can bespecified resulting in time-dependent boundary conditions. This can be done by clickingthe Time-dependent option in the Precipitation window. As a result, a Time dependentprecipitation window appears where the time-dependent variation of the precipitation canbe specified after selection of the option Use time dependent data. There is a choicebetween Linear, Harmonic or a user-defined variation using Table input.

Linear: This option can be used to describe the increase or decrease of a condition

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linearly in time. For a linear variation of groundwater head, the input of the followingparameters are required:

∆t This parameter represents the time interval for the calculationphase, expressed in unit of time. Its value is equal to the Timeinterval parameter as specified in the Parameters tabsheet of thePhase list window. The value is fixed and cannot be changed inthe Time dependent precipitation window.

q0 This parameter is the initial specific discharge through thegeometry line under consideration, expressed in unit of lengthper unit of time. Its value is fixed (already specified in thePrecipitation window) and cannot be changed in the Timedependent precipitation window.

∆q This parameter, specified in unit of length per unit of time,represents the increase or decrease of the specific discharge inthe time interval of the current calculation phase.

Harmonic: This option can be used when a condition varies harmonically in time. Theharmonic variation of the water level is described as:

q(t) = q0 + 0.5qA sin(ω0t + φ0), with ω0 = 2π/T

in which qA is amplitude of the specific discharge (in unit of length per unit of time), T isthe wave period (in unit of time) and φ0 is the initial phase angle.

Table: In addition to the pre-defined functions for variations with time, PlaxFlow providesthe possibility to enter user-defined time series. This option can be useful for aback-analysis when measurements are available. After selection of the Table radiobutton, a table appears at the right hand side of the window (see for example Figure5.21). Time series can be either entered manually by direct input in this table or byimporting a table. The time value should increase with each new line. It is not necessaryto use constant time intervals.

Clicking the Open .txt file button on the right hand side of the window will open theOpen window where the file can be selected. The file must be an ASCII file that can

be created with any text editor. For every line a pair of values (actual time andcorresponding water level value) must be defined, leaving at least one space betweenthem. Note that PLAXIS only supports the English notation of decimal numbers using adot. The resulting graph of the input data is shown in the Graph tabsheet of the Timedependent precipitation window.

5.9.5 CLUSTER PORE PRESSURE DISTRIBUTION

After double clicking a cluster, the Cluster pore pressure distribution window will appear(Figure 5.24). The options available, besides the General phreatic level and Clusterphreatic level options (see Section 5.9.2) are explained below.

Interpolation of pore pressures from adjacent clusters or lines

A third possibility to generate pore pressures in a soil cluster is the Interpolate fromadjacent clusters or lines option. This option is, for example, used if a relatively

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Figure 5.24 Cluster pore pressure distribution window

impermeable layer is located between two permeable layers with a different groundwaterhead. The pore pressure distribution in the relatively impermeable layer will not behydrostatic, so it cannot be defined by means of a phreatic level.

On selecting the option Interpolate from adjacent clusters or lines, the pore pressure inthat cluster is interpolated linearly in a vertical direction, starting from the value at thebottom of the cluster above and ending at the value at the top of the cluster below, exceptif the pore pressure in the cluster above or below is defined by means of a user-definedpore pressure distribution. In the latter case the pore pressure is interpolated from thegeneral phreatic level. This option can be used repetitively in two or more successiveclusters (on top of each other). In the case that a starting value for the verticalinterpolation of the pore pressure cannot be found, then the starting point will be basedon the general phreatic level.

Cluster dry

A fast and convenient option is available for clusters that should be made dry or, in otherwords, that should have zero pore pressures. This can be done by selecting the Clusterdry option. As a result, the steady-state pore pressures, generated by means of phreaticlevel or steady state groundwater flow, in that cluster are set to zero and the soil weight isconsidered to be the unsaturated weight.

Note that clusters representing massive (concrete) structures where pore pressuresshould be excluded permanently (like diaphragm walls or caissons) can be specified asNon-porous in the corresponding material data set. It is not necessary to set suchnon-porous clusters to Cluster dry in the Water conditions mode. The dry clusters aretreated as Non-porous material in all types of calculations and consequently no excesspore pressure (and no flow) is generated.

User-defined pore pressure distribution

If the pore pressure distribution in a particular soil cluster is very specific and cannot bedefined by one of the above options, it may be specified as a user-defined pore pressuredistribution.

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The available parameters to define this pore pressure distribution are the vertical level(y -coordinate) where the pore pressure is equal to the reference pressure (yref ), the porepressure at the reference level (pref ) and an increment of pressure (pinc).

If the cluster is (partly) located above the reference level, the pore pressure in that part ofthe cluster will also be equal to the reference pressure. Below the reference level, thepore pressure in the cluster is linearly increased, as set by the value of pinc . Please notethat the values of pref and pinc are negative for pressure and pressure increase withdepth, respectively. A user-defined pore pressure distribution cannot be used tointerpolate pore pressures in other clusters. This should be taken into account when theInterpolate pore pressures from adjacent clusters or lines option is used in the clusterabove or below.

5.9.6 BOUNDARY CONDITIONS FOR FLOW AND CONSOLIDATION

Boundary conditions for flow and consolidation can be defined on outer geometry lines bydouble clicking the geometry line. As a result, the Boundary conditions window willappear (see Figure 5.25) in which the type of boundary condition and the magnitudes canbe entered. By default, all boundaries are set to Free (seepage), except for the bottomboundary of the geometry, which is set to Closed. Apart from the direct input of boundaryconditions in the Boundary conditions window, some frequently used boundary conditionsmay be specified in a more user-friendly way.

Figure 5.25 Boundary conditions window

The boundary conditions necessary for the calculation of steady-state and/or transientgroundwater flow can always be defined in the Boundary conditions window. In this way,water pressures on the basis of a groundwater flow calculation or a Consolidationanalysis based on total pore pressure can be generated taking these boundary conditionsinto account. In case of a Consolidation analysis based on excess pore pressure, onlythe excess pore pressures will be affected by closed boundary conditions only, whereas

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the steady-state pore pressures will be generated on the basis of phreatic levels.

It is not possible to prescribe excess pore pressures as a boundary condition for aConsolidation analysis based on excess pore pressure. Excess pore pressures at thebeginning of a consolidation analysis can only be the result of earlier calculations whereundrained clusters were used, i.e. clusters where the Material type in the correspondingmaterial data set was set to Undrained (A) or Undrained (B). For more information onConsolidation analyses based of excess pore pressures, see Sections 5.5 and 5.6.4 andthe Scientific Manual.

Below the different types of boundary conditions and their input procedures are describedin detail.

Free (seepage)

A free boundary is a boundary where water can flow in or out freely. A free boundary isgenerally used at the ground surface above the phreatic level or above the external waterlevel.

If a boundary is free and completely above the (external) water level, then the seepagecondition applies to this boundary. This means that water inside the geometry may flowfreely out of this boundary. If, at the same time, precipitation is specified, the freeboundary condition automatically turns into an infiltration condition (see below), wherethe infiltration rate is determined by the recharge value of the precipitation. If theboundary is non-horizontal, the precipitation recharge is recalculated into a componentperpendicular to the boundary.

If a boundary is free and completely below the (external) water level, the free boundarycondition automatically turns into a groundwater head condition. In that case themagnitude of the groundwater head in each boundary node is determined by the verticaldistance between the boundary node and the water level.

A geometry point needs to be defined where a (external) water level crosses a geometryboundary line. In this point, the pore pressure is zero. The part of the geometry lineabove the transition point is treated as a boundary above the water level, whereas thepart of the geometry line below the transition point is treated as a boundary below thewater level. Hence, different conditions can apply to such a geometry boundary line. Thisis possible because, in general, a geometry line consists of many nodes and the actualinformation on boundary conditions as used by the calculation program is contained inthe boundary nodes rather than in geometry lines.

Flow problems with a free phreatic level may involve a seepage surface on thedownstream boundary, as shown in Figure 5.26. A seepage surface will always occurwhen the phreatic level touches an open downstream boundary. The seepage surface isnot a streamline (in contrast to the phreatic level) or an equipotential line. It is a line onwhich the groundwater head, h, equals the elevation head y (= vertical position). Thiscondition arises from the fact that the water pressure is zero on the seepage surface,which is the same condition that exists at the phreatic level.

For seepage boundaries the hydraulic head, h, needs to be equal to the vertical position,y , which is the default condition used in PLAXIS. It is not necessary to know the exactlength of the seepage surface before the calculation begins, since the same boundaryconditions (h = y ) may be used both above and below the phreatic level. ‘Free’

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axis of symmetry

seepage surface

Figure 5.26 Flow through an embankment with indication of a seepage surface

boundaries with h = y may therefore be specified for all boundaries where the hydraulichead is unknown. Alternatively, for boundaries well above the phreatic level where it isobvious that a seepage surface does not occur, it may also be appropriate to prescribethose boundaries as closed boundaries. If no specific condition is prescribed for aparticular boundary line, PLAXIS assumes that this boundary is ‘free’ and sets theseepage condition here.

Closed

A closed boundary is a geometry boundary where neither flow nor consolidation acrossthis boundary occurs. This option can also be selected by clicking the Closed boundarybutton on the tool bar (see Section 5.9.3).

Head

Selecting the option Head will use the general phreatic level to calculate the groundwaterhead.

Head (user-defined)

The prescribed groundwater head on external geometry boundaries is, by default,derived from the position of the general phreatic level, at least when the general phreaticlevel is outside the active geometry. Also internal geometry lines that have becomeexternal boundaries due to a de-activation of soil clusters are considered to be externalgeometry boundaries and are therefore treated similarly.

In addition to the automatic setting of boundary conditions based on the general phreaticlevel, a prescribed groundwater head may be entered manually. After double clicking anexisting geometry line, a window appears in which the groundwater head at the twopoints of that line can be entered. On entering the groundwater head at a point, theprogram will display the corresponding pore pressure (pore pressure = water weighttimes [groundwater head minus vertical position]).

A prescribed groundwater head can be removed by selecting the correspondinggeometry line and pressing the <Delete> key on the keyboard, or by selecting anothercondition in the Boundary conditions window.

If a groundwater head is prescribed at an outer geometry boundary, external waterpressures will be generated for that boundary. The deformation analysis program willtreat external water pressures as traction loads and they are taken into account togetherwith the soil weight and the pore pressures.

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Inflow

Inflow is a recharge without further conditions. The inflow can be applied to a boundaryabove the water level by double clicking the corresponding geometry line. In theBoundary conditions window, the inflow option can subsequently be selected and therecharge, q, can be specified at the end points of the geometry line. The programautomatically calculates the distribution over the intermediate boundary nodes.

Outflow

Outflow is a discharge without further conditions. Similar to the inflow condition theoutflow can be applied to a boundary above the water level by double clicking thecorresponding geometry line. In the Boundary conditions window, the outflow option cansubsequently be selected and the discharge, q, can be specified at the end points of thegeometry line. The program automatically calculates the distribution over theintermediate boundary nodes.

Infiltration

For each boundary, the defined precipitation is transformed into infiltration boundaryconditions, which is a conditional inflow. The recharge (q) and the minimum andmaximum pore pressure head (ψmin and ψmax) entered for the precipitation areautomatically applied as infiltration boundary conditions to all free boundaries above thewater level.

Hint: If the boundary is non-horizontal, the precipitation recharge is recalculatedinto a component perpendicular to the boundary and a component parallel tothe boundary.

» When the boundary is non-horizontal and a water level crosses it, theboundary should be consist of two sub-boundaries. The precipitation and thewater level will be effective in the upper and lower sub-boundariesrespectively.

» When the boundary is not defined as consisting of two sub-boundaries, theprecipitation on the non-linear boundary will be ignored.

Apart from the automatic generation of infiltration boundary conditions from precipitation,infiltration conditions may also be specified manually for geometry boundaries above thewater level. To this end, the appropriate geometry line should be double clicked. In theBoundary conditions window the infiltration conditions can be selected and theappropriate infiltration rate (recharge, q) and corresponding minimum and maximum porepressure head (ψmin and ψmax) can be entered (Figure 5.27).

q Recharge (infiltration), specified in the unit of length per unit oftime. Negative values can be used to model evapotranspiration(evaporation + transpiration).

ψmax Maximum pore pressure head, relative to the elevation of theboundary, specified in the unit of length (default 0.1 length units).

ψmin Minimum pore pressure head, relative to the elevation of the

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Figure 5.27 Boundary conditions window for infiltration

boundary, specified in the unit of length (default -1.0 lengthunits).

Time-dependent boundary conditions

Time-dependent conditions can be defined for all options except for Closed. Clicking theTime dependent button in the Boundary conditions window will open the Time dependentcondition window (see Figure 5.28).

Figure 5.28 Time dependent condition window in case of the Head option

When activating the Use time dependent data option in the Time dependent conditionwindow the following options are available:

Linear: This option can be used to describe the increase or decrease of a conditionlinearly in time. For a linear variation of groundwater head, the input of the followingparameters are required:

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∆t This parameter represents the time interval for the calculationphase, expressed in unit of time. Its value is equal to the Timeinterval parameter as specified in the Parameters tabsheet of thePhase list window. The value is fixed and cannot be changed inthe Time dependent head window.

y0 This parameter represents the actual height of the water level,expressed in unit of length. Its value is taken from the water levelas entered for the current calculation phase and cannot bechanged in the Time dependent head window.

∆y This parameter, specified in unit of length, represents theincrease or decrease of the water level in the time interval for thecurrent calculation phase. Hence, together with the time intervalthis parameter determines the rate of the water level increase ordecrease.

For a linear variation of infiltration, inflow or outflow the input of the following parametersare required:

q − 0 This parameter is the initial specific discharge through thegeometry line under consideration, expressed in unit of lengthper unit of time. Its value is fixed (already specified in theBoundary conditions window) and cannot be changed in theTime dependent condition window.

∆q This parameter, specified in unit of length per unit of time,represents the increase or decrease of the specific discharge inthe time interval of the current calculation phase.

Harmonic: This option can be used when a condition varies harmonically in time. Theharmonic variation of the water level is described as:

y (t) = y0 + 0.5H sin(ω0t + φ0), with ω0 = 2π/T

in which H is wave height (in unit of length), T is the wave period (in unit of time) and φ0is the initial phase angle.

In case of infiltration, inflow or outflow, the parameter qA needs to be entered insteadof H. qA represents the amplitude of the specific discharge and is specified in unit oflength per unit of time.

Table: In addition to the pre-defined functions for variations with time, PLAXIS providesthe possibility to enter user-defined time series. This option can be useful for aback-analysis when measurements are available. After selection of the Table radiobutton, a table appears at the right hand side of the window (see for example Figure5.21). Time series can be either entered manually by direct input in this table or byimporting a table. The time value should increase with each new line. It is not necessaryto use constant time intervals.

Clicking the Open .txt file button on the right hand side of the window will open theOpen window where the file can be selected. The file must be an ASCII file that can

be created with any text editor. For every line a pair of values (actual time andcorresponding water level value) must be defined, leaving at least one space between

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them. Note that PLAXIS only supports the English notation of decimal numbers using adot. The resulting graph of the input data is shown in the Graph tabsheet of the Timedependent condition window.

5.9.7 SPECIAL OBJECTS

Several special objects, like interfaces, drains and wells can be activated or de-activatedin the Water conditions mode.

Interfaces and plates

When using interfaces in a consolidation analysis or a groundwater flow calculation, theinterfaces are, by default, fully impermeable, which means that no flow takes placeacross the interface. In this way interfaces have a similar functionality as a Closedboundary, except that interfaces can be used at the inside of a geometry whereas closedboundaries can only be used at the geometry boundary. In this way, interfaces may beused to simulate the presence of an impermeable screen. Plates are fully permeable. Infact, it is only possible to simulate impermeable walls or plates when interface elementsare included between the plate elements and the surrounding soil elements. On the otherhand, if interfaces are present in the mesh it may also be the user’s intension to explicitlyavoid any influence of the interface on the flow process, for example in extendedinterfaces around corner points of structures (Section 3.4.5). In such a case the interfaceshould be de-activated in the Water conditions mode. This can be done separately for aconsolidation analysis and a groundwater flow calculation. For inactive interfaces theexcess pore pressure degrees-of-freedom of the interface node pairs are fully coupledwhereas for active interfaces the excess pore pressure degrees-of-freedom are fullyseparated.

In conclusion:

• An active interface is fully impermeable (separation of excess pore pressuredegrees-of-freedom of node pairs).

• An inactive interface is fully permeable (coupling of excess pore pressuredegrees-of-freedom of node pairs).

Drains

Drains are used to prescribe lines inside the geometry model where (excess) porepressures are reduced. Drains can be activated or de-activated just by clicking the

drain. The pore pressure head of drains can be modified only when the type of porepressure generation of the phase is set to Groundwater flow (steady state or transient).When the drain is double clicked in the Water conditions mode , the Drains windowappears in which the pore pressure head can be specified Figure 5.29. Drains appear asblue dashed lines in the water mode if they are active and grey dashed lines if they areinactive.

Hint: In a Consolidation analysis based on excess pore pressure, the excess porepressures in a drain will be set to zero rather than using the defined porepressure head.

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Figure 5.29 The Drains window

Wells

Wells are used to prescribe points inside the geometry model where a specific flux(discharge) is extracted from or infiltrated into the soil. To select the type of well(extraction of infiltration) and the amount of discharge, the user should double click in themiddle of the well line. The Well window will appear (Figure 5.30) in which the type ofwell (Extraction or Infiltration), discharge and minimum groundwater head (in case of anextraction well) can be specified. The minimum groundwater head is used to limit thesuction pore pressure in the case that the well is located in unsaturated area. This headis by default equal to the well elevation (y-coordinate) however any value can be chosen.

Figure 5.30 The Well window

5.9.8 WATER PRESSURE GENERATION

After the input of phreatic levels and/or the input of boundary conditions, the waterpressures can be generated. This can be done by selecting the appropriate type ofgeneration of water pressures from the tool bar (Figure 5.31).

Figure 5.31 Types of water pressure generation

Generated water pressures may be used as input data for a deformation analysis. Thewater pressures are not active until they are actually applied in a calculation. Activation of

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water pressures is associated with the activation of the soil weight using the ΣMweightparameter. In principle, stress points in elements with a zero steady pore pressure areconsidered to be unsaturated whereas stress points that have a non-zero steady porepressure are considered to be saturated. Hence, the value of the pore pressuredetermines whether the saturated soil weight (γsat ) or the unsaturated soil weight (γunsat )is applied in a deformation analysis. In the Advanced mode, the actual weight that isapplied depends on the actual degree of saturation S:

γapplied = (1− Se)γunsat + Seγsat

where

Se =S − Smin

Ssat − Smin

Generate by phreatic level

The water pressure generation by Phreatic level is based on the input of a generalphreatic level, cluster phreatic levels and other options as described in Section 5.9.2

and Section 5.9.5. This generation is quick and straightforward.

When generating water pressures on the basis of phreatic levels when some clusters areinactive, no distinction is made between active clusters and inactive clusters. This meansthat steady pore pressures are generated both for active clusters and inactive clustersaccording to the corresponding phreatic level or user-defined pore pressure distribution.If it is desired to exclude water pressures in certain clusters, the Cluster dry option shouldbe used or a cluster phreatic level should be defined below the cluster.

After selection of the option Generate by phreatic level, the Water pressures buttoncan be clicked to start the calculation of the water pressures. After the generation of

water pressures the Output program is started and a plot of the water pressures and thegeneral phreatic level is displayed. To return to the Input program, the Close buttonshould be clicked.

Groundwater flow steady-state

Geotechnical engineers regularly need to deal with pore pressuresand groundwater flow when solving geotechnical problems. Many situations involve

permanent flow or seepage. Dams and embankments are subjected to permanentseepage of groundwater. Similarly, permanent flow occurs around retaining walls whichseparate different groundwater levels. Flow of this sort is governed by pore pressuresthat are more or less independent of time. Hence, these pore pressures can beconsidered to be steady-state pore pressures. PLAXIS includes a steady-stategroundwater flow calculation module. The water pressure generation by Groundwatercalculation is based on a finite element calculation using the generated mesh, thepermeabilities of the soil clusters and the hydraulic boundary conditions (prescribedgroundwater head, inflow, outflow and closed flow boundaries; see Section 5.9.6). Thisgeneration is more complex and therefore more time consuming than a generation bymeans of phreatic levels, but the results can be more realistic, provided that theadditional input parameters are properly selected.

When clusters have been de-activated in the Staged construction mode (Section 5.8.2),

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the inactive clusters do not take part in the groundwater flow calculation itself, but thepore pressure at stress points within the inactive clusters is determined afterwards fromthe general phreatic level. Hence, if inactive clusters are located (partly) below thegeneral phreatic level, there will be a hydrostatic water pressure distribution below thegeneral phreatic level, whereas the water pressure above the general phreatic level ispositive in these clusters. The water pressure generation window allows for a directswitch to the geometry configuration mode to activate or de-activate clusters. This can bedone by clicking on the Staged construction button. After the desired selection has beenmade, you can return to the water pressure generation window by clicking on the Waterconditions button in the tool bar.

When using interfaces in a groundwater flow calculation, the interfaces are, by default,fully impermeable. In this way interfaces may be used to block the flow perpendicular tothe interface, for example to simulate the presence of an impermeable screen. Plates arefully permeable. For more information about interfaces and plates in flow calculations,see Section 5.9.7.

A steady-state groundwater flow calculation may be used for confined as well as forunconfined flow problems. The determination of the position of the free phreatic surfaceand the associated length of the seepage surface is one of the main objectives of anunconfined groundwater flow calculation. In this case it is necessary to use an iterativesolution procedure. For confined flow problems, however, an iterative solution procedureis not strictly necessary, since a direct solution can be obtained. Nevertheless, whenperforming a groundwater flow calculation in PLAXIS the user must select the settings forthe control parameters of the iterative procedure, since it is not clear beforehand whetherthe flow is confined or unconfined. In general, the implemented Standard settings may beused, which will normally lead to an acceptable solution. Alternatively, the user mayspecify the control parameters manually (see Section 5.7.1).

Generation of the water pore pressures by a steady-state groundwater flow calculationwill be done in the calculation program, prior to the deformation analysis.

Groundwater flow transient

In addition to steady-state groundwater flow, PLAXIS allows for a time-dependentcalculation of pore water pressures in saturated and unsaturated conditions due to

changing boundary conditions on the groundwater head with time. This option isavailable in the list of Water generation if a value is entered for the time interval in thecalculation program. The results of such a transient flow calculation, i.e. thetime-dependent distribution of pore pressures, can be used as input data for adeformation analysis. This option requires the presence of the PlaxFlow module, which isavailable as an extension to PLAXIS 2D. The definition of a time-dependent distributionof pore pressures can only be done during the definition of calculation stages. It is notavailable during the definition of the initial conditions.

In case of performing a groundwater flow calculation, inactive clusters do not take part inthe groundwater flow calculation itself, but the pore pressure at stress points within thede-activated clusters is determined afterwards from the general phreatic level. Hence, ifinactive clusters are located (partly) below the general phreatic level, there will be ahydrostatic water pressure distribution below the general phreatic level, whereas thewater pressure above the general phreatic level is zero in these clusters. The boundarybetween active and inactive clusters is considered to be a free boundary so that water

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can flow across such a boundary. In order to make such a boundary impermeable, theboundary must be closed. To do this, click the Closed boundary button and draw a linealong the geometry. Please note that this option has changed in PLAXIS 2D compared toprevious PLAXIS versions.

Generation of the water pore pressures by groundwater flow will be done in thecalculation program. According to the type of calculation and the activated loads, thegroundwater flow calculation is performed parallel to or before the deformation analysis.If the out of balance force of the current phase is only due to the change in the pore waterpressure and the type of groundwater flow is transient, then the groundwater flow anddeformation can be done in parallel, otherwise the groundwater flow is done prior to thedeformation analysis.

From previous calculated step

As the pore pressure can also be a result of calculation (for example Consolidationanalysis based on total pore pressure), this option can be used to indicate that the

calculation kernel should use the pore pressures of the previous step (phase) instead ofthe pore pressures generated in the current phase.

5.10 CALCULATION USING DESIGN APPROACHES

PLAXIS 2D enables multiple calculations of the defined phases in design approaches.Note that the layout of the Staged construction window has changed. Besides the layoutof the project for the selected phase, the design approach to be used should be selectedin the drop-down menu. By default the Reference values are selected.

The partial factors for materials and the loads are already defined in the Input program.However, in the Staged construction window, besides the activations of the loads, thecorresponding labels should be assigned as well.

5.11 LOAD MULTIPLIERS

During a deformation analysis, it is necessary to control the magnitude of all types ofloading. In general, loads are activated in the framework of staged construction byentering an appropriate input value. Nevertheless, the loadings to be applied arecalculated from the product of the input value of the load and the correspondingmultiplier. Hence, as an alternative to staged construction, loads can globally beincreased by changing the corresponding multiplier. Distinction is made betweenIncremental multipliers and Total multipliers. Incremental multipliers represent theincrement of load for an individual calculation step, whereas total multipliers represent thetotal level of the load in a particular calculation step or phase. The way in which thevarious multipliers are used depends on the Loading input as selected in the Parameterstabsheet. Both the incremental multipliers and the total multipliers for a particularcalculation phase are displayed in the Multipliers tabsheet (Figure 5.32). All incrementalmultipliers are denoted by M … whereas all total multipliers are denoted by ΣM …. Amultiplier does not have a unit associated with it, since it is just a factor.

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Figure 5.32 Multipliers tabsheet of the Calculations window

Input values and reached values

The input values of the multipliers might differ from the values that were actually reachedafter the calculation. This may be the case if failure of the soil body occurs. The radiobuttons in the Show group can be used to display either the Input values or the Reachedvalues.

If the Reached values option is selected another group box appears in which some othermultipliers and calculation parameters are displayed.

5.11.1 STANDARD LOAD MULTIPLIERS

Descriptions of the various load multipliers are given below.

MdispX, ΣMdispX, MdispY, ΣMdispY

These multipliers control the magnitude of prescribed displacements as entered in theStaged construction mode (Section 5.8.4). The total value of the prescribed displacementapplied in a calculation is the product of the corresponding input values as entered in theStaged construction mode and the parameters ΣMdispX and ΣMdispY . When applyingprescribed displacements by entering an input value of prescribed displacement in thestaged construction mode, and the value of ΣMdispX or ΣMdispY is still zero, thismultiplier is automatically set to unity. The values of ΣMdispX and ΣMdispY may beused to globally increase or decrease the applied prescribed displacement. Incalculations where the Loading input was set to Incremental multipliers, MdispX andMdispY are used to specify a global increment of the prescribed displacement in the firstcalculation step.

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MloadA, ΣMloadA, MloadB, ΣMloadB

These multipliers control the magnitude of the distributed loads and point loads asentered in the load systems A and B (Section 5.8.3). The total value of the loads of eitherload system applied in a calculation is the product of the corresponding input values asentered in the Staged construction mode and the parameter ΣMloadA or ΣMloadBrespectively. When applying loads by entering an input value of load in the Stagedconstruction mode, and the value of the corresponding multiplier is still zero, thismultiplier is automatically set to 1.0. The values of ΣMloadA and ΣMloadB may be usedto globally increase or decrease the applied load. In calculations where the Loading inputwas set to Incremental multipliers, MloadA and/or MloadB are used to specify a globalincrement of the corresponding load systems of the first calculation step.

Mweight, ΣMweight

It is possible in PLAXIS to carry out calculations in which gravity loading is applied to theproblem. The multipliers Mweight and ΣMweight control the proportion of standardgravity applied in the analysis and thus the portion of the material weights (soil, water andstructures) as specified in the Input program. The total proportion of the material weightsapplied in a calculation is given by the parameter ΣMweight . In calculations where theLoading input was set to Incremental multipliers, Mweight is used to specify theincrement of weight in the first calculation step.

The multiplier is applied to the material weights as well as to the water weight. Hence, ifΣMweight is zero then the soil weight is not taken into account and all water pressures(excluding eventual excess pore pressures generated during undrained loading) will alsobe zero. If ΣMweight is set to 1.0 then the full soil weight and water pressures will beapplied. A value of ΣMweight larger than 1.0 is generally not used, except for thesimulation of a centrifuge test.

Maccel, ΣMaccel

These multipliers control the magnitude of the pseudo-static forces as a result of theacceleration components as entered in the Project properties window of the Inputprogram (Section 3.1.1). The total magnitude of the acceleration applied during thecalculation is the product of the input values of the acceleration components and theparameter ΣMaccel . Initially, the value of ΣMaccel is set to zero. In calculations wherethe Loading input was set to Incremental multipliers, Maccel can be used to specify theincrement of acceleration of the first calculation step.

Pseudo-static forces can only be activated if the weight of the material is already active(ΣMweight = 1). For ΣMweight = 1 and ΣMaccel = 1 both gravity forces andpseudo-gravity forces are active. The figure below gives an overview of differentcombinations of soil weight and acceleration. Note that the activation of an accelerationcomponent in a particular direction results in a pseudo-static force in the oppositedirection. When increasing ΣMweight without increasing ΣMaccel the resulting force willbe increased without a change of the resulting direction.

Msf, ΣMsf

These multipliers are associated with the Safety option in PLAXIS for the computation ofsafety factors (Section 5.5.5). The total multiplier ΣMsf is defined as the quotient of the

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g

-a

r

rrr

Σ-MWeight = 1Σ-MWeight = 1Σ-MWeight = 1 Σ-MWeight = 2

Σ-Maccel = 1Σ-Maccel = 1Σ-Maccel = 0 Σ-Maccel = -1

(r = resulting direction)

Figure 5.33 Resulting force direction r due to combinations of gravity and acceleration a

original strength parameters and the reduced strength parameters and controls thereduction of tanϕ and c at a given stage in the analysis. ΣMsf is set to 1.0 at the start ofa calculation to set all material strengths to their unreduced values. Msf is used to specifythe increment of the strength reduction of the first calculation step. This increment is bydefault set to 0.1, which is generally found to be a good starting value.

5.11.2 OTHER MULTIPLIERS AND CALCULATION PARAMETERS

Descriptions of the other multipliers and calculation parameters displayed when theoption Reached values has been selected are given below.

Stiffness

As a structure is loaded and plasticity develops then the overall stiffness of the structurewill decrease. The Stiffness parameter gives an indication of the loss of stiffness thatoccurs due to material plasticity. The parameter is a single number that is 1.0 when thestructure is fully elastic and reduces in magnitude as plasticity develops.

At failure the value is approximately zero. It is possible for this parameter to havenegative values if softening occurs.

Force-X, Force-Y

These parameters indicate the forces corresponding to the non-zero prescribeddisplacements (Section 3.5.8). In plane strain models, Force-X and Force-Y areexpressed in the unit of force per unit of width in the out-of-plane direction. Inaxisymmetric models, Force-X and Force-Y are expressed in the unit of force per radian.In order to calculate the total reaction force under a circular footing simulated byprescribed displacements, Force-Y should be multiplied by 2π. Force-X and Force-Y arethe value of the total force in the x- and y -directions respectively, applied to non-zeroprescribed displacements.

Pmax

The Pmax parameter is associated with undrained material behaviour and represents themaximum absolute excess pore pressure in the mesh, expressed in the unit of stress.During undrained loading in a plastic calculation Pmax generally increases, whereas

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Pmax generally decreases during a consolidation analysis. Note that in case of aConsolidation analysis based on total pore pressure the Pmax parameter represents themaximum absolute total pore pressure in the mesh.

ΣMstage

The ΣMstage parameter is associated with the Staged construction option in PLAXIS(Section 5.8). This total multiplier gives the proportion of a construction stage that hasbeen completed. Without input from the user, the value of ΣMstage is always zero at thestart of a staged construction analysis and at the end it will generally be 1.0. It is possibleto specify a lower ultimate level of ΣMstage using the Advanced option of the Parameterstabsheet. However, care should be taken with this option. In calculations where theloading input is not specified as Staged construction, the value of ΣMstage remains zero.

5.11.3 DYNAMIC MULTIPLIERS

When performing a Dynamic analysis, multipliers are used to activate the dynamic loadsby clicking on the Dynamics button to the right of the multipliers ΣMdispX , ΣMdispY ,ΣMloadA and ΣMloadB in the Multipliers tabsheet. Note that independent multiplierscan be used for the horizontal (x) and the vertical (y) components of prescribeddisplacements. The Dynamic loading window will appear in which it is possible to definea harmonic load (option Harmonic load multiplier) or to read a dynamic load multiplierfrom a data file (option Load multiplier from data file), see Figure 5.34. The Dynamicsbutton is only available if the corresponding load is set as dynamic load in the Loadsmenu of the Input program.

Figure 5.34 Dynamic loading window

The active load that is used in a dynamic calculation is the product of the input value ofthe load, as specified in the Input program, and the corresponding dynamic loadmultiplier:

Active load = Dynamic multiplier ∗ Input value (5.1)

Harmonic loads

In PLAXIS harmonic loads are defined as:

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F = M̂ F̂ sin (ω t + φ0)

in which

M̂ Amplitude multiplier

F̂ Input value of the load, as defined in the Input program

ω 2π f with f = Frequency in Hz

φ0 Initial phase angle in degrees

Hint: A dynamic load can also suddenly be applied in a single time step or substep (block load). In case of a Harmonic load multiplier, a block load can bemodelled by setting the Amplitude multiplier equal to the magnitude of theblock load, the Frequency to 0Hz and Initial phase angle to 90◦ giving therelation F = M̂ F̂ . In case of a Load multiplier from data file, a block loadcan directly be defined.

Load multiplier from data file

Besides harmonic loading there is also the possibility to read data from a file withdigitised load signal. This file may be in plain ASCII or in SMC format. Note that PLAXISonly supports the English notation of decimal numbers using a dot.

In case of a dynamic prescribed displacement, a selection has to be made whether theinput has to be considered as Displacements, Velocities or Accelerations. The velocitiesand accelerations are converted into displacements in the Calculations program, takinginto account the time step and integration method.

Hint: PLAXIS assumes the data file is located in the current project directory whenno directory is specified in the Dynamic loading window.

» Note that the signal is considered to start from rest. The value of the velocityor acceleration at the starting time (t = 0) should be 0.

The option Drift correction is used to correct the displacement drift. Due to the integrationof the accelerations and velocities, a drift might occur in the displacements. Thedisplacement drift is corrected by applying a low frequency motion from the beginning ofthe calculation and by correcting the acceleration accordingly.

ASCII file: An ASCII file can be created by the user with any text editor. In every line apair of values (actual time and corresponding multiplier) is defined, leaving at least onespace between them. The time should increase in each new line. It is not necessary touse constant time intervals.

If the time steps in the dynamic analysis are such that they do not correspond with thetime series given in the file, the multipliers at a given (Dynamic) time will be linearlyinterpolated from the data in the file. If the Dynamic time in the calculation is beyond thelast time value in the file a constant value, equal to the last multiplier in the file, will be

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used in the calculations.

SMC file: In addition, it is possible to use earthquake records in SMC-format as input forearthquake loading. The SMC (Strong Motion CD-ROM) format is currently used by theU.S. Geological Survey National Strong-motion Program to record data of earthquakesand other strong vibrations. This format uses ASCII character codes and provides textheaders, integer headers, real headers, and comments followed by either digitisedtime-series coordinates or response values. The header information is designed toprovide the user with information about the earthquake and the recording instrument.

Most of the SMC files contain accelerations, but they may also contain velocity ordisplacement series and response spectra. It is strongly recommended to use correctedearthquake data records, i.e. time series, that are corrected for final drift and non-zerofinal velocities.

The strong motion data are collected by the U.S. Geological Survey and are availablefrom the National Geophysical Data Center (NGDC) of the National Oceanic andAtmospheric Administration. Information on NGDC products is available on theWorld-wide Web at http://www.ngdc.noaa.gov/hazard or by writing to:

National Geophysical Data Center NOAA/EGC/1325 BroadwayBoulder, Colorado 80303USA

Hint: The unit of length used in the SMC files is [cm], so accelerations are given in[cm/s2]. This has consequences for the input value of the prescribeddisplacements.

SMC files should be used in combination with prescribed boundary displacements at thebottom of a geometry model. When using the standard unit of length [m] it is necessaryto use input values of 0.01 [m] for prescribed displacements. Alternatively, when using aunit of length of [ft] it is necessary to use input values of 0.0328 [ft] (1/[feet in cm]) forprescribed displacements. In this way the SMC file can directly be used for dynamicanalysis of earthquakes.

5.12 SENSITIVITY ANALYSIS & PARAMETER VARIATION

After a project has been completely defined, the Calculations program allows for ananalysis of the influence of variations of parameters on the computational results.Preferably, the project should have been calculated and the user should have verified thatthe project is consistent and the results are useable. Variations that can be consideredinclude mainly model parameters of material data sets for Soil and interfaces, Plates,Geogrids and Anchors and are referred to as Material variations. These variations ofmodel parameters can be done by performing a Sensitivity analysis to analyse theinfluence of individual parameter variations on the results, or performing a Parametervariation to analyse the upper and lower bounds of results.

Note that it is not possible to perform a Sensitivity analysis or a Parameter variation to

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study small geometric variations such as a variation in water pressures or a variation inthe magnitude of a load. These small geometric variations and combinations ofgeometric variations must be made manually on a copy of the original project.

Sensitivity analysis and Parameter variation analysis are supported for Linear Elasticmodel, Mohr-Coulomb model, Hardening Soil model, HS small model, Soft Soil model,Soft Soil Creep model, Jointed Rock model and Modified Cam-Clay model.

5.12.1 SENSITIVITY ANALYSIS

The Sensitivity option is used to analyse the influence of individual parameter variationson the results with the purpose to evaluate the relative influence of those parameters.The relative influence (sensitivity) is evaluated on the basis of a user-defined criterion; forexample the horizontal displacement of a particular node. Please note that nodes orstress points used in these criteria can only be taken from the set of nodes and stresspoints that have been selected for load-displacement curves or stress-strain curves (seeSection 8.1).

In a Sensitivity analysis the upper and lower bound values of parameters are variedindividually. If n is the number of parameters to be varied, the total number of completecalculations is 2n + 1 (where +1 is a copy of the original project). Note that for n > 2 thenumber of calculations required for a sensitivity analysis is less than the number ofcalculations required for Parameter variation. Therefore, it may be efficient to first performa sensitivity analysis in order to identify the parameters with the largest influence on theresults, and then perform a parameter variation analysis with a reduced number ofparameters to be varied.

5.12.2 PARAMETER VARIATION

The Parameter variation option is used to analyse the upper and lower bounds of resultsby performing complete calculations for all combinations of the upper and lower boundvalues of the parameters to be varied. In this respect, a complete calculation involves alldefined calculation phases after the initial phase. If n is the number of parameters to bevaried, the total number of complete calculations is 2n + 1 (where +1 is a copy of theoriginal project). Hence, if n is a large number, the complete analysis may take hours oreven days to perform. Some parameters will have a larger influence on the variation ofresults than others, and there may be even parameters whose influence on the variationof results is negligible. Therefore, it may be useful to analyse the influence of individualparameter variations during a Sensitivity analysis first and then perform the Parametervariation analysis with only those parameters that have a significant influence.

5.12.3 DEFINING VARIATIONS OF PARAMETERS

Both the Sensitivity and the Parameter variation option can be selected from theCalculate submenu. To define the variations of parameters, select the Run analysisoption in the corresponding menu. As a result, a new window appears showing an emptylist of material variations (Figure 5.35).

To define variations of model parameters, click on the Define button in the Materialvariations group box. As a result, a new window opens with tabsheets for the differenttypes of material data sets, i.e. Soil and interfaces, Plates, Geogrids and Anchors. Each

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Figure 5.35 Sensitivity analysis and Parameter variation window

tabsheet shows the corresponding predefined material data sets. After selecting a dataset from the list of predefined sets, the lower part of the window shows the correspondingparameters with their input value.

A parameter for which a variation is considered can be selected by clicking on thecorresponding check box. The lower and upper bound values of the parameter can bespecified in the Min and Max boxes behind the original input value. The Min-value mustbe smaller or equal to the input value. The Max-value must be larger or equal to the inputvalue. If not all of the model parameters fit in the window, a scroll bar is available at theright-hand side, which may be used to reach the model parameters below the visibleones. After all desired parameters have been selected and their upper and lower boundvalues have been specified, press the OK button to return to the Sensitivity or Parametervariations window. The selected parameters are now listed in this window. The check boxbefore each parameter can be used to select whether or not to take the variation of theparameter into account.

5.12.4 STARTING THE ANALYSIS

After all variations of parameters have been defined and the desired parameters havebeen selected in the Sensitivity or Parameter variation window, the analysis can bestarted by pressing the Run button. The Analysis info group box at the bottom of theSensitivity or Parameter variation window shows the total number of calculations that isrequired, which is 2n + 1 for a Sensitivity analysis or 2n + 1 for a Parameter variationanalysis, where n is the number of model parameters to be varied. The calculationprogram creates copies of the original project (Project_#) inside the <Project>.P2DTSfolder for a Sensitivity analysis or the <Project>.P2DTP folder for Parameter variation.Project_1 is always a copy of the original project with its original model parameters,whereas Project_# (with #>2) are copies in which the material data in the data.plxmatfile is changed according to the defined material variations.

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Figure 5.36 Material parameters window

When clicking the Preview variations button in the Sensitivity analysis window orParameter variation window, a list of all copies with their corresponding parameter

values can be viewed. In case of the Parameter variation, this overview is also givenwhen selecting the option View permutations in the Parameter variation submenu of theCalculate menu of the Calculations program.

All projects are passed on to the PLAXIS Calculation manager (see Section 5.13.3). TheCalculation manager controls the execution of the calculations and shows the status.When all calculations have finished, the Calculation manager window will be closed andthe results can be evaluated.

5.12.5 SENSITIVITY — VIEW RESULTS

The result of a Sensitivity analysis is an overview of the relative influence (sensitivity) ofthe parameter variations. This sensitivity is evaluated on the basis of user-definedcriteria. Criteria can be based on nodal displacements, stress or strain components orthe factor of safety (if the project involves a Safety analysis). The points used for thesecriteria can be selected from the set of points as defined for load-displacement curves orstress-strain curves. These points have to be predefined for the original project, beforethe sensitivity analysis is started. The results of the Project_1 are used as referencevalues for the calculation of the parameter sensitivity. See Chapter 6 of the ScientificManual for background information on the calculation of sensitivities.

To view the result of a sensitivity analysis, select the View results in the Sensitivitysubmenu of the Calculate menu. When doing so, a new window appears (Figure 5.37).The upper part of the window is used to define the criteria on the basis of which thesensitivity is evaluated.

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Figure 5.37 Sensitivity analysis results window

To add a criterion, the following steps need to be performed:

1. Select the Calculation phase from which the results are considered.

2. Select Displacement, Stress/Strain or Factor of safety from the Criterion group box.

3. Select the desired point (node or stress point) from the Point combo box.

4. Select the desired displacement, stress or strain component from the Result combobox.

5. Click Add to add the criterion to the list of selected criteria.

6. If necessary, select and add more criteria. Each of the defined criteria has the same’weight’. To give a criterion a ‘double weight’, it should be added twice. A falselyadded criterion can be removed by selecting it from the list of selected criteria andpressing the Remove button.

Hint: In the case when the Factor of safety criterion is selected, the user shouldmake sure that a failure mechanism has fully developed by viewing thedevelopment of ΣMsf for the whole calculation using the Curves option(Chapter 8). If a failure mechanism has not fully developed, then thecalculation of the original phase must be repeated with a larger number ofadditional steps (Section 5.5.5).

» The copies of the original project (Project_#) the ones in which the materialdata in the data.plxmat file is changed according to the defined materialvariations are available in the <Project>.P2DTS folder.

The lower part of the window is used to show the sensitivity of all varied parameters onthe basis of the selected criteria, both in graphical form in the Graph tabsheet as intabulated form in the Table tabsheet. Moreover, the Parameter variation tabsheet isavailable to directly select the parameters that will be taken into account in a Parametervariation analysis.

On the Graph tabsheet the sensitivity of a parameter is indicated by the size of thecorresponding green bar. The parameters that will be taken into account in a subsequentParameter variation analysis can be de-selected by clicking on the corresponding bar. By

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doing so, the bar colour changes from green to red. Clicking once again will select thecorresponding parameter. The selected parameters are also shown in the Parametervariation tabsheet. On the Table tabsheet an overview is given of the different copies ofthe original project, their parameter values, the absolute results of the different criteriaand the parameter sensitivity score. On the basis of the sensitivity scores, the totalsensitivity of a particular parameter is defined as the sum of the two correspondingparameter sensitivity scores divided by the total sum of sensitivity scores.

If it is desired to modify the upper and lower values of model parameters and to perform anew sensitivity analysis, the New sensitivity analysis button at the bottom of the windowshould be pressed. By doing so, the Sensitivity window is opened, where new upper andlower values can be defined.

Figure 5.38 The Sensitivity analysis window showing the Parameter variation tabsheet

From the Sensitivity results window you can directly start a Parameter variation analysisusing the Parameter variation tabsheet. On this tab sheet you can select the parametersthat should be taken into account in the Parameter variation analysis, and start theanalysis by pressing the Run button. When parameters have been selected on the Graphtabsheet (‘green’ bar), they will automatically have a check mark in the Parametervariation tabsheet.

5.12.6 PARAMETER VARIATION — CALCULATE BOUNDARY VALUES

Before the results of a Parameter variation can be viewed, upper and lower values of loadmultipliers, displacements and structural forces from all parameter variation results needto be collected and stored in separate project files. This is not automatically done afterparameter variation, but you can perform this action by selecting the Calculate boundaryvalues option in the Parameter variation submenu of the Calculate menu. As a result, asmall window appears in which the original project is shown. To start the collection ofupper and lower values, press the Start button. The program will now create anotherfolder named <Project>.P2DTM, in which copies of the original project are created,named <Project>_MIN and <Project>_MAX. In the corresponding project datadirectories (<Project>_MIN.P2D and <Project>_MAX.P2D), the output filescorresponding to the last step of each calculation phase are modified such that they willcontain the minimum (maximum) values of load multipliers, the minimum (maximum)nodal displacements and the minimum (maximum) structural forces per node of structuralelements from all parameter variation results. After this action has been finished, the

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upper and lower values can be viewed and processed in a similar way as the results of a’normal’ calculation using the Output program.

5.12.7 VIEWING UPPER AND LOWER VALUES

To view the upper (maximum) or lower (minimum) values of load multipliers,displacements, and structural forces, resulting from the parameter variation analysis,select the Open option from the File menu. In the file requester, select the<Project>.P2DTM directory and subsequently the <Project>_MAX.P2D or<Project>_MIN.P2D project. Select the desired calculation phase and press the Outputbutton. Alternatively, the Output program can be started and the desired calculationphase of the Minimum or Maximum project can be opened. Results can be viewed as forany PLAXIS project. Minimum and Maximum values may be compared by opening theMinimum and Maximum project simultaneously.

Hint: Results collected in the Minimum or Maximum project may come fromdifferent parameter variations and may therefore show discontinuities orpresent a situation that is not in equilibrium.

5.12.8 VIEWING RESULTS OF VARIATIONS

To view the results of individual parameter variations or combinations of parametervariations, the corresponding copy of the original project (Project) can be opened in theCalculation window or the Output window using the same procedures as for a normalPLAXIS project. The results of parameter variations are stored in the <Project>.P2DTSor <Project>.P2DTP folder. In order to see which of the copies contain which parametervariations, the Overview button in respectively the Sensitivity analysis window or theParameter variation window may be used (see also Section 5.12.4). In case of theParameter variation, this overview is also given when selecting the option Viewpermutations in the Parameter variation submenu of the Calculate menu of theCalculations program.

5.12.9 DELETE RESULTS

Results from a Sensitivity analysis or Parameter variation can be removed by selectingthe Delete results option in the corresponding submenu of the Calculate menu. By doingso, the <Project>.P2DTS folder or the <Project>.P2DTP folder respectively, includingall data in this folder, will be deleted.

5.13 STARTING A CALCULATION

When a calculation phase has been defined, its calculation can be started.

5.13.1 PREVIEWING A CONSTRUCTION STAGE

When a construction staged is fully defined, a preview of the situation is presented on thePreview tabsheet of the Calculations window. This option is only available if the Staged

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construction option has been selected as Loading input to define the calculation phase. Itenables a direct visual check of construction stages before the calculation process isstarted.

5.13.2 SELECTING POINTS FOR CURVES

After the calculation phases have been defined and before the calculationprocess is started, some points may be selected by the user for the generation of

load-displacement curves or stress paths by clicking the Select points for curves buttonor by selecting this option in the Tools menu.

Nodes should be selected to plot displacements, whereas stress points should beselected to plot stresses and strains. Selection of points is described in detail in Section8.1.

5.13.3 EXECUTION OF THE CALCULATION PROCESS

When calculation phases have been defined and points for curves have been selected,then the calculation process can be executed. Before starting the process, however, it isuseful to check the list of calculation phases. In principle, all calculation phases indicatedwith a blue arrow (→) will be executed in the calculation process. By default, whendefining a calculation phase, it is automatically selected for execution. A previouslyexecuted calculation phase is indicated by a green tick mark (

√) if the calculation was

successful, otherwise it is indicated by a red cross (×). To select or deselect a calculationphase for execution, the corresponding line should be double clicked .

Alternatively, the right hand mouse button may be clicked on the corresponding line andthe option Mark calculate or Unmark calculate should be selected from the cursor menu.

Starting the calculation process

The calculation process can be started by clicking the Calculate button in the toolbar. This button is only visible if a calculation phase is focused that is selected for

execution, as indicated by the blue arrow. Alternatively, the Current project option can beselected from the Calculate menu. As a result, the program first performs a check on theordering and consistency of the calculation phases. In addition, the first calculation phaseto be executed is determined and all selected calculation phases in the list aresubsequently executed, provided that failure does not occur. To inform the user about theprogress of the calculation process, the active calculation phase will be focused in the list.

Multiple projects

In addition to the execution of the calculation process of the current project it is possibleto select more projects for which calculations have to be executed subsequently. This canbe done by selecting the Multiple projects option from the Calculate menu.

As a result the Calculation manager window appears (Figure 5.39). The toolbar in thiswindow has the following options, which are also available from the Calculation menu:

Pause This option will pause the execution of the calculation process.After selecting the Calculate option, the execution of thecalculation process will be continued.

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Calculate This option will start the calculation process.

Stop This option will stop the whole calculation process.

Add This option will open the file requester to select another project toadd to the list.

Remove This option will remove the selected project from the list.

Remove all This option will remove all projects from the list.

The options Completed calculations, Waiting calculations and Failed calculations fromthe View menu can be used to filter the projects.

Figure 5.39 Calculation manager window

5.13.4 ABORTING A CALCULATION

If, for some reason, the user decides to abort a calculation, this can be done by pressingthe Stop button in the separate window that displays information about the iterationprocess of the current calculation phase.

If the Stop button is pressed, the total specified load will not be applied. In Phases list thephase is preceded by a red cross and in the General tabsheet of the Phases window thefollowing message is displayed in the Log info box: Cancelled.

In addition to aborting a calculation permanently, it is also possible to abort thecalculation temporarily by clicking the Pause button. The calculation will be resumed afterclicking the Resume button.

5.13.5 OUTPUT DURING CALCULATIONS

During a 2D finite element deformation analysis, information about the calculationprocess is presented in a separate window (Figure 5.40). The phase being calculated isindicated in the Phase tabs.

Kernel information

Start time The time indicating the start of the calculation is displayed.

Memory used The memory occupied by the calculation process is displayed.

Total multipliers at the end of the previous loading step∑MdispX ,

∑MdispY Indicates the portion of the defined prescribed displacement

applied in the current phase.∑MloadA,

∑MloadB Indicates the portion of the defined load applied in the current

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Figure 5.40 The Active tasks window.

phase.∑Mweight Indicates the total proportion of the material weights applied in a

calculation.Its value is 0 at the beginning of the calculation andchanges to 1.000, indicating that all the materials weight isapplied.∑

Maccel The value of this parameter is always 0 as PLAXIS 2D does notconsider acceleration.∑

Msf This parameter is related to the Safety analysis. It is defined asthe ratio of the original strength parameters and the reducedstrength parameters at a given stage of analysis. Its value is1.000 at the beginning of an analysis. The increment of thestrength reduction of the first calculation step is described inSection 5.5.5.∑

Mstage It gives the completed proportion of a plastic calculation. Itsvalue is always 0 at the start of the calculation and it will be1.000 at the end of a successful calculation. For other analysistypes (Consolidation and Safety) it is always 0.

Pexcess,max It represents the excess pore pressure in the mesh, expressed inthe units of stress. Pexcess,max is available in the deformationcalculation tabsheet of the Active task window for all the

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calculation types available in the Classical mode and for thePlastic and the Safety calculation types in the Advanced mode.

Pactive,max It represents the active pore pressure in the mesh, expressed inthe units of stress. Pactive,max is available in the deformationcalculation tabsheet of the Active task window for theConsolidation calculation types in the Advanced mode.

Psteady ,max It represents the steady state pore pressure in the mesh,expressed in the units of stress. Psteady is available in the flowcalculation tabsheet of the Active task window for all thecalculation types.∑

Marea It indicates the proportion of the total area of soil clusters in thegeometry model that is currently active.∑

Fx ,∑

Fy These parameters indicate the reaction forces corresponding tothe non-zero prescribed displacements.

Stiffness The Stiffness parameter gives an indication of the amount ofplasticity that occurs in the calculation. The Stiffness is definedas:

Stiffness =∫

∆ε ·∆σ∆εDe∆ε

When the solution is fully elastic, the Stiffness is equal to unity,whereas at failure the stiffness approaches zero. The Stiffness isused in determining the Global error. See Section 5.13.9 formore details.

Time The current time within the specified time interval of the loadinginput for the calculated phase, defined in the Parameterstabsheet of the Phases window.

Dyn. time The current dynamic time within the specified time interval of theloading input for the calculated phase, defined in the Parameterstabsheet of the Phases window.

Calculation progress

A small load-displacement curve for the pre-selected nodes for curves is shown in theCalculation progress group box. By default, the curve is shown for the first selected node.Curve for other pre-selected nodes is shown when the node is selected in the drop-downmenu. The presented graph may be used to roughly evaluate the progress of thecalculation.

Plastic analysis For a plastic analysis the development of the∑

Mstageparameter is plotted against the displacement.

Consolidation analysis In case of a Consolidation analysis, the maximum excess porepressure, Pexcess,max , in case of a Consolidation analysis basedon excess pore pressure or the maximum active pore pressure,Pactive,max , in case of a Consolidation analysis based on totalpore pressure is plotted against the logarithm of time.

Safety analysis In case of Safety analysis, the development of∑

Msf is plottedagainst the displacement.

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Dynamic analysis In case of Dynamic analysis, the displacement is plotted againstthe logarithm of time.

Free vibration In case of Free vibration, the displacement is plotted against thelogarithm of time.

Groundwater flow (steady-state)In case of Groundwater flow (steady-state), the maximum steadypore pressure, Psteady ,max , at steady state is plotted.

Groundwater flow (transient)In case of Groundwater flow (transient), the maximum steadypore pressure, Psteady ,max , is plotted against the logarithm oftime.

Iteration process of current step

Current step Indicates the number of the current calculation step.

Iteration Indicates the number of the iterations in the current calculationstep.

Global error The value of this error is an indication of the global equilibriumerror within the calculation step. As the number of iterationsincreases, its value tend to decrease. For further details on thisparameter see Section 5.13.9.

Max. local error in flow The value of this error is an indication of possible entrapment ofwater in saturated regions in the current calculation step. Thetolerated value is 0.05.

Relative change in saturationThe value is an indication of variation of saturation degree inconsecutive calculation steps. The tolerated value is 0.1. Whenthe relative change in saturation is higher than the tolerate value,the time step is automatically decreased. When the relativechange in saturation is lower than the tolerate value, the timestep is automatically increased. Note that the values of the timestep are always in the range defined by Desired minimum andDesired maximum parameters.

Relative change in relative permeabilityThe value is an indication of variation of relative permeability inconsecutive calculation steps. The tolerated value is 0.1. Whenthe relative change in relative permeability is higher than thetolerate value, the time step is automatically decreased. Whenthe relative change in relative permeability is lower than thetolerate value, the time step is automatically increased. Note thatthe values of the time step are always in the range defined byDesired minimum and Desired maximum parameters.

Max. step Indicates the last step number of the current calculation phaseaccording to the Additional steps defined in the Parameterstabsheet in the Phases window.

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Max. iterations The value of Maximum iteration steps for the calculated phase,defined for the Iterative procedure in the Parameters tabsheet ofthe Phases window.

Tolerance This value indicates the maximum global equilibrium error that isallowed. The value of the tolerance corresponds to the value ofthe Tolerated error in the settings for the iterative procedure. Theiteration process will at least continue as long as the Global erroris larger than the Tolerance. For details see Section 5.13.9.

Element The number of soil elements in the calculated phase.

Decomposition Progress of the decomposition of the phase being calculated.

Calc. time Indicates the calculation time of the current calculation step.

Plastic points in current step

Plastic stress points The total number of stress points in soil elements that are inplastic state.

Plastic interface point The total number of stress points in interface elements that are inplastic state.

Inaccurate This value indicates the number of plastic stress points in soilelements and interface elements respectively, for which the localerror exceeds the tolerated error.

Tolerated This value indicates the maximum number of inaccurate stresspoints in soil elements and interface elements respectively thatare allowed. The iteration process will at least continue as longas the number of inaccurate points is larger than the toleratednumber.

Tension points A Tension point is a point that fails in tension. These points willdevelop when the Tension cut-off is used in any of the materialsets in the model. This parameter indicates the total number ofpoints that fail in tension.

Cap/Hardening points A Cap point occurs if the Hardening Soil model, HS small modelor Soft Soil Creep model are used and the stress state in a pointis equivalent to the pre-consolidation stress, i.e. the maximumstress level that has previously been reached (OCR ≤ 1.0). AHardening point occurs if the Hardening Soil model or HS smallmodel is used and the stress state in a point corresponds to themaximum mobilised friction angle that has previously beenreached.

Apex points These are special plastic points where the allowable shear stressis zero. The iterative procedure tends to become slow when thenumber of plastic apex points is large. Apex points can beavoided by selecting the Tension cut-off option in the materialdatasets for soil and interfaces.

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Calculation status

The calculation status indicates what part of the calculation process is currently beingexecuted. The following processes are indicated:

Decomposing. . . Decomposing the global stiffness matrix.

Calculating stresses. . . Calculating the strain increments and constitutive stresses.

Writing data. . . Writing output data to disk.

Previewing of intermediate results during calculation

The Preview button in the Active tasks window enables previewing the results of theintermediate calculation steps of the phase being calculated. The intermediate steps arelisted in the drop-down menu (Section 6.3.9) and the list is updated when the calculationof new intermediate steps is complete.

The results of the intermediate calculation steps can be used in curves as well. When acurve is created, the newly calculated steps can be included in the plot by using theRegenerate button available in the Settings window (Section 8.5).

Note that when the calculation of the phase is completed, a warning will appear indicatingthat the intermediate results are no longer available. A more detailed description on howto display the results of a calculated phase is given in Section 5.13.6.

5.13.6 SELECTING CALCULATION PHASES FOR OUTPUT

After the calculation process has finished, the calculation list is updated. Calculationphases that have been successfully finished are indicated by a green tick mark (

√),

whereas phases that did not finish successfully are indicated by a red cross (×). Inaddition, messages from the calculations are displayed in the Log info box of the Generaltabsheet.

When a calculation phase is selected that has been executed, the tool bar will showthe View results button. Clicking this button will directly display the results of the

selected phase in the Output program.

5.13.7 RESET STAGED CONSTRUCTION SETTINGS

If a calculation phase has been defined using the Staged construction option andsubsequently changes are made to previous phases these changes are not carried outinto the subsequent phases as is the case when a staged construction phase is definedfor the first time. It is of course possible to also make these changes manually in allsubsequent staged construction phases but sometimes it is more practical to clear theStaged construction settings and start over. It is possible to clear the staged constructionsettings and set them to those of the preceeding staged construction phase by firstselecting the corresponding phase in the list of calculation phases, click the right mousebutton and then select the option Reset staged construction from the popup menu.Similarly the water conditions can be reset to those of the preceeding staged constructionphase by selecting the option Reset water conditions from the popup menu.

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5.13.8 ADJUSTMENT TO INPUT DATA IN BETWEEN CALCULATIONS

Care should be taken with the change of input data (in the Input program) in betweencalculation phases. In general, this should not be done since it causes the input to ceaseto be consistent with the calculation data. In most cases there are other ways to changedata in between calculation phases instead of changing the input data itself.

Modification of geometry

When the geometry is slightly modified (small relocation of objects, slight modification oftheir geometry or deleting objects) in the Input program, the program will try to regenerateall data related to construction stages as soon as mesh regeneration is performed.However, in the Calculations program, the user has to check the construction stagescarefully, since some settings may not have been generated properly. The calculationprocess must restart from the initial phase.

If significant changes in the geometry are made then all settings need to be redefined,since PLAXIS is not able to properly regenerate the settings automatically.

Modification of material parameters and feature properties

When changing material properties in existing data sets without changing the geometry,then all calculation information is retained as well. In this case, clusters refer to the samedata sets, but the properties as defined in these data sets have changed. However, thisprocedure is not very useful, since PLAXIS allows for a change of data sets within theStaged construction calculation option (Section 5.8.5). Hence, it is better to create thedata sets that will be used in later calculation phases beforehand and to use the Stagedconstruction option to change data sets during calculations. The same applies to achange in water pressures and a change in input values of existing loads, since the latteris also possible using the Staged construction option (Sections 5.8 and 5.9).

5.13.9 AUTOMATIC ERROR CHECKS

During each calculation step, the PLAXIS calculation kernel performs a series ofiterations to reduce the out-of-balance errors in the solution. To terminate this iterativeprocedure when the errors are acceptable, it is necessary to establish theout-of-equilibrium errors at any stage during the iterative process automatically.

Two separate error indicators are used for this purpose, based on the measure of eitherthe global equilibrium error or the local error. The values of both of these indicators mustbe below predetermined limits for the iterative procedure to terminate. These two errorindicators and the associated error checking procedures are described below.

Global error check

The global error checking parameter used in the PLAXIS calculation kernel is related tothe sum of the magnitudes of the out-of-balance nodal forces. The term ‘out-of-balancenodal forces’ refers to the difference between the external loads and the forces that are inequilibrium with the current stresses. To obtain this parameter, the out-of-balance loadsare non-dimensionalised as shown below:

Global error =Σ ‖Out of balance nodal forces‖

Σ ‖Active loads‖ + CSP · ‖Inactive loads‖

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In case of a flow calculation, the out-of-balance nodal flux will be used instead of theout-of-balance nodal forces.

CSP is the current value of the Stiffness parameter, defined as:

Stiffness =∫

∆ε ·∆σ∆εDe∆ε

which is a measure for the amount of plasticity that occurs during the calculation. See theChapter 2.3 of the Material Models Manualfor more information on the stiffnessparameters. When the solution is fully elastic, the Stiffness is equal to unity, whereas atfailure the Stiffness approaches zero. In the latter case the global error will be larger forthe same out of balance force. Hence, it will take more iterations to fulfill the tolerance.This means that the solution becomes more accurate when more plasticity occurs.

Local error check

Local errors refer to the errors at each individual stress point. To understand the localerror checking procedure used in PLAXIS it is necessary to consider the stress changesthat occur at a typical stress point during the iterative process. The variation of one of thestress components during the iteration procedure is shown in Figure 5.41.

stre

ss

equilibrium stress

constitutive stress

strain

A

B

Figure 5.41 Equilibrium and constitutive stresses

At the end of each iteration, two important values of stress are calculated by PLAXIS. Thefirst of these, the ‘equilibrium stress’, is the stress calculated directly from the stiffnessmatrix (e.g. point A in Figure 5.41). The second important stress, the ‘constitutive stress’,is the value of stress on the material stress-strain curve at the same strain as theequilibrium stress, i.e. point B in Figure 5.41.

The dashed line in Figure 5.41 indicates the path of the equilibrium stress. In general thisequilibrium stress path depends on the nature of the stress field and the applied loading.For the case of a soil element obeying the Mohr-Coulomb criterion, the local error for theparticular stress point at the end of the iteration is defined:

Local error =‖σe — σc‖

Tmax

In this equation the numerator is a norm of the difference between the equilibrium stresstensor, σe, and the constitutive stress tensor, σc . This norm is defined by:

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‖σe−σc‖ =√

(σexx − σc

xx )2 +(σe

yy − σcyy)

2 +(σezz − σc

zz)2+(σe

xy − σcxy)

2 +(σe

yz − σcyz)

2 +(σezx − σc

zx )2

The denominator of the equation for the local error is the maximum value of the shearstress as defined by the Coulomb failure criterion. In case of the Mohr-Coulomb model,Tmax is defined as:

Tmax = max(½(σ’3 − σ’1), c cosϕ)

When the stress point is located in an interface element the following expression is used:

Local error =

√(σe

n − σcn)2 +(τe − τ c)2

ci − σcn tanϕi

where σn and τ represent the normal and shear stresses respectively in the interface. Toquantify the local accuracy, the concept of inaccurate plastic points is used. A plasticpoint is defined to be inaccurate if the local error exceeds the value of the user specifiedtolerated error (see Section 5.4).

Termination of iterations

For PLAXIS to terminate the iterations in the current load step, all of the following threeerror checks must be satisfied. For further details of these error-checking procedures,see Vermeer & van Langen (1989).

Global error ≤ Tolerated error

No. of inaccurate soil points ≤ 3 +No. of plastic soil points

10

No. of inaccurate interface points ≤ 3 +No. of plastic interface points

10

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6 OUTPUT PROGRAM — GENERAL OVERVIEW

This icon represents the Output program. The main output quantities of a finiteelement calculation are the displacements and the stresses. In addition, when a

finite element model involves structural elements, the structural forces in these elementsare calculated. An extensive range of facilities exists within the PLAXIS 2D Outputprogram to display the results of a finite element analysis. This chapter gives adescription of the features available in the program.

If the Output program is activated by running its executable file or by clicking the Outputprogram button in the Calculations program, the user has to select the model and theappropriate calculation phase or step number for which the results are to be viewed(Figure 6.1). More options on how to activate the Output are given in Section 6.3.1.

Figure 6.1 File requester of Output program

When a particular project is selected, the file requester displays the corresponding list ofcalculation phases from which a further selection should be made. If it is desired to selectan intermediate calculation step, then a single mouse click should be given on the plusicon (+) at the left of the desired phase. As a result, the calculation list expands a list withall available step numbers for this phase, from which the desired step number can beselected.

Hint: Please note that the number of the individual steps available depends on thevalue assigned to Max steps saved in the Parameters tabsheet of thePhases window.

Once an output step of a particular project has been opened, the combo box in thetoolbar will contain a list of available output steps, indicated by the step number andcorresponding phase number.

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6.1 LAYOUT OF THE OUTPUT PROGRAM

The layout of the Output program is shown in Figure 6.2:

Figure 6.2 Main window of the Output program

Title bar

The title bar gives information about the project name, the step number and the type ofinformation/results displayed.

Menu bar

The menu bar contains all output items and operations facilities of the Output program(Section 6.2).

Toolbars

Buttons for different features in the Output program are located above and at the left sideof the plot area. A hint about the function of each tool is given as the cursor is located onit.

Plot area

The calculation results are displayed in the Plot area. The results can be displayed ingraphical or tabular form. More information on how to handle the plot is given in Section6.4.

Status bar

The status bar displays the locations of the cursor and the viewpoint and a hint about theobject in the model and their element numbers.

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6.2 MENUS IN THE MENU BAR

The menu bar contains drop-down menus covering the options available in the Outputprogram. The main results from a finite element calculation are deformations andstresses. Hence, these two aspects form the major part of the Output menu. Whendisplaying a basic 2D geometry model, the menu consists of the File, View, Project,Geometry, Mesh, Deformations, Stresses, Tools, Window and Help menus. Note that theavailability of the menus in the bar depends on the type of data that is presented on theoutput form.

6.2.1 FILE MENU

Open project To open the output of an existing project.

Close active project To close all forms of the active project.

Close all projects To close all forms of all opened projects.

Work directory Set the default directory where PLAXIS 2D project files arestored.

Export to file To export the information displayed, depending on theinformation type, to a text file (for results in tables) or image file(for plot).

Report generator To generate a report of the project.

Create animation Create an animation from selected output steps. The Createanimation window is presented.

Print To print the active output on a selected printer.

(List of recent projects) A list of the five most recent projects.

Exit To leave the output program.

6.2.2 VIEW MENU

Zoom out To restore to view before the most recent zoom action.

Reset view To restore the original plot.

Save view To save the current view (image or table). The saved views canbe included in a report of the project.

Show saved views To open or delete saved views.

Scale To modify the scale factor of the presented quantity.

Legend settings To modify the range of values of the presented quantity incontour line plots and plots with shadings.

Scan line To change the scan line for displaying contour line labels. Afterselection, the scan line must be drawn using the mouse. Pressthe left mouse button at one end of the line; hold the mousebutton down and move the mouse to the other end. A contourline label will appear at every intersection of the scan line with acontour line.

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Use result smoothing To reduce the numerical noise resulting from the extrapolation ofthe results obtained in stress points (e.g. stress, force) to nodes.This option is available for plots and tables. Note that the optionis by default selected in plot presentation of the results.

Rulers To toggle the display of the rulers along the active plot.

Title To toggle the display of the title of the active plot in the caption.

Legend To toggle the display of the legend of contours or shadings.

Axes To toggle the display of the global x- and y -axes in the active plot(displayed in the lower right corner).

Local axes To toggle the display of the local 1- and 2-axes of the structures.This option is only available when viewing structures.

Settings To set various graphical attributes, such as object andbackground colours, symbol size, font size and diffuse shading.

Move cross section forwardTo move the created cross section through the model enabling avisual display of the results in the model. This option is availablein the Cross section view.

Move cross section backwardTo move the created cross section through the model enabling avisual display of the results in the model. This option is availablein the Cross section view.

Arrows To display the results as arrows.

Contour lines To display the results as contour lines.

Shadings To display the results as shadings.

Node labels To display the results at nodes.

Stress point labels To display the results at stress points.

Deformation plane To display the deformed shape of cross sections, geogrids orplates.

Distribution plane To project the results perpendicularly to the plane creating adistribution plane for cross sections and plates.

Deformation To display the deformed shape for beams, embedded piles andanchors.

Distribution To project the results perpendicularly to the structure, creating adistribution line for beams, embedded piles and anchors.

Principal directions To display the principal directions in each stress point of the soilelement.

Center principal directionsTo display the principal directions of stresses and strains at thecenter of each soil element.

Coloured principal directionsTo display the principal directions in each stress point of the soil

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element. Colours are used to distinguish the principal directions.

Coloured center principal directionsTo display the principal directions of stresses and strains at thecenter of each soil element. Colours are used to distinguish theprincipal directions.

6.2.3 PROJECT MENU

Input nodes View the table of the geometry input points.

Node fixities View the table of the node fixities.

Load information View the table of the active loads and bending moments in thecurrent step.

Water load information View the table of the external water loads on the geometryboundaries in the current step.

Prescribed displacement informationView the table of the prescribed displacements in the currentstep.

Virtual interface thicknessView the table of the virtual interface thickness.

Applied volume strain View the table of the volume strain resulting at the end of thecalculation phase.

Volume information View the boundaries of the soil volume, the total volume of soiland the volume of each cluster in the project.

Material information (all load cases)View the material data of all load cases.

Material information (current load case)View the material data of the current load case.

General information View the general project information.

Calculation information View the calculation information of the presented step.

Calculation info per phaseView the calculation information for each calculation phase.

Calculation info per stepView the calculation information for each calculation step.

Step info View the step information of the presented step.

Structures per phase View the active structures per calculation phase.

6.2.4 GEOMETRY MENU

Phreatic level Toggle the display of the phreatic level in the model. For phasescalculated in the Classical and Flow modes, the phreatic levelindicates the level of zero steady state water pressure. Forphases calculated in the Advanced mode, the phreatic levelindicates the level of the zero active water pressure.

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Loads Toggle the display of the external loads in the model.

Fixities Toggle the display of the fixities in the model.

Prescribed displacementsToggle the display of the prescribed displacements in the model.

Filter Filter the nodes displayed in the model according to a definedcriteria.

6.2.5 MESH MENU

Quality View the quality of the elements in the mesh defined as innercircle divided by the outer circle of the soil element where anequal sided triangle is normalized at 1.0. The displayed meshelements in the model vary according to the quality valueselected as the yellow bar is dragged through the legend.

Quality table View the table of the quality of the soil elements according todifferent criteria.

Area View the distribution of the area of the soil elements.

Area table View the table of the distribution of the area of the soil elements.

Connectivity plot View the connectivity plot (Section 7.1).

Cluster borders Toggle the display of the cluster borders in the model.

Element contours Toggle the display of the element contours in the model.

Element deformation contoursToggle the display of the deformed element contours in themodel.

Materials Toggle the display of the materials in the model.

Element numbers Toggle the display of the soil element numbers.

Material set numbers Toggle the display of the material set numbers in the soilelements.

Structure material set numbersToggle the display of the material set numbers of the structuralelements.

Group numbering Toggle the display of the group numbers. Groups are createdaccording to the material sets and the assigned designapproaches.

Cluster numbers Toggle the display of the cluster numbers in the soil elements.

Node numbers Toggle the display of the nodes in the model.

Input Nodes To display the input geometry points in the model.

Stress point numbers Toggle the display of the stress points in the model.

Node numbers Toggle the display of the node numbers. Only possible whennodes are displayed.

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Stress point numbers Toggle the display of the stress point numbers. Only possiblewhen stress points are displayed.

Selection labels Toggle the display of the labels of the selected nodes or stresspoints.

6.2.6 DEFORMATIONS MENU

The Deformations menu contains various options to visualise the deformations(displacements, strains), the velocities and the accelerations (in the case of a dynamicanalysis) in the finite element model (Section 7.2). These quantities can be viewed for thewhole analysis (total values), for the last phase (phase values) or for the last calculationstep (incremental values). In principle, displacements are contained in the nodes of thefinite element mesh, so displacement related output is presented on the basis of thenodes, whereas strains are usually presented in integration points (stress points).

6.2.7 STRESSES MENU

The Stresses menu contains various options to visualise the stress state and other stateparameters in the finite element model (Section 7.3). Stresses are contained in theintegration points of the finite elements mesh, so stress related output is presented on thebasis of the integration points (stress points).

6.2.8 FORCES MENU

The Forces menu contains various options to visualise the resulting forces in structuralelements (Section 7.4).

6.2.9 TOOLS MENU

Copy To copy the active output to the Windows clipboard .

Select points for curves To enable selection of nodes and stress points to be consideredin curves. All the nodes and stress points in the project aredisplayed enabling selection by clicking on them. The Selectpoints window is activated, where the location of interest can bedefined and the appropriate nodes or stress points can beselected form the list.

Mesh point selection To activate the Mesh selection window. This option is activewhen the Select points for curves has been previously selectedand the Select points window is closed.

Curves manager To activate the Curves manager (Chapter 8).

Table To open a new form with a table of numerical values of thepresented quantity.

Cross section To select a user-defined cross section with a distribution of thepresented quantity. The cross section must be selected by themouse or by defining two points. Press the left mouse button atone end of the cross section; hold the mouse button down andmove the mouse to the other end of the line. The cross section is

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presented on a new form.

Forces view To open a new form with the possibility to visualise contactstresses and resulting forces on an arbitrary configuration ofelements.

Structural forces in volumesTo compute the forces in a structure which is modeled using soilwith the material properties of the structure (e.g. concrete), afterthe calculation has already been finished. More information onthe usage of this option is given in Section 7.4.8.

Cross section curves To display a plot of the results along the cross sections. Thevalues in the x-axis in the plot are the distances of the pointsfrom the first point in the cross section.

Hint box To display a hint box with information in individual nodes orstress points (if nodes or stress points are displayed).

Cross section points To display the points defining the cross section. These points aredisplayed as greyed out in the Cross section points window.Their location can not be modified. This option is valid only whenthe Cross section view is active.

Distance measurement To measure the distance between two nodes in the model. Thisoption is valid in the Model view only when nodes and/or stresspoints are displayed in the plot.

6.2.10 WINDOW MENU

Project manager To view the projects and forms currently displayed in Output.

Duplicate model view To duplicate the active view.

Close window To close the active output form.

Cascade To cascade the displayed output forms.

Tile horizontally To tile horizontally the displayed output forms.

Tile vertically To tile vertically the displayed output forms.

(List of recent views) A list of the output forms.

6.2.11 HELP MENU

Manuals To display the manuals.

Instruction movies To reach the PLAXIS TV website where instruction movies aredisplayed.

http://www.plaxis.nl/ To reach the PLAXIS website.

Disclaimer The complete disclaimer text is displayed.

About Information about the program version and license are displayed.

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6.3 TOOLS IN THE OUTPUT PROGRAM

Besides displaying the calculation results, the Output program provides tools to handlethe view and enable a better examination of the results. The buttons are grouped in thetoolbar below the menu bar and in the side tool bar. The tools and their functionality isdescribed in the following sections.

6.3.1 ACCESSING THE OUTPUT PROGRAM

All the results are displayed in the Output program. There are different ways to accessthe Output program. Besides the option of activating the program as described at thebeginning of this chapter, the results can be displayed before or after the calculation ofthe phases is completed.

The results that can be displayed before calculating the phases are:

The generated mesh The generated mesh is automatically displayed in the Outputprogram as it is generated in the Input program.

Pore pressures The generated pore pressures can be displayed when they aregenerated according to the phreatic level.

Connectivity plot The Connectivity plot displays the distribution of the finiteelements in the mesh and the nodes and stress points available.The Connectivity plot is displayed when the Select point forcurves button is selected in the Calculations program. A moredetailed description is given in Section 7.1.

Hint: Note that the groundwater calculations are performed when the phase iscalculated. As a result, the pore pressure distribution is available only afterthe phase is calculated.

The calculation results of a project are displayed in the Output program by selecting acalculated phase in the Phases explorer and clicking the View calculation results buttonin the Calculation program.

While the Output program is already active, the results of other projectscan be accessed either by clicking the Open project button or by selecting the

corresponding option in the File menu (Section 6.2.1).

6.3.2 EXPORTING OUTPUT DATA

The PLAXIS 2D Output program enables exporting the displayed results such as plots orvalues. This is possible by clicking the corresponding button in the toolbar.

Copy to clipboard

Data as displayed in output forms may be exported to other programs usingthe Windows clipboard function. When clicking on the Copy to clipboard button, the

Copy window appears in which selections can be made of the various plot componentsthat are to be included in the copy (Figure 6.3).

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Figure 6.3 Copy window

Print

Hardcopies of graphs and tables can be produced by sending the output toan external printer. When the Print button is clicked or the corresponding option is

selected in the File menu, the Print window appears, in which various plot componentsthat are to be included in the hardcopy can be selected (Figure 6.4).

Figure 6.4 Print window

When pressing the Setup button, the standard printer setup window is presented in whichspecific printer settings can be changed. When the Print button is clicked, the plot is sendto the printer. This process is fully carried out by the Windows® operating system.

Hint: When the Copy to clipboard option or the Print option is used on a plot thatshows a zoomed part of the model, only the part that is currently visible willbe exported to the clipboard or the printer.

Export

Data in output forms may be exported to files. When the Export to file button isclicked, the Export window appears. Note that a text scaling factor can be defined.

Instead of the PLAXIS logo in the frame, it is also possible to insert a company logo. Thislogo has to be provided as a bitmap and can be selected in the Print window afterclicking on the logo.

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Figure 6.5 Export window

6.3.3 CURVES MANAGER

Clicking the Curves manager button activates the Curves manager window wherecurves can be generated to evaluate the results at specified locations in the model.

Selection of points of interest and the generation of curves is described in detail inChapter 8.

6.3.4 STORE THE VIEW FOR REPORTS

The views in the Output program can be saved to be used when reportsare generated by clicking on the Store the view for reports button. The Save view

window pops up as the button is clicked. Description can be given to the view in the Saveview window (Figure 6.6) which can be beneficial when the report is generated. Reportgeneration is described in detail in Section 6.6.

Figure 6.6 Save view window

6.3.5 ZOOMING THE PLOT

It is possible to zoom in and out in the view of the plots by scrolling the mouse wheel.Other options for zooming are available by clicking the corresponding buttons in thetoolbar.

As this feature is selected, the mouse can be dragged on the model to define a localzooming rectangle. In the window, only the results in the defined rectangle will be

displayed.

Clicking the Zoom out button or selecting the corresponding option in theView menu (Section 6.2.2) restores the view of before the most recent zoom action.

Clicking the Reset view or selecting the correspondingoption in the View menu (Section 6.2.2) button enables restoring the original plot.

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6.3.6 RELOCATION OF THE PLOT

The plot can be moved using the mouse.

When this button is clicked, the plot will be relocated (moved) by clickingon the plot area and dragging it while keeping the left mouse button pressed.

6.3.7 SCALING THE DISPLAYED RESULTS

Whenever the results are indicated by length entities such as Arrows, Distribution,Axis, etc. (Section 6.3.10), the Scale factor button can be used to receive a better

overview. When the button is clicked or the corresponding option in the View menu isselected, a window pops up (Figure 6.7) where the factor can be defined. Note that thisoption is also available in the right mouse click pop-up menu.

Figure 6.7 Scale factor window

Hint: The default value of the Scale factor depends on the size of the model.» The Scale factor may be used to increase or reduce the displayed (virtual)

thickness of interfaces in the Connectivity plot.

6.3.8 TABLES

The tabular form of the results given in the plot can be obtained by clicking on theTable button or by selecting the corresponding option in the menu. Note that this

option is also available in the right mouse click pop-up menu.

Hint: The table of displacements may be used to view the global node numbersand corresponding coordinates of individual elements.

Displaying of tables

By default, a table is presented in ascending order according to the global elementnumber and local node or stress point. However, a different ordering may be obtained byclicking on the small triangle in the column header of the desired quantity on which theordering should be based. Another click on the same column header changes the

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ordering from ascending to descending.

The options available in the right click pop-up menu are:

Select for curves To select the right clicked point in the table to be considered incurves.

Align To align the text in the selected part of the table.

Decimal To display data in decimal representation.

Scientific To display data in scientific representation.

Decimal digits To define the number of decimal digits displayed.

View factor To define a factor to the values in the table.

Copy To copy the selected values in the table.

Find value To find a value in the table.

Find soil element To find a soil element with a specified ID in the table when theresults are displayed for soil elements.

Find structural element To find a structural element with a specified ID in the table whenthe results are displayed for structures.

Filter To filter the results in the table.

Hint: The values in the tables contain the most accurate information, whereasinformation in plots can be influenced or be less accurate due to smoothingor extrapolation of information from stress points to nodes.

6.3.9 SELECTION OF RESULTS

As the type of result is selected from the Deformations, Stresses or Structures menu, theresults are displayed either in plots or tables according to the selection made.

While the Output program is running, other steps of the project can be selected from thedrop-down list in the toolbar. The button in front of the drop-down menu can be used totoggle between the end results of phases, or individual output steps:

A list of the calculation phases and their final calculation steps is given. The resultsat the end of the final calculation steps can be shown for each phase.

A list the saved calculation steps and the calculation phase they belong to is given.The results of each calculation step can be shown.

In addition to the drop-down menu, the spinner at the right of the drop-down list or usingthe <Ctrl-Up> and <Ctrl-Down> keys will select the end results of the previous or nextcalculation step or calculation phase.

6.3.10 DISPLAY TYPE OF RESULTS

The plot type options are located at the right of the drop-down menu:

The results are displayed as contours.

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The results are displayed as shadings.

The results for Displacements can be displayed as arrows. Scaling of the results ispossible.

The results are displayed at each stress point of the soil elements. The length ofeach line represents the magnitude of the principal quantity (stress or strain) and thedirection indicates the principal direction. Positive direction is indicated by arrows.Scaling of the results is possible.

The average results are displayed at the center of each soil element. The length ofeach line represents the magnitude of the principal quantity (stress or strain) and thedirection indicates the principal direction. Positive direction is indicated by arrows.Scaling of the results is possible.

The results are displayed in different colours at each stress point of the soilelements. The length of each line represents the magnitude of the principal quantity(stress or strain) and the direction indicates the principal direction. Positive directionis indicated by arrows. Scaling of the results is possible.

The average results are displayed in different colours at the center of each soilelement. The length of each line represents the magnitude of the principal quantity(stress or strain) and the direction indicates the principal direction. Positive directionis indicated by arrows. Scaling of the results is possible.

The deformed shape of cross sections, plates, geogrids or interfaces is displayed.The relative deformation is indicated by arrows. Scaling of the results is possible.

The distributions of the results in cross sections, plates, geogrids or interfaces isdisplayed. Scaling of the results is possible.

The wireframe distributions of the results in cross sections, plates, geogrids orinterfaces is displayed. Scaling of the results is possible.

The distribution of the maximum and the minimum values of the resulting forces inplates, geogrids and node-to-node anchors up to the current calculation step isdisplayed. Scaling of the results is possible.

The wireframe distribution of the maximum and the minimum values of the resultingforces in plates, geogrids and node-to-node anchors up to the current calculationstep is displayed. Scaling of the results is possible.

The Plastic points option shows the stress points that are in a plastic state,displayed in a plot of the undeformed geometry (Section 7.3.8). Scaling of theresults is possible. When scaling is used, it is possible to pull the interfaces out ofthe plates, however the stress points will remain at their physical locations.

The availability of the display type buttons in the toolbar can be toggled on/off byselecting the corresponding options in the View menu.

6.3.11 SELECT STRUCTURES

By default, all the active structures and interfaces in the selected phase are displayed inthe plot. The disabled structures can be displayed by selecting the corresponding optionin the Geometry menu.

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Output for structures and interfaces can be obtained by clicking the Selectstructures button and then double clicking the desired object in the 2D model. As a

result, a new form is opened on which the selected object appears. At the same time themenu changes to provide the particular type of output for the selected object.

Another option of selecting structural elements in the output is by clicking on theSelect structures in a rectangle and drawing a rectangle in the model. As a result,

the structures in the rectangle will be selected.

To clear the selection, press <Esc>. Only structural elements of the same type can beselected at the same time. For example, if a geogrid is selected, only other geogrids canbe added to the selection and no plates.

6.3.12 PARTIAL GEOMETRY

To enable the inspection of certain internal parts of the geometry (for example individuallayers or volume clusters) it is possible to make other parts of the geometry invisible inthe Model explorer by clicking the button in front of them (Figure 6.8).

Figure 6.8 Model explorer in Output

Visible model components are indicated by an open eye, whereas invisible ones areindicated by a closed eye. By clicking on the button, the view of the components(individual and/or groups) can be toggled from being visible to being invisible and viceversa. A group is expanded by clicking on the + sign in front of the group. Clusters thathave been set inactive in the framework of staged construction are always invisible andcannot be made visible.

Hint: The cluster numbers are activated by selecting the Cluster numbers option inthe Mesh menu.

The information in the Model explorer can be narrowed according to the filtering criteriaspecified at the corresponding cell.

The Model explorer can be fully expanded by selecting the Expand all in menu displayedwhen the Model explorer is right-clicked. The displaying menu provides the optionCollapse all that reverts the effect of the Expand all option.

The Show all option will make all the object active in the selected phase visible. The Hide

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all will revert the action.The Invert selection option will toggle all visible elements invisibleand all invisible elements visible. The Deselect all button will set all elements to invisible.On pressing the Close button the Partial geometry window is closed without furtherchanges.

Apart from the Model explorer, individual volume elements or entire clusters of volumeelements can be made invisible by holding down the <Ctrl> key, the <Shift> key or bothkeys at the same time, respectively, while clicking on an element in the 2D model. Theseelements can be visible again by clicking the corresponding check boxes in the Modelexplorer.

Clicking the Hide soil button in the side bar menu enables hiding parts of the soil.To hide soil elements, click the Hide soil button first and hold the <Ctrl> key pressed

while clicking on the soil elements. To hide soil clusters, click the Hide soil button firstand hold the <Shift> key pressed while clicking on the soil clusters.

Clicking on the Hide soil in the rectangle button enables hiding the soilin the rectangle drawn in the model. The drawing order of the rectangle effects the

resulting hidden soil elements.

To hide only the soil elements that fall completely in the defined rectangle, first click theHide soil in the rectangle button. In the model, click at the point defining the upper leftcorner of the rectangle, drag the mouse to the point defining the lower right corner of therectangle and click again.

To hide all the soil elements that are intersected by the defined rectangle, first click theHide soil in the rectangle button. In the model, click at the point defining the lower rightcorner of the rectangle, drag the mouse to the point defining the upper left corner of therectangle and click again.

6.3.13 VIEWING RESULTS IN CROSS SECTIONS

To gain insight in the distribution of a certain quantity in the soil it is often useful to viewthe distribution of that quantity in a particular cross section of the model. This option isavailable in PLAXIS for all types of stresses and displacements in soil elements.

A cross section can be defined by clicking the Cross section button in the sidebutton bar or by selecting the Cross section option in the View menu. Note that this

option is also available in the right mouse click pop-up menu. Upon selection of thisoption, the Cross section points window pops up in which the two cross sectioncoordinates can be defined.

After the cross section has been selected, a new form is opened in which the distributionof a quantity is presented on the indicated cross section. At the same time, the menuchanges to allow for the selection of all other quantities that may be viewed on theindicated cross section.

Hint: The distribution of quantities in cross sections is obtained from interpolationof nodal data, and may be less accurate than data presented in the 2Dmodel.

Multiple cross sections may be drawn in the same geometry. Each cross section will

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appear in a different output form. To identify different cross sections, the end points of across section are indicated with characters in alphabetical order. The points defining thecross section can be viewed by selecting the Cross section points option in the Toolsmenu.

In addition to the output quantities that are available for the 2D model, a cross sectionallows for the display of cross section stresses, i.e. effective normal stresses σ’N , totalnormal stresses σN , vertical shear stresses τs and horizontal shear stresses τt .

Hint: It is possible to move a cross section in the direction of its normal while thepresentation of results is updated for the new location of the cross section.• Using the <Ctrl–> and <Ctrl-+> keys will move the cross section 1/100

times the diagonal of the geometry model.• Using the <Ctrl-Shift–> and <Ctrl-Shift-+> will move the cross section

1/1000 times the diagonal of the geometry model.

6.3.14 PLOT ANNOTATIONS

PLAXIS 2D enables addition of user-defined information to the output plots. The buttonsin the side toolbar provide different annotation options.

Label annotations in plots

PLAXIS 2D enables adding labels as annotations in plots. To add a label annotation to aplot:

Click the Add label-annotation button in the side toolbar.

• Double click the location on the plot where the label is to be located. The Annotationwindow for the label pops up (Figure 6.9).

• Define the type by selecting the corresponding option in the Caption type drop downmenu. The options available for the Caption type are:

User defined To enter a label defined by the user.

Node ID To display the ID of the double clicked node.

Result value To display the result (i.e. the displacement, groundwaterhead or other result, depending on the selected Output plot)at the double clicked node.

Hint: The information available for the annotation depends on whether a node isdouble clicked or not. When a node is double clicked, besides User-definedtext, information such as the node ID, result value at the node, the type ofelement to which the node corresponds and the number of that element isprovided. If a random location is double clicked in the plot the only optionavailable for the Caption type, is User-defined.

• If the User-defined option is selected, specify the label in the Caption type cell.

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Figure 6.9 Annotation window for labels

• If either the ID or the Result value is selected from the Caption drop down menu, inthe Context box, select the element type to which the node belongs in the Elementtype drop down menu. Depending on the model, the options might be Soil-elementor Structural-element.

• A node can be shared by multiple elements. To specify the element of interest selectthe corresponding option from the Element ID drop down menu in the Context box.Note that the Context box is only available if an annotation is assigned to a node (anode is double clicked).

• Select one of the options available for the Scope box to prevent undesired display ofthe annotation in the plot. The defined annotations can be relevant for the wholeproject (Project option), only the current phase (Phase option) or only the currentcalculation step (Step).

• To limit the display of the annotation to the current view select the correspondingcheckbox in the window. Note that if this option is selected, the current view shouldbe saved to preserve the defined annotation.

Line annotations in plots

PLAXIS 2D enables adding lines or arrows as annotations in plots. To add a lineannotation to a plot:

Click the Add line-annotation button in the side toolbar.

• Define the start and the end points of the line by clicking on the plot. When the endpoint is defined the Annotation window for lines pops up (Figure 6.9).

• Use the Style options available in the drop down menus for the start and end pointof the line and for the line itself to modify the style of the line.

• Specify the thickness of the line and the arrows in the corresponding cell.

• Select one of the options available for the Scope to prevent undesired display of theannotation in the plot. The defined annotations can be relevant for the whole project(Project option), only the current phase (Phase option) or only the current

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calculation step (Step).

• To limit the display of the annotation to the current view select the correspondingcheckbox in the window. Note that if this option is selected, the current view shouldbe saved to preserve the defined annotation.

• The Delete button is only available when editing the annotations (see below).

Figure 6.10 Annotation window for editing

Measurement annotations in plots

PLAXIS 2D enables adding measurement annotations in plots displaying the distancebetween two locations in the model. To add a measurement annotation to a plot:

Click the Add measurement-annotation button in the side toolbar.

• Define the start and the end points of the line by clicking on the plot. The distancebetween the specified locations is displayed in the model.

Editing annotations

To modify or remove an annotation from the plot:

Click the Edit annotation button in the side toolbar.

• Click the annotation to be modified. The Annotation window will appear displayingthe modification options depending on the clicked annotation. Note that a newbutton (Delete) is available in the window, enabling the removal of the annotation(Figure 6.10).

6.3.15 MISCELLANEOUS TOOLS

Distance measurement

The distance between two nodes in the model can be measured by either clickingon the Distance measurement button or by selecting the Distance measurement

option in the Tools menu and by subsequently selecting the nodes in the model. TheDistance information window pops up displaying the information about the distance(Figure 6.11).

The distance can be given according to the original node position or in deformed shape(i.e. using shifted node positions according to their displacements).

A description of the information available in the table is given as follows:

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Figure 6.11 Distance information

Coordinates The Original and Deformed coordinates for the first node/stresspoint and the second node/stress point.

∆x The Original and Deformed x-component of the distancebetween the points.

∆y The Original and Deformed y-component of the distancebetween the points.

Distance The Original (v) and Deformed (v’) distance between the points.

Orientation The original and after deformation angle between the line drawnbetween the selected nodes/stress points with respect to thex-axis.

Elongation Increase of the distance between the selected points before andafter deformation without considering the rotation of the linebetween the two points.

|∆u| The change in the distance between the selected points beforeand after deformation.

|∆u|perpendicular The deformation in the direction perpendicular to the original linebetween the selected points.

Rotation The angle between the original line and the deformed linebetween the points. The sign of the rotation is determined usingthe right-hand rule (clockwise rotation is negative,counter-clockwise is positive).

Tilt The ratio of the deformation in the direction perpendicular to theline between the selected points (|∆u|perpendicular ) to the originaldistance between the selected points. Tilt is given both as ratioand percentage.

Draw scanline

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P1

P2

P’1

P’2

v = P2 — P1

v’= P’2 — P’1

∆u = v’- v

Rotation

x

x

orientation

orientation

Elongation

|∆u|perpendicular

Figure 6.12 Deformation measurement

Hint: The computation of the Elongation depends on the type of calculation. If anUpdated mesh analysis is performed, Elongation is simply the difference inlength between the old and new vectors. Otherwise it is the projection of thedeformation vector onto the original vector.

When the Contour lines option is selected , a distribution of the values can bedisplayed by clicking on the Draw scanline button in the side toolbar and drawing a

line on the regions of interest. Note that this option is also available in the right mouseclick pop-up menu.

Hint box with node or stress point data

When nodes or stress points are displayed in the model using the correspondingoption in the Tools menu, it is possible to view data of these points in a hint box.

This can be done by clicking on the corresponding button in the side bar menu. If thisoption is active and the mouse is moved over a node, the hint box shows the global nodenumber, the node coordinates and the current displacement components.

If the Hint box option is active and the mouse is moved over a stress point, the hint boxshows the global stress point number, the current Young’s modulus E , the currentcohesion c, the current over-consolidation ratio OCR, the current principal stresses and asketch of Coulomb’s envelope and Mohr’s circles for that stress point.

Selecting nodes or stress points for curves

Nodes and stress points can be selected in the Output program by clickingthe Select nodes and stress points button in the side toolbar. Make sure the Nodes

and/or Stress points option has been selected in the Mesh menu. Nodes are generallyused to draw displacements whereas stress points are generally used to draw stresses orstrains.

Note that for the nodes and stress points selected after the calculation processinformation is only valid for the saved calculation steps. For a more detailed descriptionsee Section 8.1.

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Interactive ruler

The result value at a specific location in a structure or cross section can bedisplayed by clicking the Interactive ruler button in the side toolbar and by moving

the cursor to the point of interest. The current value (corresponding to the point on thecross section line), a minimum value (based on the minimum value in the distribution),and a maximum value (based on the maximum value in the distribution) are shown alongthe ruler. The Interactive ruler is available in the Structure and Cross section views.

6.4 DISPLAY AREA

The distribution of the results in the model is shown in the display area.

Figure 6.13 Display area

The presence of the legend, title bar, and axes in the draw area is arranged using theoptions in the View menu (Section 6.2.2).

Hint: The icon in the title bar indicates the view in which the results are displayed.A more detailed description on Views is given in Section 6.5.

6.4.1 LEGEND

The Legend is available for the display options where a variation in colour describes thevariation in the displayed result values. It is activated by selecting the correspondingoption in the View menu. When the Legend is double clicked, a window pops up, wherethe scaling and the colouring can be defined (Figure 6.14). Note that this option is alsoavailable in the right mouse click pop-up menu.

The distribution of values in the legend can be locked by clicking the Lock thelegend button. When the legend is locked, the value distribution will not change as

the <Ctrl>+<+> or <Ctrl>+<-> keys are used to move the cross section through the model.

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Figure 6.14 Legend settings window

6.4.2 MODIFYING THE DISPLAY SETTINGS

The view settings can be defined in the Settings window, that is activated when thecorresponding option in the View menu is selected. Note that this option is also availablein the right mouse click pop-up menu.

The visualization settings can be defined in the Visualization tabsheet of the Settingswindow (Figure 6.15).

Symbol size To modify the size of the symbols in the display for nodes,forces, etc.

Diffuse shading To make the appearance of the 3D model even more realistic,the Diffuse shading option may be used. Using this option,object surfaces that have the same colour by definition (such assoil elements with the same material data set) appear ‘brighter’or ‘darker’, depending on their orientation with respect to theviewer. Object surfaces appear most bright when the normal tothe surface points in the direction of the viewer. The surfacesbecome darker the more the normal deviates from this direction.The contrast can be set to the desired magnitude using the slidebar.

Anti aliasing To select a convenient anti aliasing method from the optionsavailable in the drop-down menu.

Rendering method To select a convenient rendering method from the optionsavailable in the drop-down menu.

Display Toggle the display of the Cluster borders.

The displaying colours can be arranged in the Colours tabsheet of the Settings window(Figure 6.16).

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Figure 6.15 Visualization tabsheet of the Settings window

Figure 6.16 Colours tabsheet of the Settings window

The function of the left and the middle mouse buttons can be defined in the Manipulationtabsheet of the Settings window (Figure 6.17).

Figure 6.17 Manipulation tabsheet of the Settings window

The display of particular results can be toggled on/off in the Results tabsheet of theSettings window (Figure 6.18).

Figure 6.18 Results tabsheet of the Settings window

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6.5 VIEWS IN OUTPUT

In the Output program the results are displayed in different views. The view type isindicated by the corresponding icon in the title bar (Figure 6.13). The available views are:

6.5.1 MODEL VIEW

In the Model viewthe results are displayed in the whole model. This is the default display of results.

6.5.2 STRUCTURES VIEW

When a structure (or multiple structures) is selectedand double clicked, the variation of the result is displayed in the Structures view.

6.5.3 CROSS SECTION VIEW

In the Cross section the results in the defined cross section are displayed. A crosssection can be moved perpendicular to the cross section using the <Ctrl-[ > and

<Ctrl-] > keys. Simultaneously pressing the <Shift> key moves in small steps.

6.5.4 FORCES VIEW

The Forces view enables a view of the mesh with contact stresses and (resulting)forces on the boundaries of the visible active parts of the mesh. This option can be

selected from the Tools menu.

For stresses:

Water load Only external water pressures and pore pressures are shown

Normal stress Only effective normal stresses are shown

Shear stress Only shear stresses are shown

Total stress Effective normal stresses (red) as well as external waterpressures and pore pressures (blue) are shown

It can be selected whether external loads and resulting forces from prescribeddisplacements are taken into account. It can be selected whether resulting forces fromwater loads, effective soil stresses, forces from structures, gravity forces, external loadsand forces from prescribed displacements are taken into account.

The Partial geometry option can be used to make parts of the mesh invisible, ifnecessary. In this way, all stresses and forces on sub-structures can be visualized.

The Table option may be used to view the actual values of stresses and forces. The tableof forces also shows the resulting force below the table, both as an actual value and as apercentage of the total applied forces. The latter can be used to evaluate if there is asignificant unbalance of the (sub-)structure. If necessary, the calculation may berepeated using a smaller tolerated error or a finer mesh.

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6.6 REPORT GENERATION

To document project input data and computational results, a Report Generatorfacility is available in the PLAXIS Output program. The Report generator option can

be selected from the File menu. The data files for the report are generated in thefollowing eight steps.

Step 1: The report can be generated in a group of files or all the information can becombined in a single file (a RTF, PDF or HTML document). The directory where thereport is stored should be defined (Figure 6.19).

Figure 6.19 Report generator — Setup

Step 2: Select the phases for which results will be included in the report (Figure 6.20).

Figure 6.20 Report generator — Phases

Step 3: Select general information sets to be included in the report. Note that theselection can be saved as a new set besides All and None sets (Figure 6.21).

Figure 6.21 Report generator — General information

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Step 4: Select model view sets to be displayed in the report. Note that the selection canbe saved as a new set besides All and None sets (Figure 6.22).

Figure 6.22 Report generator — Model

Step 5: Select structure view sets to be displayed in the report are selected. Note that theselection can be saved as a new set besides All and None sets (Figure 6.23).

Figure 6.23 Report generator — Structures

Step 6: Select saved views to be included in the report (Figure 6.24). For more details onsaved views, see Section 6.3.4.

Figure 6.24 Report generator — Saved views

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Step 7: Select generated charts to be included in the report (Figure 6.25).

Figure 6.25 Report generator — Charts

Step 8: A summary of the number of rows and the number of figures in the report is given(Figure 6.26). The report is created as the Export button is clicked. A progress barappears displaying the number of the remaining rows and images.

Figure 6.26 Report generator — Results

6.6.1 CONFIGURATION OF THE DOCUMENT

When the RTF, PDF or HTML document option is selected in the first step, aftercompleting the steps required to generate the report another window pops up (Figure6.27) where the document type, name, the storage location and the display propertiessuch as page setup (for RTF and PDF documents), the table configuration and the typeand size of the used font can be defined.

Figure 6.27 Document properties

6.7 CREATING ANIMATIONS

The Create animation option is available in the View menu. If the option isselected, the Create animation window appears (see Figure 6.28). The phases and

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calculation steps to be included in the animations can be selected. After selecting thephase(s), click OK to start the process. The progress of this process is indicated in aseparate window.

If a large number of steps is to be included in the animation, the process may take someminutes after which the animation is presented. The result is stored in an animation file(*.AVI) in the project data directory.

Figure 6.28 Selection of phases from Create animation window

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7 RESULTS AVAILABLE IN OUTPUT PROGRAM

7.1 CONNECTIVITY PLOT

A Connectivity plot is a plot of the mesh in which the element connections are clearlyvisualised. It is the result of the meshing process. It is available only in the representationof spatial variation of the results. This plot is particularly of interest when interfaceelements are included in the mesh. Interface elements are composed of pairs of nodes inwhich the nodes in a pair have the same coordinates. In the Connectivity plot however,the nodes in a pair are drawn with a certain distance in between so that it is made clearhow nodes are connected to adjacent elements. This option is available from the Meshmenu.

In the Connectivity plot it can, for example, be seen that when an interface is presentbetween two soil elements, that the soil elements do not have common nodes and thatthe connection is formed by the interface. In a situation where interfaces are placedalong both sides of a plate (Positive interface and Negative interface), the plate and theadjacent soil elements do not have nodes in common. The connection between the plateand the soil is formed by the interface. An example of Connectivity plot is given in Figure7.1.

Figure 7.1 Example of the Connectivity plot

7.2 DEFORMATIONS

The Deformations menu contains various options to visualise the displacements andstrains in the finite element model. By default, the displayed quantities are scaledautomatically by a factor (1, 2 or 5) ·10n to give a diagram that may be read conveniently.

The scale factor may be changed by clicking the Scale factor button in the toolbaror by selecting the Scale option from the View menu. The scale factor for strains

refers to a reference value of strain that is drawn as a certain percentage of the geometrydimensions. To be able to compare plots of different calculation phases or differentprojects, the scale factors in the different plots must be made equal.

7.2.1 DEFORMED MESH

The Deformed mesh is a plot of the finite element model in the deformed shape. Bydefault, the deformations are scaled up to give a plot that may be read conveniently. If itis desired to view the deformations on the true scale (i.e. the geometry scale), then theScale option (Section 6.3.7) may be used. The deformed mesh plot may be selected from

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the Deformations menu.

7.2.2 TOTAL DISPLACEMENTS

The Total displacements option contains the different components of the accumulateddisplacements at the end of the current calculation step, displayed on a plot of thegeometry. This option may be selected from the Deformations menu. A further selectioncan be made among the total displacement vectors, |u|, and the individual totaldisplacement components, ux and uy . The total displacements may be presented asArrows, Contour Lines or Shadings by clicking the appropriate button in the toolbar(Section 6.3.10).

7.2.3 PHASE DISPLACEMENTS

The Phase Displacements option contains the different components of the accumulateddisplacement increments in the whole calculation phase as calculated at the end of thecurrent calculation step, displayed on a plot of the geometry. In other words, the phasedisplacements are the differential displacements between the end of the currentcalculation phase and the end of the previous calculation phase. This option may beselected from the Deformations menu.

A further selection can be made among the phase displacement vectors, |Pu|, and theindividual phase displacement components, Pux and Puy . The phase displacementsmay be presented as Arrows, Contour lines or Shadings by clicking the appropriatebutton in the toolbar (Section 6.3.10).

7.2.4 SUM PHASE DISPLACEMENTS

In Staged construction calculations elements that are switched from inactive to active are,by default, pre-deformed such that the displacement field across the boundary betweenthe new elements and the existing elements is continuous. However, in someapplications, such as the staged construction of dams and embankments, this will lead tothe undesired situation that the top of the embankment shows the largest settlements(Figure 7.2a) and is lower than what has been designed, because of the accumulatedsettlements of the different construction layers. When the Sum phase displacementsoption is selected, the pre-deformation of newly activated elements is avoided, so theywill have zero initial displacements (except for the nodes where these new elementsconnect to existing elements). In this way, the settlement of the last construction layer willbe limited and the largest settlement will most likely occur in the middle of theembankment, as expected. When plotting the settlements in a vertical cross sectionthrough the embankment, the results are somewhat discontinuous, but the overallsettlement profile is more realistic than without choosing this option (Figure 7.2b). Themore construction layers are used, the smoother the settlement profile is (Figure 7.2c).

7.2.5 INCREMENTAL DISPLACEMENTS

The Incremental displacements option contains the different components of thedisplacement increments as calculated for the current calculation step, displayed on aplot of the geometry. This option may be selected from the Deformations menu. A furtherselection can be made among the displacement increment vectors, |∆u|, and the

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a. b. c.

Figure 7.2 Settlement profile of an embankment on a stiff foundation layer: a. Phase displacementresults; b. Sum phase displacements results (5 construction layers); c. Sum phasedisplacements results (10 construction layers)

individual incremental displacement components, ∆ux and ∆uy . The displacementincrements may be presented as Arrows, Contour lines or Shadings by clicking theappropriate button in the toolbar (Section 6.3.10). The contours of displacementincrement are particularly useful for the observation of localisation of deformations withinthe soil when failure occurs.

7.2.6 EXTREME TOTAL DISPLACEMENTS

The Extreme total displacements option contains the different components of the extremevalues of the total displacements in the model, displayed on a plot of the geometry. Thisoption may be selected from the Deformations menu. A further selection can be madeamong the maximum and the minimum of the total displacement components (ux ,min,ux ,max , uy ,min, uy ,max ) and the maximum overall value (|u|max ). The extreme totaldisplacements may be presented as Contour lines or Shadings by clicking theappropriate button in the toolbar (Section 6.3.10).

7.2.7 VELOCITIES

The option Velocities contains the different components of the velocities at the end of thecurrent calculation step, displayed on a plot of the geometry. This option may be selectedfrom the Deformations menu. A further selection can be made among the velocityvectors, |v |, the individual velocity components, vx and vy , as well as the extreme valuesof the total velocities in the calculation phase. The velocities may be presented asArrows, Contour lines or Shadings by clicking the appropriate button in the toolbar(Section 6.3.10).

7.2.8 ACCELERATIONS

The option Accelerations contains the different components of the accelerations at theend of the current calculation step, displayed on a plot of the geometry. This option maybe selected from the Deformations menu. A further selection can be made among theacceleration vectors, |a|, the individual acceleration components, ax and ay , as well asthe extreme values of the total accelerations in the calculation phase. The accelerationsmay be presented as Arrows, Contour lines or Shadings by clicking the appropriatebutton in the toolbar (Section 6.3.10).

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7.2.9 ACCELERATIONS IN ‘G’

The option Accelerations in ‘g’ contains the different components of the accelerations atthe end of the current calculation step, displayed on a plot of the geometry as multiples ofthe gravity acceleration. This option may be selected from the Deformations menu. Afurther selection can be made among the acceleration vectors, |a(‘g’ )|, the individualacceleration components, ax (‘g’ ) and ay (‘g’ ), as well as the extreme values of the totalaccelerations in the calculation phase. The accelerations may be presented as Arrows,Contour lines or Shadings by clicking the appropriate button in the toolbar (Section6.3.10).

7.2.10 TOTAL CARTESIAN STRAINS

The Total cartesian strains option contains the different components of the accumulatedstrains at the end of the current calculation step, displayed in a plot of the geometry. Thisoption may be selected from the Deformations menu. A further selection can be madeamong the three or four individual Cartesian strain components εxx , εyy , εzz (foraxisymmetric models only) and γxy . In case of a plain strain model, εzz will be zero. Incase of an axisymmetric model, the value of the strain in this direction can be calculatedas εzz = ∂uz/∂z = ux/R = ux/x . The individual strain components may be presented asContour lines or Shadings by clicking the appropriate button in the toolbar (Section6.3.10).

7.2.11 PHASE CARTESIAN STRAINS

The Phase cartesian strains option contains the different components of the accumulatedstrain increments in the whole calculation phase as calculated at the end of the currentcalculation step, displayed in a plot of the geometry. This option may be selected from theDeformations menu. A further selection can be made among the three or four individualCartesian strain components Pεxx , Pεyy , Pεzz (for axisymmetric models only) and Pγxy .In case of a plain strain model, Pεzz will be zero. In case of an axisymmetric model, thevalue of the strain in this direction can be calculated asPεzz = ∂Puz/∂z = Pux/R = Pux/x .

The individual strain components may be presented as Contour lines or Shadings byclicking the appropriate button in the toolbar (Section 6.3.10).

7.2.12 INCREMENTAL CARTESIAN STRAINS

The Incremental cartesian strains option contains the different components of the strainincrements as calculated for the current calculation step, displayed in a plot of thegeometry. This option may be selected from the Deformations menu. A further selectioncan be made among the three or four individual Cartesian strain components ∆εxx , ∆εyy ,∆εzz (for axisymmetric models only) and ∆γxy . In case of a plain strain model, ∆εzz willbe zero. In case of an axisymmetric model, the value of the strain in this direction can becalculated as ∆εzz = ∂∆uz/∂z = ∆ux/R = ∆ux/x .

The individual strain components may be presented as Contour lines or Shadings byclicking the appropriate button in the toolbar (Section 6.3.10).

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7.2.13 TOTAL STRAINS

The Total strains option contains various strain measures based on the accumulatedstrains in the geometry at the end of the current calculation step, displayed in a plot of thegeometry. This option may be selected from the Deformations menu. A further selectioncan be made among the principal strain directions, the individual principal straincomponents ε1, ε2, ε3 (for axisymmetric models only), (ε1 + ε3)/2, (ε1 — ε3)/2, the angle,the volumetric strain εv , the deviatoric strain γs and the void ratio e.

• Note that the principal strain components are arranged in algebraic order:

ε1 > ε2 > ε3

Hence, ε1 is the largest compressive principal strain and ε3 is the smallestcompressive principal strain.

• The volumetric strain is calculated as:

In normal calculations:

εv = εxx + εyy + εzz

In Updated mesh calculations:

εv = εxx + εyy + εzz + εxxεyy + εxxεzz + εyyεzz + εxxεyyεzz

• The deviatoric strain is calculated as:

γs =

√23

[(εxx −

εv

3

)2 +(εyy −

εv

3

)2 +(εzz −

εv

3

)2 +

12

(γ2

xy + γ2yz + γ2

zx)]

• The void ratio is calculated as:

e = e0 + (1 + e0)εv

7.2.14 PHASE STRAINS

The Phase strains option contains various strain measures based on the accumulatedstrain increments in the whole calculation phase as calculated at the end of the currentcalculation step, displayed in a plot of the geometry. This option may be selected from theDeformations menu. A further selection can be made among the volumetric strain (Pεv )and the deviatoric strain (Pγs).

7.2.15 INCREMENTAL STRAINS

The Incremental strains option contains various strain measures based on the strainincrements as calculated for the current calculation step, displayed in a plot of thegeometry. This option may be selected from the Deformations menu. A further selectioncan be made among the volumetric strain (∆εv ) and the deviatoric strain (∆γs).

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7.3 STRESSES

Various options are available to visualize the stress state in the finite element model.

Hint: By default, the stresses developed in non-porous materials are not displayedin the plot. To display them select the Show stress for nonporous materialoption in the Results tabsheet of the Settings window (Section 6.4.2).

7.3.1 CARTESIAN EFFECTIVE STRESSES

The Cartesian effective stresses are different components of the effective stress tensor(i.e. the stresses in the soil skeleton). A further selection can be made among the threeindividual Cartesian stress components σ’xx , σ’yy , σ’zz (for axisymmetric models only),and σxy .

Figure 7.3 shows the sign convention adopted for Cartesian stresses. Note that pressureis considered to be negative.

y

z

x

σσ

σ

σ

σ

σσ

σ

σ

xx

xy

xz

yy

yxyz

zz zx

zy

Figure 7.3 Sign convention for stresses

7.3.2 CARTESIAN TOTAL STRESSES

The Cartesian total stresses are different components of the total stress tensor (i.e.effective stresses + pore pressures). A further selection can be made among the threeindividual Cartesian stress components σxx , σyy , σzz (for axisymmetric models only), andσxy . The latter quantity is equal to the corresponding one in the Cartesian effective stressoption, but are repeated here for convenience (Section 7.3.1). The individual stresscomponents may be presented as Contour lines or Shadings by clicking the appropriatebutton in the toolbar.

7.3.3 PRINCIPAL EFFECTIVE STRESSES

The Principal effective stresses are various stress measures based on the effectivestresses σ’ (i.e. the stresses in the soil skeleton). A further selection can be made amongthe effective principal stresses, the individual principal effective stress components σ’1,σ’2, σ’3, (σ’1 + σ’3)/2, the principal stress directions, the mean effective stress p’, thedeviatoric stress q, the relative shear stress τrel and the mobilised shear strength τmob.

Note that the effective stress components are arranged in algebraic order:

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σ’1 ≤ σ’2 ≤ σ’3

Hence, σ’1 is the largest compressive (or smallest tension) principal stress and σ’3 is thesmallest compressive (or largest tension) principal stress.

The Mobilised shear strength τmob is the maximum value of shear stress (i.e. the radiusof the Mohr stress circle or half the maximum principal stress difference).

The Relative shear stress τrel gives an indication of the proximity of the stress point to thefailure envelope, and is defined as:

τrel =τmob

τmax

where τmax is the maximum value of shear stress for the case where the Mohr’s circle isexpanded to touch the Coulomb failure envelope while keeping the center of Mohr’s circleconstant.

τmax = −σ1′ + σ3′

2sinϕ + c cosϕ

Hint: Particularly when the soil strength has been defined by means of effectivestrength parameters (c’, ϕ’) it is useful to plot the mobilised shear strengthτmob in a vertical cross section and to check this against a known shearstrength profile.

When using the Hoek-Brown model to describe the behaviour of a rock section, thedefinition of the maximum shear stress τmax is slightly modified. Starting from theHoek-Brown failure criterion:

fHB = σ’1 − σ’3 + f (σ’3) = 0 (7.1)

the maximum shear stress is defined by :

τmax =12

f (σ’3) where f (σ’3) = σci

(mb−σ’3σci

+ s)

a (7.2)

The relative shear stress is correspondingly defined by:

τrel =τmob

τmax=|σ’1 − σ’3|

f (σ’3)(7.3)

The principal stress directions are defined by:

α =12

arctan (2σxy

σyy − σxx) (−90◦ ≤ α ≤ 90◦) (7.4)

For α = 0, the major principal stress is vertical and the minor principal stress is horizontal.In this case, the cartesian shear stress is zero (for example initial stress generated by theK0 procedure). This situation corresponds to an active stress state.

A passive stress state is equivalent to α = +90◦ or α = -90◦. Zones of positive stress may

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show a jump from α = +90◦ to α = -90◦ and as a result discontinuous colour shadings aredisplayed.

A positive value of cartesian shear stress will lead to a clockwise rotation of the principalstress direction (α > 0), whereas a negative cartesian shear stress will rotate theprincipal stress counter-clockwise (α < 0). The plot of principal stress directions is onlyavailable in PLAXIS 2D. A graphical description of the principal stress directions is shownin Figure 7.4.

α = 0◦

α = −90◦ or +90◦ α = 45◦

α = −45◦

Figure 7.4 Example of principal stress directions

7.3.4 PRINCIPAL TOTAL STRESSES

The Principal total stresses are various stress measures based on the total stresses σ(i.e. effective stresses + pore pressures). A further selection can be made among theprincipal total stress directions, the individual principal total stress components σ1, σ2, σ3,(σ1 + σ3)/2, (σ1 − σ3)/2, the principal stress directions, the mean total stress p, thedeviatoric stress q, the relative shear stress τrel and the mobilised shear strength τmob.The latter three quantities are equal to the corresponding ones in the Principal effectivestress option, but are repeated here for convenience (Section 7.3.3).

Note that the total stress components are arranged in algebraic order:

σ1 ≤ σ2 ≤ σ3

Hence, σ1 is the largest compressive (or the smallest tension) principal stress and σ3 isthe smallest compressive (or the largest tension) principal stress.

7.3.5 STATE PARAMETERS

The State parameters are various additional quantities that relate to the state of thematerial in the current calculation step, taking into account the stress history. A further

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selection can be made among the Permeabilityactual , the User-Defined parameters (foruser-defined soil models; see Material Models Manual), the actual permeability, the strainhistories εxx − εv , εyy − εv , εxy , the secant shear modulus Gs, the ratio between theactual shear modulus and the unloading reloading stiffness G/Gur , the equivalentisotropic stress peq , the isotropic pre-consolidation stress pp, the isotropicover-consolidation ratio OCR, the hardening parameter γp, the actual stiffness Eur forunloading and reloading, the actual Young’s modulus E and the actual cohesion c,depending on the soil models being used.

The actual permeability: The actual permeability (Permeabilityactual ,x ,Permeabilityactual ,y ) is the relative permeability times the saturated permeability. Thisvalue depends on the degree of saturation according to the Van Genuchten (or other)relationship as defined in the flow parameters of the material set. This parameter is onlyavailable in calculations performed in the Advanced mode.

The strain history: The strain histories εxx − εv , εyy − εv , εzz − εv (for axisymmetricmodels only), and εxy are only available in the HS small model.

The secant shear modulus Gs: The secant shear modulus Gs is only available in theHardening Soil model with small-strain stiffness. This option may be used to check theactual secant shear modulus used in the current calculation step. More information aboutthis parameter can be found in Section 7.1 of the Material Models Manual.

The ratio between the actual shear modulus and the unloading reloading stiffnessG/Gur : The ratio between the actual shear modulus G and the unloading reloadingstiffness Gur is only available in the Hardening Soil model with small-strain stiffness.

The equivalent isotropic stress peq: The equivalent isotropic stress peq is onlyavailable in the Hardening Soil model, Hardening Soil model with small-strain stiffness,Soft Soil model, Soft Soil Creep model and Modified Cam-Clay model. The equivalentisotropic stress is defined as the intersection point between the stress contour (withsimilar shape as the yield contour) through the current stress point and the isotropicstress axis. Depending on the type of model being used it is defined as:

peq =

√p2 + q̃2

α2 for the Hardening Soil model and HS smallmodel

peq = p’− q2

M2 (p’− c cotϕ)for the Soft Soil model, Soft Soil Creep modeland Modified Cam-Clay model. For the ModifiedCam-Clay model, the cohesion c is defined as 0kN/m2.

peq = q

exp(− q̃Mp

)for the Sekiguchi-Ohta model

The isotropic pre-consolidation stress pp: The isotropic pre-consolidation stress pp isonly available in the Hardening Soil model, Hardening Soil model with small-strainstiffness, Soft Soil model, Soft Soil Creep model, Modified Cam-Clay model andSekiguchi-Ohta model. The isotropic pre-consolidation stress represents the maximumequivalent isotropic stress level that a stress point has experienced up to the current loadstep.

The isotropic over-consolidation ratio OCR: The isotropic over-consolidation ratio

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OCR is only available in the Hardening Soil model, Hardening Soil model withsmall-strain stiffness, Soft Soil model, Soft Soil Creep model, Modified Cam-Clay modeland Sekiguchi-Ohta model. The isotropic over-consolidation ratio is the ratio between theisotropic pre-consolidation stress pp and the equivalent isotropic stress peq .

The hardening parameter γp: The hardening parameter γp is only available for theHardening Soil model and Hardening Soil model with small-strain stiffness. This optionmay be used to check the actual hardening during the current calculation step.

The actual Young’s modulus E : The actual Young’s modulus E is the unconstrainedelastic stiffness modulus as used during the current calculation step. This option is onlyavailable in the Linear Elastic model and Mohr-Coulomb model.

When the Linear Elastic model or the Mohr-Coulomb model is utilised with an increasingstiffness with depth (Eincrement > 0), this option may be used to check the actual stiffnessprofile used in the calculation. Note that in the Linear Elastic model and theMohr-Coulomb model the stiffness is NOT stress-dependent.

The actual stiffness Eur for unloading and reloading: The actual Young’s modulusEur for unloading and reloading is the unconstrained elastic stiffness modulus as usedduring the current calculation step. This option is only available in the Hardening Soilmodel, Hardening Soil model with small-strain stiffness, Soft Soil model, Soft Soil Creepmodel, Modified Cam-Clay model and Sekiguchi-Ohta model.

The stiffness Eur depends on the stress level. In models with stress-dependency ofstress, the actual stiffness Eur is calculated on the basis of the stresses at the beginningof the current step. The option may be used to check the actual stress-dependentstiffness used in the current calculation step.

The actual cohesion c: The actual cohesion c is the cohesive strength as used duringthe current calculation step. This option is only available in the Mohr-Coulomb model,Hardening Soil model, Hardening Soil model with small-strain stiffness, Soft Soil modeland Soft Soil Creep model.

When the Mohr-Coulomb model, Hardening Soil model or the Hardening Soil model withsmall-strain stiffness is utilised with an increasing cohesive strength with depth(cincrement > 0), this option may be used to check the actual cohesive strength profileused in the calculation.

7.3.6 PORE PRESSURES

The Pore pressures are quantities that relate to the stress in the pores of the material.The pores of soil are usually filled with water; therefore pore pressures can generally beinterpreted as water pressures inside the soil material, but they are not limited to that. Afurther selection can be made among Groundwater head, active pore pressures pactive,excess pore pressures pexcess, , minimum excess pore pressures pexcess,min, steady-statepore pressures psteady and Suction. Note that compression is considered to be negative.

Although pore pressures do not have principal directions, the Principal directionspresentation can be useful to view pore pressures inside the model. In that case thecolour of the lines represents the magnitude of the pore pressure and the directionscoincide with the x-, y — and z-axis.

Groundwater head: The groundwater head is an alternative quantity of the active pore

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pressure. The Groundwater head is defined as:

h = y − pwγw

where y is the vertical coordinate, pw is the active pore pressure and γw is the unit weightof water. The groundwater head can only be presented as Contour lines, Shadings or Isosurfaces.

Active pore pressures pactive: The active pore pressures, pactive, are the total waterpressures pw (i.e. steady-state pore pressures + excess pore pressures) at the end of thecurrent calculation step, taking into account positive pore stresses in the unsaturatedzone above the phreatic level, displayed in a plot of the undeformed geometry. In fact,positive pore stresses are defined as effective degree-of-saturation times suction (sr ,eff *suction).

Excess pore pressures pexcess: Excess pore pressures, pexcess, are the extra porepressures due to loading or unloading of undrained clusters (Undrained (A) or Undrained(B)), or the extra pore pressures resulting from a consolidation analysis based on excesspore pressure.

Extreme excess pore pressures pexcess,min, pexcess,max : Extreme excess porepressures are the maximum and minimum values of extra pore pressures due to loadingor unloading of undrained clusters (Undrained (A) or Undrained (B)), or the extra porepressures resulting from a dynamic analysis.

Steady-state pore pressures psteady : The steady-state pore pressures, psteady , are thepore pressures as generated on the basis of the water conditions of the individualclusters, taking into account positive pore stresses in the unsaturated zone above thephreatic level. The input for the steady-state pore pressure generation is described inSection 5.9.

Change in pore pressures per phase ∆Pphase: The change in pressures per phase,∆Pphase, is the change in pore pressures in the selected phase resulting from aconsolidation analysis based on total pore pressure. For situations in which the phreaticsurface does not change, ∆Pphase is supposed to represent the excess pore pressures.

Suction: Positive pore stresses in the unsaturated zone above the phreatic level can bedisplayed as the Suction option is selected. Note that only a part of the suctioncontributes to the active pore pressure, namely sr ,eff * suction.

7.3.7 GROUNDWATER FLOW

When a groundwater flow calculation has been performed to generate the pore pressuredistribution, then the specific discharges at the element stress points are available in theOutput program in addition to the pore pressure distribution. The specific discharges canbe viewed by selecting the Groundwater Flow option from the Stresses menu. A furtherselection can be made among the flow resulting from the Consolidation based on excesspore pressure, (|qEPP |, qEPP,x , qEPP,y ) and the groundwater flow, (|q|, qx , qy ).

The flow field may be viewed as Arrows, Contour lines or Shadings by selecting theappropriate option from the presentation box in the tool bar. When the specific dischargesare presented as arrows, then the length of the arrow indicates the magnitude of thespecific discharge whereas the arrow direction indicates the flow direction.

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Saturation

The PlaxFlow module within PLAXIS may be used to calculate a pore pressuredistribution for confined as well as for unconfined flow problems. The determination of theposition of the free phreatic surface and the associated length of the seepage surface isone of the main objectives of an unconfined groundwater flow calculation. In this case arelationship is used between the pore pressure and the degree of saturation. Bothquantities are calculated in a groundwater flow calculation and are made available in theOutput program.

The degree of saturation is only relevant in the Flow and Advanced modes. The degreeof saturation is generally 100% below the phreatic level and it reduces to the residualsaturation within a finite zone above the phreatic level. Note that the residual saturationvalue is equal to zero in Classical mode. The saturation can only be presented asContour lines or Shadings.

Effective saturation (Saturationeff )

The effective saturation is used as the Bishop coefficient in the definition of Bishop stressand also to calculate the weight of soil in the advanced mode. The effective saturation isnot relevant in the classical mode. The effective saturation can only be presented asContour Lines or Shadings

Relative permeability (Permeabilityrel )

The relative permeability can be visualised by selecting the Permeabilityrel option. Therelative permeability can only be presented as Contour Lines or Shadings.

7.3.8 PLASTIC POINTS

The Plastic points option shows the stress points that are in a plastic state,displayed in a plot of the undeformed geometry. Plastic points can be shown in the

2D mesh or in the elements around a cross section. The plastic stress points areindicated by small symbols that can have different shapes and colours, depending on thetype of plasticity that has occurred:

• A red cube (Failure point) indicates that the stresses lie on the surface of the failureenvelope.

• A white cube (Tension cut-off point) indicates that the tension cut-off criterion wasapplied.

• A blue upside-down pyramid (Cap point) represents a state of normal consolidation(primary compression) where the preconsolidation stress is equivalent to the actualstress state. The latter type of plastic points only occurs if the Hardening Soil model,the Hardening Soil model with small-strain stiffness, the Soft Soil model, Soft SoilCreep model or Modified Cam-Clay model is used.

• A brown diamond (Cap+Hardening point) represents points that are on the shearhardening and cap hardening envelope. Such plastic points can only occur in theHardening Soil model or the HS small model.

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• A green pyramid (Hardening point) represents points on the shear hardeningenvelope. Such plastic points can only occur in the Hardening Soil model or the HSsmall model.

The failure points are particularly useful to check whether the size of the mesh issufficient. If the zone of plasticity reaches a mesh boundary (excluding the centre-line ina symmetric model) then this suggests that the size of the mesh may be too small. In thiscase the calculation should be repeated with a larger model.

Figure 7.5 Plastic points window

When Plastic points is selected in the Stresses menu the Plastic points dialog is shown(Figure 7.5). Here the user can select which types of plastic points are displayed. Whenthe Stress points option is selected, all other stress points are indicated by a purplediamond shape (�). For details of the use of advanced soil models, the user is referred tothe Material Models Manual.

By default both accurate and inaccurate plastic points are displayed in the model. Onlythe inaccurate plastic points are displayed as the corresponding check box is selected inthe Plastic points window. Inaccurate plastic points are points where the local error islarger then the tolerated error (Section 5.13.9).

Hint: The Plastic point history option in the Stresses menu enables displaying inthe model all the plastic points (depending on the specified criteria, Failure,Tension cut-off, etc.) generated up to the current calculation phase.

7.3.9 FIXED END ANCHORS

When Fixed end anchors is selected in the Stresses menu a table appears displaying thefixed end anchors available in the model, their location, the resulting axial force, therotation angle and the equivalent length.

7.3.10 NODE TO NODE ANCHORS

When Node to node anchors is selected in the Stresses menu a table appears displayingthe node to node anchors available in the model, the location of the nodes and theresulting axial forces.

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7.3.11 WELLS

When Wells is selected in the Stresses menu a table appears displaying the wellsavailable in the model, the nodes representing the well and their location, the dischargeof the well and the defined minimum groundwater head.

7.3.12 DRAINS

When Drains is selected in the Stresses menu a table appears displaying the drainsavailable in the model, the nodes representing the drain and their location, the totaldischarge and the defined groundwater head of the drain.

7.4 STRUCTURES AND INTERFACES

By default, structures (i.e. anchors, geogrids and plates) and interfaces are displayed inthe geometry. Otherwise, these objects may be displayed by selecting the Structures orInterfaces option from the Geometry menu.

Output for structures and interfaces can be obtained by clicking the Selectstructures button and then double clicking the desired object in the 2D model. As a

result, a new form is opened on which the selected object appears. At the same time themenu changes to provide the particular type of output for the selected object.

All objects of the same type with the same local coordinate system are automaticallyselected. When multiple objects or multiple groups of objects of the same type need tobe selected, the <Shift> key should be used while selecting the objects. The last object tobe included in the plot should then be double clicked. When all objects of the same typeare to be selected, select one of the objects while pressing <Ctrl-A> simultaneously. If itis desired to select one or more individual elements from a group, the <Ctrl> key shouldbe used while selecting the desired element.

Another option of selecting structural elements in the output is by clicking the Draga window to select structures button and drawing a rectangle in the model. As a

results, the structures in the rectangle will be selected.

7.4.1 DEFORMATION IN STRUCTURAL ELEMENTS

The deformation options for the structural elements are given in the Deformations menu.The user may select the Total displacements, the Phase displacements or theIncremental displacements (Section 7.2). For each item a further selection can be madeamong the displacement vectors |u|, and the individual total displacement components,ux and uy .

The deformation options in the direction of local axis of the structures are available aswell. The user may select the Total local displacements, the Phase local displacementsor the Incremental local displacements. For each item a further selection can be madeamong the individual displacement components u1 and u2.

7.4.2 RESULTING FORCES IN PLATES

When a plate is displayed, the options Axial Forces N, Shear Forces Q and BendingMoment M are available from the Forces menu. For axisymmetric models the Forces

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Hint: The Rotation option is available for Plates displaying the total rotation(Rotation) and the phase rotation (∆Rotation) of the selected plates withrespect to the global axes.

menu also includes the forces in the out-of-plane direction (Hoop Forces Nz ). Hoopforces are expressed in unit of force per unit of length. The values are constant over thecircumference. Integration of the hoop forces over the in-plane length of the plate will givethe total hoop force. All of these forces represent the actual forces at the end of thecalculation step.

In addition to the actual forces, PLAXIS keeps track of the historical maximumand minimum forces in all subsequent calculation phases. These maximum and

minimum values up to the current calculation step may be viewed after clicking theDistribution envelope button in the top toolbar.

Note that axial forces or hoop forces are positive when they generate tensile stresses, asindicated in Figure 7.6.

Figure 7.6 Sign convention for axial forces and hoop forces in plates

If a circular tunnel (bored tunnel) is modelled and a contraction is applied to the tunnellining, then the Total Realised Contraction and the Realised Contraction Increment aredisplayed in the plot title.

7.4.3 RESULTING FORCES IN GEOGRIDS

When a geogrid is displayed, the option Axial force is available. Forces in geogrids arealways positive (tension). Compressive forces are not allowed in these elements.

In addition to the actual forces, PLAXIS keeps track of the historical maximumand minimum forces in all subsequent calculation phases. These maximum and

minimum values up to the current calculation step may be viewed after clicking theDistribution envelope button in the top toolbar.

7.4.4 RESULTING FORCES IN EMBEDDED PILE ROWS

When an embedded pile row is displayed, the options Axial force N, Shear force Q,Bending moment M, Skin force Tskin (in axial pile direction) the lateral force T2, themaximum shear stress Tmax and the relative shear stress Trel are available from theForces menu. The latter four options relate to the pile-soil interaction (see below).

Hint: The Axes option from the View menu may be used to display the pile’s localsystem of axes.

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The pile-soil interaction forces are obtained from the special interface that isautomatically applied between the embedded beam elements and the surrounding soilvolume elements. The Skin force Tskin, expressed in the unit of force per unit of pilelength per unit of width in the out-of-plane direction, is the force related to the relativedisplacement in the pile’s first direction (axial direction). This force is limited by the skinresistance as defined in the embedded pile row material data set (Section 4.6).

The interaction force T2 relates to the relative displacement perpendicular to the pile inthe pile’s second direction. These quantities are expressed in the unit of force per unit ofpile length per unit of width in the out-of-plane direction.

The maximum shear stress Tmax is the limit defined for the material dataset. The relativeshear stress Trel gives an indication of the proximity of the stress point to the failureenvelope.

The pile foot force Ffoot , expressed in the unit of force per unit of width in the out-of-planedirection, is obtained from the relative displacement in the axial pile direction between thefoot or tip of the pile and the surrounding soil. The foot force is shown in the plot of theAxial force N. The foot force is limited by the base resistance as defined in the embeddedpile row material data set (Section 4.6).

In addition to the actual forces, PLAXIS keeps track of the historical maximumand minimum forces in all subsequent calculation phases. These maximum and

minimum values up to the current calculation step may be viewed after clicking theDistribution envelope button in the top toolbar.

7.4.5 ANCHORS

Output for anchors (fixed-end anchors as well as node-to-node anchors) involves onlythe anchor force expressed in the unit of force on the anchor (on the nodes innode-to-node anchor). The anchor force appears in a table after double clicking theanchor in the model. The program displays the values of the historical maximum andminimum forces in all subsequent calculation phases in node-to-node anchors.

7.4.6 INTERFACES

Interface elements are formed by node pairs, i.e. two nodes at each node position: oneat the ‘soil’ side and one at the ‘structure’ side or the other ‘soil’ side. Interfaces can bevisualised by activating the corresponding option in the Geometry menu. Output forinterfaces can be obtained by double clicking on the interface elements in the 2Dmodel.The output for interfaces comprises deformations and stresses.

When an interface is displayed, the options Effective σ’N , Total σN , Shear τ , RelativeShear τrel , active pore pressure pactive, steady-state pore pressure psteady , excess porepressure pexcess and Groundwater head are available from the Interface stresses menu.The effective normal stress is the effective stress perpendicular to the interface. Note thatpressure is considered to be negative. The relative shear stress τ rel gives an indication ofthe proximity of the stress point to the failure envelope, and is defined as:

τrel =τ

τmax

where τmax is the maximum value of shear stress according to the Coulomb failure

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envelope for the current value of the effective normal stress.

7.4.7 RESULTS IN HINGES AND ROTATION SPRINGS

The resulting bending moment in a rotation spring can be viewed in the windowappearing as the plate connection where it is assigned is double clicked (Figure 7.7).Note that the properties assigned to the rotation spring are displayed as well.

Figure 7.7 Resulting bending moment in a rotation spring

7.4.8 STRUCTURAL FORCES IN VOLUMES

The Structural forces in volumes feature is available in the toolbar or as an optionin the Tools menu in the Output program (Section 6.2.9). Using this feature, it is

possible to visualise structural forces (bending moments M, shear forces Q and axialforces N) in a regular structure (rectangular or tapered) that is composed of volumeelements in which only stresses have been calculated. In this way it is possible, forexample, to display the structural forces in a diaphragm wall that is composed of volumeelements with an assigned data set with concrete properties.

Hint: Note that the structural forces are calculated by integrating the results in thestress points along the region perpendicular to the cross section line.Structures such as culverts can be considered as an assembly of regularsubstructures. Special care is required when the structural forces in theregion of connection of the subparts are evaluated.

Creating a cross section line

When selecting the Structural forces in volumes option, a cross section line should bedrawn in longitudinal direction through the centre of the area that forms the structure.

When the feature is selected the Draw a centerline button in the side toolbaris automatically selected and the Centerline points window pops up. The cross

section line may consist of several line sections. The points defining the segmentscomposing the centerline can be defined either by directly clicking on the model or by

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defining the coordinates of the location in the Centerline points window. The process ofcenterline definition can be quited by either clicking the OK button in the Centerlinepoints window or by right clicking and selecting the Finish option in the appearing menu.The structural forces are then computed on-the-fly and visualised along the created line.

At the drawn cross section line, the selected structural force is calculated on the basis ofthe integral of the stresses perpendicular to the cross section line. The extent of the areathat is used to integrate the stresses is limited by a radius. The default radius, for eachpoint of the cross section, is defined by the elements that contain the same material dataset as the element in which the cross section point is drawn. However, this radius may beredefined by the user (see below).

Changing the extent of the stress range

The range of the stress to be taken into account can be modified by specifying the radiusof the extension from the centerline. The initial radius is determined by the distance,across the cross section line (centerline), to the nearest cluster which has a differentmaterial assigned.

When the Edit radii button is clicked in the side toolbar, the extent ofthe stress range is indicated in the plot by a transparent green colour (Figure 7.9).

Figure 7.8 Figure displaying the structural force in volume and the default radii

It is possible to modify the stress range by clicking on the highlightened area anddragging this area by the mouse (Figure 7.9).

Figure 7.9 Figure displaying the structural force in volume and the modified radii

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Note that the dragging location affects the way how the radii are modified. If the area isdragged near the start or near the end of the centerline, only the radius for that location(start radius or end radius) will be modified. This option may be used for taperedstructures. However if the dragging location is approximately in the middle of both ends ofthe centerline, both radii will be modified.

Additionally, if the segment is double-clicked, a dialog will be opened in which the radiican be specified precisely (Figure 7.10).

Figure 7.10 Edit radii window

The defined cross section lines (centerlines) can be removed from the plot by rightclicking on the plot and by selecting the Clear all option appearing when the Lines optionis pointed in the appearing menu.

Hint: The Create animation feature can be used to view the evolution of thestructural forces in volumes in calculation phases.

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CURVES

8 CURVES

The development of quantities over multiple calculation steps at a specified location inthe model can be viewed using the Curve manager facility. This facility allows for thegeneration of load-displacement curves, force-displacement curves, stress-paths, strainpaths, stress-strain curves and time-related curves.

8.1 SELECTING POINTS FOR CURVES

The location in the model where the variation of results through calculation steps is to beanalyzed is specified by selecting nodes or stress points in the model. The selection ofpoints should be done preferably before but may also be done after calculating theproject.

In order to specify points to be considered in curves, the Select points for curvesoption should be selected. This option is available as a button in the toolbar of the

Calculations program and as an option in the Tools menu of the Calculations program.Selecting this option will open the Output program displaying the Connectivity plot andthe Select points window.

Nodes and stress points can be selected in the Output program either by clicking theSelect points for curves button in the side toolbar or by selecting the corresponding optionin the Tools menu. More information on selecting procedure is given in Section 8.1.1.

It is important to consider the differences in selecting the points before or after startingthe calculation process. A more detailed description is given in Section 8.1.2 and Section8.1.3.

8.1.1 MESH POINT SELECTION

Nodes and stress points can directly be selected by clicking them in the 2Dmodel. Makesure that the Nodes and/or Stress points option has been selected in the Mesh menu.

The amount of visible nodes and stress points can be decreased using the Partialgeometry option in the Geometry menu or by clicking the Hide soil button in the

side toolbar.

In the Select points window (Figure 8.2), the coordinates of the location of interest can bespecified. The program lists the number of the nearest node and stress points at thelower part of the window when the Search closest button is clicked. The nodes andstress points can be selected by defining their ID as well. The displayed nodes or stresspoints are selected as the corresponding button at the right of the cell is checked. Theselections are listed in the upper part of the window.

Selected nodes can be deselected by selecting the point in the list and pressing Delete orby clicking the point in the model.

Hint: When the Select points for curves option is selected but the Select pointswindow is closed, it can be displayed by selecting the Mesh point selectionoption in the Tools menu.

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Figure 8.1 Select points window

If the finite element mesh is regenerated (after being refined or modified), the position ofnodes and stress points will change. As a result, previously selected nodes and stresspoints may appear in completely different positions. Therefore nodes and stress pointsshould be reselected after regeneration of the mesh.

8.1.2 PRE-CALCULATION POINTS

After the calculation phases have been defined and before the calculation process isstarted, some points may be selected by the user for the generation of load-displacementcurves or stress paths. During the calculation, information for these selected points for allthe calculation steps is stored in a separate file. The precalculation points provide moredetailed curves.

Hint: Pre-calculation points provide detailed information related to stress and strainat those points. However information about structural forces and stateparameters is not provided.

8.1.3 POST-CALCULATION POINTS

When the calculations are started without the selection of nodes and stress points forcurves, the user will be prompted to select such points. The user can then decide toselect points or, alternatively, to start the calculations without pre-selected points. In this

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case, it is still possible to generate load-displacement curves or stress-strain curves afterthe calculation, but such curves may be less detailed.

When a node or stress point is selected after calculating the project, only the informationfor the saved calculation steps is available. For more detailed curves the value of the Maxnumber of steps stored should be increased.

The information available for selected points (nodes or stress point) depends on the viewin which they have been selected in the Output program.

The points selected in the Model view, can be used to generate curves related todisplacements, stresses, strains and state parameters in soil elements. The Model

view is the default view in the Output program.

The points selected in the Structure view, can be used to generate curves relatedto resulting structural forces. The points should be selected after selecting the

structure first (Section 6.3.11). The Structure view is displayed when structures areselected and double clicked.

Hint: The type of the active view is indicated by the corresponding icon under theplot.

8.2 GENERATING CURVES

To generate curves, the Curves manager option should be selected from the Toolsmenu or the corresponding button in the toolbar should be clicked. As a result, the

Curves manager window appears with three tabsheets named Charts, Curve points andSelect points.

The Charts tabsheet contains the saved charts that were previously generated for thecurrent project. The Curve points tabsheet gives an overview of the nodes and stresspoints that were selected for the generation of curves, with an indication of theircoordinates. The list includes the points selected before the calculation (pre-calc) as wellas the points selected after the calculation (post-calc) (Figure 8.2). For points that arepart of a structure further information is given in the list about the type of structure andthe corresponding structure element number.The Select points window is described inSection 8.1.1

As a next step to generate curves, the New button should be pressed while the Chartstabsheet is active. As a result, the Curve generation window appears, as presented inFigure 8.3.

Two similar groups with various items are shown, one for the x-axis and one for they -axis of the curve. The x-axis corresponds to the horizontal axis and the y -axiscorresponds to the vertical axis. For each axis, a combination of selections should bemade to define which quantity is plotted on that axis. First, for each axis a selectionshould be made whether the data to be shown is related to the general project (Project)or a particular selected node or stress point. The tree in the Curve generation window willthen show all quantities which are available depending for this type of data. The tree canbe expanded by clicking the + sign in front of a group. The Invert sign option may be

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Figure 8.2 Select points window

selected to multiply all values of the x-quantity or the y -quantity by -1. When bothquantities have been defined and the OK button is pressed, the curve is generated andpresented in a chart window.

The combination of the step-dependent values of the x-quantity and the y -quantity formsthe points of the curve to be plotted. The number of curve points corresponds to theavailable calculation step numbers plus one. The first curve point (corresponding to step0) is numbered as 1.

Figure 8.3 Curve generation window

Hint: When curves are generated from points selected after the calculation, onlyinformation of saved steps can be considered. The number of the savedsteps for each calculation phase is defined by the Maximum number of stepsstored option in the Parameters tabsheet of the Phases window (Section5.7).

» All the calculation results are available for the pre-selected points.

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8.2.1 LOAD-DISPLACEMENT CURVES

Load-displacement curves can be used to visualise the relationship between the appliedloading and the resulting displacement of a certain point in the geometry. In general, thex-axis relates to the displacement of a particular node (Deformations), and the y -axiscontains data relating to load level. The latter is related with the value of ΣMstage in thefollowing way: Applied load = Total load applied in previous phase + ΣMstage · (Totalload applied in current phase — Total load applied in previous phase). Also other types ofcurves can be generated.

The selection of Displacement must be completed with the selection of a node in thedrop-down menu and the selection of a displacement component in the Deformationssubtree. The type of displacement can be either the length of the displacement vector(|u|) or one of the individual displacement components (ux , uy or uz ). The displacementsare expressed in the unit of length, as specified in the Project properties window of theInput program.

To define a multiplier on the y -axis, first the Project option should be selected as theactivation of a load system is not related to a particular point in the geometry. Theselection must be completed with the selection of the desired load system, representedby the corresponding multiplier in the Multiplier subtree. Note that the ‘load’ is notexpressed in units of stress or force but in a multiplier value without unit. To obtain theactual load, the presented value should be multiplied by the input load as specified bymeans of staged construction.

Another quantity that can be presented in a curve is the Pore pressure. This quantity isavailable for selected nodes as well as stress points. In the Pore pressures subtree of theStresses tree pactive, psteady or pexcess can be selected. Pore pressures are expressed inthe unit of stress.

When non-zero prescribed displacements are activated in a calculation, the reactionforces against the prescribed displacements in the x- and y -direction are calculated andstored as output parameters. These force components can also be used in theload-displacement curves by selecting the option Project and then selecting one of theforces in the Forces subtree.In plain strain models the Force is expressed in the units ofwidth in the out-of-plane direction. In axisymmetric models the Force is expressed in theunit of force per radian. Hence, to calculate the total reaction force under a circularfooting that is simulated by means of prescribed displacements, the Fy value should bemultiplied by 2π.

8.2.2 FORCE-DISPLACEMENT CURVES

Force-displacement curves can be used to visualise the relationship between thedevelopment of a structural force quantity and a displacement component of a certainpoint in the geometry. A structural force quantity can only be selected for nodes beingselected after the calculation. In general, the x-axis relates to the displacement of aparticular node (Displacement), and the y -axis relates to the corresponding structuralforce of a node of a structural element.

To define a displacement on the x-axis, first the desired node should be selected. Theselection must be completed with the selection of the type of displacement. Thisdisplacement can be either the length of the displacement vector (|u|) or one of theindividual displacement components (ux , uy or uz ). The displacements are expressed in

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the unit of length, as specified in the General settings window of the Input program.

To define a structural force on the y -axis, first the desired node of the structural elementshould be selected. The selection of Structural force must be completed with theselection of type of force. Depending on the type of structural element, a selection can bemade among axial forces N, shear forces Q or bending moments M . In case ofinterfaces, a selection can be made among the interface stresses (Section 7.4).

8.2.3 DISPLACEMENT-TIME OR FORCE-TIME CURVES

Displacement-time or force-time curves can be useful to interpret the results ofcalculations in which the time-dependent behaviour of the soil plays an important role(e.g. consolidation and creep). In this case, the Time option is generally selected for thex-axis, and the y -axis contains data for a displacement component or structural forcequantity of a particular node. The selection of Time requires the Project option to beselected. Time is expressed in the unit of time, as specified in the Project propertieswindow of the Input program.

Instead of selecting time for the horizontal axis, it is also possible to select the calculationstep number (Step). This may also give useful curves for time independent calculations.When interpreting such a curve it should be noted that during the calculation the step sizemight change as a result of the automatic load stepping procedures.

8.2.4 STRESS AND STRAIN DIAGRAMS

Stress and strain diagrams can be used to visualise the development of stresses (stresspaths) or strains (strain paths) or the stress-strain behaviour of the soil in a particularstress point. These types of curves are useful to analyse the local behaviour of the soil.Stress-strain diagrams represent the idealised behaviour of the soil according to theselected soil model. Since soil behaviour is stress-dependent and soil models do not takeall aspects of stress-dependency into account, stress paths are useful to validatepreviously selected model parameters.

First a stress point should be selected before the desired quantity can be selected in theStress or Strain tree. The selection must be completed with the selection of the type ofstress or strain. As a stress quantity all scalar quantities available in the Stresses menucan be selected (Section 7.3). However, the State parameters option is only available forstress points selected after the calculation Section 8.1.3). As a strain quantity all scalarstrain quantities available in the Deformations menu can be selected (Section 7.2).

See the Scientific Manual for a definition of the stress and strain components. The phrase’in absolute sense’ in the description of the principal components is added because, ingeneral, the normal stress and strain components are negative (compression is negative).Stress components are expressed in the units of stress; strains are dimensionless. Adefinition of the stress and strain components is given in the Material Models Manual.

8.2.5 CURVES IN DYNAMIC CALCULATIONS

The Curve generation window differs when dynamic calculations are executed in theproject. The normal tabsheet is similar to the tabsheet when no dynamic calculations areperformed. However the Dynamic time option is available in the tree when Project isselected in the axis parameter drop down menu. When a point is selected, the Velocities,

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Accelerations and Acceleration (‘g’) options are available under Deformation (Figure 8.4).

Figure 8.4 Options available in Normal tabsheet for dynamic calculations

The PSA spectrum may be generated in the corresponding tabsheet (Figure 8.5) bydefining the values of damping ratio (Zeta) and the maximum time period (End time).

Figure 8.5 Pseudo-spectral acceleration response spectrum generation

The Amplification tabsheet enables obtaining the plot which shows the ratio of theacceleration response of any point (Top) to the acceleration response of another point(Bottom) which is preferably the point where input load is applied (Figure 8.6). This givesthe magnification of the response at one point with respect to given excitation.

Transformation of curves from time to frequency domain

Once a time curve has been generated, it is possible to transform this curve into afrequency spectrum using the Fast Fourier Transform (FFT). This can be done in theChart tabsheet of the Settings window (Figure 8.7).

For curves created in the Normal and Amplifications tabsheets of the Curve generationwindow, you can select the option Use frequency representation (spectrum) and one ofthe three types of spectrum (Standard frequency (Hz), Angular frequency (rad/s) or Waveperiod(s)). Upon clicking on OK button the existing time curve will be transformed into aspectrum. The original curve can be reconstructed by selecting again in the Chart

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Figure 8.6 Amplification spectrum generation

tabsheet by de-selecting the frequency representation.

Figure 8.7 Fast Fourier Transform

For the curves created in the PSA tabsheet of the Curve generation window, theDisplacement response factor can be selected (Figure 8.8), to display the variation ofdisplacement with frequency.

Hint: The Settings window is displayed by right clicking the chart and selecting thecorresponding option in the appearing menu or by selecting the option in theFormat menu.

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Figure 8.8 Displacement response factor option available for PSA curves

8.3 FORMATTING CURVES

Once a curve has been generated, a new chart window is opened in which the generatedcurve is presented. The quantities used to generate the curve are plotted along the x-and y -axis. By default, a legend is presented at the right hand side of the chart. For allcurves in a chart, the legend contains the Curve title, which is automatically generatedwith the curve. An example of the curves in Output program is given in Figure 8.9.

Figure 8.9 Curves in Output program

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8.3.1 MENUS FOR CURVES

The menus in menu bar when curves are displayed vary slightly from the ones in theOutput nu bar when curves are displayed vary slightly from the ones in the Outputprogram. A description of the menus and the options available in them is given as follows.

File menu

The File menu is basically the same with the one available in the Output program. For amore detailed description see Section 6.2.1.

Edit menu

Note that Edit menu is only available when the curves are displayed. The optionsavailable can be used to include curves in the current chart. These options are:

Copy To export the chart to other programs using the Windowsclipboard function. This feature is described in detail in Section6.3.2.

Add curve from current projectTo add a new curve to the active chart from the current project.

Add curve from another projectTo add a new curve to the active chart from another project.

Add curve from clipboardTo add a new curve to the active chart from clipboard.

Hint: The added curves are redefined using the data from either the currentproject, another project or clipboard. It is not possible to mount a generatedcurve to the current chart.

» It is possible to add a curve to the active chart using the Add curve option inthe corresponding option in the right mouse click pop-up menu.

View menu

The display of the results in the window is arranged using the options available in theView menu. These options are:

Reset view To reset a zoomed view.

Hint: For a more detailed view of particular regions in curves, press the left mousebutton at a corner of the zoom area; hold the mouse button down and movethe mouse to the opposite corner of the zoom area; then release the button.The program will zoom into the selected area. The zoom option may be usedrepetitively.The zoomed view can be reset by clicking the corresponding button in thetoolbar as well.

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Table To display the data series in a table. More information on tablesis given in the Section 6.3.8.

Legend To toggle the display of the legend in the chart.

Legend in chart To locate the legend in the chart.

Value indication To toggle the display of information about the points in the curveswhen the mouse pointer is located on them.

Format menu

The Format menu contains the Settings option, selecting which displays thecorresponding window where the layout of the chart and curves can be modified.

Window and Help menus

These menus contain the same options as defined in Sections 6.2.10 and 6.2.11.

8.3.2 EDITING CURVE DATA IN TABLE

In contrast to the general Output program, the Curves part allows for editing of the tableby the user using the options in the menu appearing as the table is right clicked.

Delete rows To delete selected rows in the table.

Update chart To update chart according to the modifications made in the table.

Align To align the text in the selected part of the table.

Decimal To display data in decimal representation.

Scientific To display data in scientific representation.

Decimal digits To define the number of decimal digits displayed.

View factor To define a factor to the values in the table.

Copy To copy the selected values in the table.

Find value To find a value in the table.

Filter To filter the results in the table.

Editing load-displacement curves is often needed when gravity loading is used togenerate the initial stresses for a project. As an example of the procedures involved,consider the embankment project indicated in Figure 8.10.

In this example project soil is to be added to an existing embankment to increase itsheight. The purpose of this example analysis is to calculate the displacement of point Aas the embankment is raised. One approach to this problem is to generate a mesh for thefinal embankment and then deactivate the clusters corresponding to the additional soillayer by using the Initial geometry configuration item of the Input program.

An alternative procedure would be to generate the initial stresses for the project, i.e. thestresses for the case where the original embankment has been constructed but the newmaterial has not yet been placed. This should be done using the gravity loadingprocedure. In this procedure the soil self-weight is applied by increasing ΣMweight fromzero to 1.0 in a Plastic calculation using Total multipliers as Loading input.

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Figure 8.10 Raising an embankment

The settlement behaviour of point A when gravity loading is applied is shown by the initialhorizontal line in Figure 8.11a. This line will, in general, consist of several plasticcalculation steps, all with the same value of ΣMarea.

To model the behaviour of the soil structure as a whole as the additional material isplaced, then the cluster of the additional material should be activated using a stagedconstruction calculation. At the start of this staged construction calculation, alldisplacements should be reset to zero by the user. This removes the effect of thephysically meaningless displacements that occur during gravity loading.

a. Before editing b. After editing

Figure 8.11 Load-displacement curves of the embankment project.

The load-displacement curve obtained at the end of the complete calculation for point Ais shown in Figure 8.11a. To display the settlement behaviour without the initial gravityloading response it is necessary to edit the corresponding load-displacement data. Theunwanted initial portion, with the exception of point 1, should be deleted. Thedisplacement value for point 1 should then be set to zero. The resulting curve is shown inFigure 8.11b.

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As an alternative to the above editing procedure, the gravity loading phase can beexcluded from the list of calculation phases that are included in the curve (Section 8.4).

8.3.3 VALUE INDICATION

If the Value indication option in the View menu is active and the mouse is moved over adata point in a curve, the hint box shows the precise value of the x- and y -quantities atthat point. In addition, it shows the curve point number and the step and phase numberscorresponding with that curve point.

8.4 FORMATTING OPTIONS

The layout and presentation of charts can be modified by clicking the Settingsbutton available in the toolbar or by selecting the corresponding option in the

Format menu. Alternatively, the Settings option can be selected from the Format menu ofthe right mouse button menu. As a result, the Settings window will appear. Distinction ismade between the chart settings displayed on the first tabsheet and the curve settingsdisplayed on a separate tabsheet for each curve. The options available in the Charttabsheet can be used to customize the frame and axes of the chart (Section 8.4.1). Theoptions available in the tabsheets of the curves can be used to customize the plot(Section 8.4.2).

If the correct settings are defined, the OK button may be pressed to activate the settingsand to close the window. Alternatively, the Apply button may be pressed to activate thesettings, keeping the Settings window active. The changes to the settings can be ignoredby pressing the Cancel button.

8.4.1 CHART SETTINGS

The Settings window contains a tabsheet with options to customise the layout andpresentations of the chart (see Figure 8.12).

Titles By default, a title is given to the x-axis and the y -axis, based onthe quantity that is selected for the curve generation. However,this title may be changed in the Title edit boxes of thecorresponding axis group. In addition, a title may be given to thefull chart, which can be entered in the Chart name edit box. Thistitle should not be confused with the Curve title as described inabove.

Scaling of x- and y-axis By default, the range of values indicated on the x- and y -axis isscaled automatically, but the user can select the Manual optionand enter the desired range in the Minimum and Maximum editboxes. As a result, data outside this range will not appear in theplot. In addition, it is possible to plot the x- and/or y -axis on alogarithmic scale using the Logarithmic check box. The use of alogarithmic scale is only valid if the full range of values along anaxis is strictly positive.

Grid Grid lines can be added to the plot by selecting items Horizontalgrid or Vertical grid. The grid lines may be customised by means

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Figure 8.12 Chart settings tabsheet

of the Style and Colour options.

Orthonormal axes The option Orthonormal axes can be used to ensure that thescale used for the x-axis and the y -axis is the same. This optionis particularly useful when values of similar quantities are plottedon the x-axis and y -axis, for example when making diagrams ofdifferent displacement components.

Exchange axes The option Exchange axes can be used to interchange thex-axis and the y -axis and their corresponding quantities. As aresult of this setting, the x-axis will become the vertical axis andthe y -axis will become the horizontal axis.

Flip horizontal or verticalSelecting the option Flip horizontal or Flip vertical willrespectively reverse the horizontal or the vertical axis.

8.4.2 CURVE SETTINGS

The Settings window contains for each of the curves in the current chart a tabsheet withthe same options (Figure 8.13).

Title A default title is given to any curve during its generation. Thistitle may be changed in the Curve title edit box. When a legendis presented for the active chart in the main window, the Curvetitle appears in the legend.

Show curve When multiple curves are present within one chart, it may beuseful to hide temporarily one or more curves to focus attentionon the others. The Show curve option may be deselected for this

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Figure 8.13 Curve settings tabsheet

purpose.

Phases The Phases button may be used to select for which calculationphases the curve has to be generated. This option is usefulwhen not all calculation phases should be included in the curve.

Fitting To draw a smooth curve, the user can select the Fitting item.When doing so, the type of fitting can be selected from the Typecombo box. The Spline fitting generally gives the mostsatisfactory results, but, as an alternative, a curve can be fitted toa polynomial using the least squares method.

Line and marker presentationVarious options are available to customise the appearance of thecurve lines and markers.

Arrow buttons The arrow buttons can be used to change the order of the curvesin the legend.

Regenerate The Regenerate button may be used to regenerate a previouslygenerated curve to comply with new data (Section 8.5).

Add curve The Add curve button may be used to add new curves to thecurrent chart (Section 8.6).

Delete When multiple curves are present within one chart, the Deletebutton may be used to erase a curve.

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8.5 REGENERATION OF CURVES

If, for any reason, a calculation process is repeated or extended with new calculationphases, it is generally desirable to update existing curves to comply with the new data.This can be done by means of the Regenerate facility. This facility is available in theSettings tabsheet (Figure 8.12), which can be opened by selecting the Settings optionfrom the Format menu. When clicking on the Regenerate button, the Curve generationwindow appears, showing the existing setting for x- and y -axis. Pressing the OK buttonis sufficient to regenerate the curve to include the new data. Another OK closes theSettings window and displays the newly generated curve.

When multiple curves are used in one chart, the Regenerate facility should be used foreach curve individually. The Regenerate facility may also be used to change the quantitythat is plotted on the x- or y -axis.

8.6 MULTIPLE CURVES IN ONE CHART

It is often useful to compare similar curves for different points in a geometry, or even indifferent geometries or projects. Therefore PLAXIS allows for the generation of morethan one curve in the same chart. Once a single curve has been generated, the Addcurve options in the Edit menu can be used to generate a new curve in the current chart.As an alternative, the Add curve option from the Settings window or from the right mousebutton menu can be used. Distinction is made between a new curve from the currentproject, a new curve from another project or curves available on the clipboard.

The Add curve procedure is similar to the generation of a new curve (Section 8.2).However, when it comes to the actual generation of the curve, the program imposessome restrictions on the selection of data to be presented on the x- and the y -axis. Thisis to ensure that the new data are consistent with the data of the existing curve.

When the Add curve option is used, the current chart is modified. In order to preserve thecurrent chart, a copy of it can be created by selecting it first in the list and then by clickingthe Copy button in the Curves manager window.

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9 REFERENCES

[1] Bakker, K.J., Brinkgreve, R.B.J. (1990). The use of hybrid beam elements to modelsheet-pile behaviour in two dimensional deformation analysis. Proc. 2nd EuropeanSpecialty Conference on Numerical Methods in Geotechnical Engineering, 559–572.

[2] Bathe, K.J. (1982). Finite element analysis in engineering analysis. Prentice-Hall,New Jersey.

[3] Bathe, K.J. (1996). Finite Element Procedures. Prentice Hall.

[4] Bauduin, C., Vos, M.D., Simpson, B. (2000). Some considerations on the use of finiteelement methods in ultimate limit state design. In LSC 2000: International workshopon Limit State Design in Geotechnical Engineering. Melbourne, Australia.

[5] Benz, T., Schwab, R., Vermeer, P.A., Kauther, R.A. (2007). A Hoek-Brown criterionwith intrinsic material strength factorization. Int. J. of Rock Mechanics and MiningSci., 45(2), 210–222.

[6] Bolton, M.D. (1986). The strength and dilatancy of sands. Geotechnique, 36(1),65–78.

[7] Brinkgreve, R.B.J., Bakker, H.L. (1991). Non-linear finite element analysis of safetyfactors. In Proc. 7th Int. Conf. on Comp. Methods and Advances in Geomechanics.Cairns, Australia, 1117–1122.

[8] Brinkgreve, R.B.J., Kappert, M.H., Bonnier, P.G. (2007). Hysteretic damping insmall-strain stiffness model.

[9] Burd, H.J., Houlsby, G.T. (1989). Numerical modelling of reinforced unpaved roads.Proc. 3rd Int. Symp. on Numerical Models in Geomechanics, 699–706.

[10] Das, B.M. (1995). Fundamentals of soil dynamics. Elsevier.

[11] de Borst, R., Vermeer, P.A. (1984). Possibilities and limitations of finite elements forlimit analysis. Geotechnique, 34(20), 199–210.

[12] Galavi, V. (2010). Groundwater flow, fully coupled flow deformation and undrainedanalyses in PLAXIS 2D and 3D. Technical report, Plaxis BV.

[13] Goodman, R.E., Taylor, R.L., Brekke, T.L. (1968). A model for mechanics of jointedrock. Journal of the Soil Mechanics and Foundations Division, 94, 19–43.

[14] Hird, C.C., Kwok, C.M. (1989). Finite element studies of interface behaviour inreinforced embankments on soft grounds. Computers and Geotechnics, 8, 111–131.

[15] Nagtegaal, J.C., Parks, D.M., Rice, J.R. (1974). On numerically accurate finiteelement solutions in the fully plastic range. Comp. Meth. Appl. Mech. Engng., 4,153–177.

[16] Owen, D.R.J., Hinton, E. (1982). Finite Elements in Plasticity. Pineridge PressLimited, Swansea.

[17] Rheinholdt, W.C., Riks, E. (1986). Solution techniques for non-linear finite elementequations. In A.K. Noor, W.D. Pilkey (eds.), State-of-the-art Surveys on FiniteElement Techniques, chapter 7.

[18] Rowe, R.K., Ho, S.K. (1988). Application of finite element techniques to the analysis

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of reinforced soil walls. In P.M. Jarett, A. McGown (eds.), The Application ofPolymeric Reinforcement in Soil Retaining Structures. 541–553.

[19] Schank, O., Gärtner, K. (2006). On fast factorization pivoting methods for symmetricindefinite systems. Electronic Transactions on Numerical Analysis, 23, 158–179.

[20] Schank, O., Wächter, A., Hagemann, M. (2007). Matching−based preprocessingalgorithms to the solution of saddle−point problems in large−scale nonconvexinterior−point optimization. Computational Optimization and Applications, 36 (2-3),321–341.

[21] Schikora, K., Fink, T. (1982). Berechnungsmethoden moderner bergmännischerbauweisen beim u-bahn-bau. Bauingenieur, 57, 193–198.

[22] Sloan, S.W. (1981). Numerical analysis of incompressible and plastic solids usingfinite elements. Ph.D. thesis, University of Cambridge, U.K.

[23] Sloan, S.W., Randolph, M.F. (1982). Numerical prediction of collapse loads usingfinite element methods. Int. J. Num. Analyt. Meth. in Geomech., 6, 47–76.

[24] Sluis, J. (2012). Validation of embedded pile row in plaxis 2d.

[25] Smith, I.M. (1982). Programming the finite element method with application togeomechanics. John Wiley & Sons, Chichester.

[26] Song, E.X. (1990). Elasto-plastic consolidation under steady and cyclic loads. Ph.D.thesis, Delft University of Technology, The Netherlands.

[27] van Langen, H. (1991). Numerical analysis of soil structure interaction. Ph.D. thesis,Delft University of Technology, The Netherlands.

[28] van Langen, H., Vermeer, P.A. (1990). Automatic step size correction fornon-associated plasticity problems. Int. J. Num. Meth. Eng., 29, 579–598.

[29] van Langen, H., Vermeer, P.A. (1991). Interface elements for singular plasticitypoints. Int. J. Num. Analyt. Meth. in Geomech., 15, 301–315.

[30] Vermeer, P.A., van Langen, H. (1989). Soil collapse computations with finiteelements. In Ingenieur-Archive 59. 221–236.

[31] Vermeer, P.A., Verruijt, A. (1981). An accuracy condition for consolidation by finiteelements. Int. J. for Num. Anal. Met. in Geom., 5, 1–14.

[32] Zienkiewicz, O.C. (1977). The Finite Element Method. McGraw-Hill, London.

296 Reference Manual | PLAXIS 2D 2012

INDEX

INDEX

A

Accelerations · 261g · 262

Anchorfixed-end anchor · 40node-to-node anchor · 40prestressing · 182properties · 135

Arc-length control · 151Automatic

error checks · 226mesh generation · 60step size · 157

Avoid predeforming · 260

B

Boundary conditionsadjustments during calculation · 226displacements · 50groundwater head · 195submerged boundaries · 154

C

Calculationabort · 220Advanced mode · 150automatic step size · 157manager · 219mode · 140phase · 143plastic · 149staged construction · 125type

Consolidation · 149Dynamic · 153Gravity · 147Groundwater flow (steady-state) ·

153Groundwater flow (transient) · 154K0 procedure · 146Plastic · 149Plastic nil-step · 148Safety · 150

Calculation stepsmax steps saved · 174

CalculationsMode

Advanced · 142Classical · 141Flow · 142

CamClay · 68Cavitation cut-off · 168Clipboard

output · 235Cluster · 243Command

line · 25Connectivity plot · 60Contraction · 183Coordinate

x-coordinate · 24y-coordinate · 24

Copy to clipboardInput · 26Output · 237

Coulomb point · 148Create animation · 231Cross section · 236

output · 244Curve

generation · 281regeneration · 294settings · 291

Curves manager · 239

D

DampingRayleigh · 71

Deformations · 259Displacement

incremental · 261phase · 260prescribed · 50reset · 174total · 260

Distributed load · 52Drained behaviour · 69Drains · 47Dynamic analysis · 153

E

ElementEmbedded pile · 34plate · 31

PLAXIS 2D 2012 | Reference Manual 297

REFERENCE MANUAL

soil · 18Embedded pile

element · 34Embedded pile row · 32Error

equilibrium · 162global error · 222, 226local error · 226tolerated · 162

Excess pore pressure · 186Export

Output · 238Extrapolation · 166

F

Fliphorizontal · 292vertical · 292

Forceanchor · 134prestressing · 182unit of · 209

G

Generationmesh · 60

Geogrids · 36Geometry

line · 29Global coarseness · 61Global error · 222, 226Gravity

loading · 208Gravity loading · 146Groundwater · 186Groundwater flow

steady-state · 153transient · 154

H

Hardening Soil model · 68Hardening Soil model with small-strain

stiffness · 68Hinges · 46

I

Ignore undrained behaviour · 174Incremental multiplier · 169, 170, 172Initial stress · 146Input

bending moment · 54Interface

output · 272real interface thickness · 101strength · 98virtual thickness · 98

Interface element · 37Interface permeability · 101

J

Jointed Rock · 68

K

K0 procedure · 146

L

Linegeometry line · 29scan line · 231

Load advancement · 157number of steps · 157ultimate level · 157

Load multiplier · 178incremental · 165total · 206

Load stepping · 157Load-displacement · 283

curves · 283Local coarseness · 61

M

Maccel · 208Manual

input · 25Marea · 176Material

model · 67type · 69

Material data setsanchors · 133embedded piles · 128geogrids · 126plates · 121

Maximum iterations · 163Mdisp · 51, 179MdispX · 207MdispY · 207Mesh

generation · 60Mesh generation · 60

298 Reference Manual | PLAXIS 2D 2012

INDEX

MloadA · 52, 53, 54, 178MloadB · 52, 53, 54, 178Mobilised shear strength · 265Model

axisymmetric · 16plane strain · 16

Model see Material model · 16Mohr-Coulomb · 151Msf · 151Mstage · 171Mweight · 123

N

Nodes · 234Input · 234

O

Outputlayout · 230menu bar · 230plot area · 230status bar · 230title bar · 230toolbar · 230

Over-relaxation · 163

P

Phasesselection for output · 225

Phreatic level · 188Plastic nil-step · 154Plastic point

Coulomb point · 148inaccurate · 228

Plateelement · 31

Plates · 30Point

geometry point · 29points for curves · 140

Point loads · 53Pore pressure · 69

active · 186excess · 154

Precipitation · 192Print

Output · 238output · 231

R

Radius · 43Real interface thickness · 101Refine

around point · 62cluster · 62global · 61line · 62

Relative shear stress · 265Report

Generation · 254Store view · 239

Report generation · 254Report generator · 231Reset displacements · 174Rotation · 25Rotation springs · 46

S

Safety · 145, 150Scaling · 240Scan line · 231Seepage surface · 197Sign convention · 273Soft Soil Creep model · 267Soft Soil model · 68Soil

dilatancy angle · 97friction angle · 99material properties · 60saturated weight · 69undrained behaviour · 69unsaturated weight · 70

Soil elements · 18Spline fitting · 293Staged construction · 158Standard setting · 161Strains

incremental Cartesian · 262phase Cartesian · 262total Cartesian strains · 262

Stresseffective · 186inaccurate · 227

Stress point · 17Stresses

Cartesian effective · 264Cartesian total · 264principal effective · 264

PLAXIS 2D 2012 | Reference Manual 299

REFERENCE MANUAL

principal total · 266Structures

output · 272

T

Tablesoutput · 240

Timeunit of · 171

Tolerated error · 151Total multiplier · 206Tunnel

centre point · 43designer · 41reference point · 41, 46

U

Undo · 26Undrained behaviour · 69

V

Velocities · 261Void ratio · 71Volume strain · 181

W

Waterconditions · 186

Water boundary conditionsclosed · 191free · 197infiltration · 199inflow · 199outflow · 199

Water pressuregeneration · 203

Weightsaturated weight · 69soil weight · 70unsaturated weight · 70

Wells · 48Window

calculations · 143generation · 146input · 41

X

x-coordinate · 24

Y

y-coordinate · 24

Z

Zoomzoom in · 26zoom out · 26

300 Reference Manual | PLAXIS 2D 2012

APPENDIX A — POSSIBILITIES AND LIMITATIONS OF PLAXIS 2D

APPENDIX A — POSSIBILITIES AND LIMITATIONS OF PLAXIS 2D

As many changes have been done as of the release of PLAXIS 2D 2010 compared toearlier versions, the features available from PLAXIS 2D 2010 are described here. Themain features are the use of Bishop’s stress in Advanced mode (to describe partiallysaturated behaviour of soils) and a change in the use of water conditions.

In the following sections these features are investigated.

A.1 CLASSICAL MODE

This mode is similar to PLAXIS 2D version 9.0 and earlier. The following features are thesame for all types of calculation:

Stress Use of Terzaghi’s stress.

Soil weight The soil weight is defined by the unsaturated soil weight γunsatabove the phreatic level and by the saturated soil weight γsatbelow the phreatic level.

Saturation The value of saturation is always equal to 1 below the phreaticlevel and equal to 0 above the phreatic level. However, this isjust for the visualisation and is not used in the calculations. Forunsaturated soil models, suction is always equal to 0 and thedegree of saturation is always equal to 1.

Groundwater flow Features are unsaturated flow (steady-state as well as transient),a change of permeability with deformation and a change ofelastic storage with stress (in stress dependent models). Thelast two features are new features as of PLAXIS 2D 2010.

K0-procedure

Features of the K0-procedure are:

Phreatic level Should be horizontal

Soil layers Should be horizontal. Tunnels and vertical clusters in which oneof them is deactivated are not allowed.

Plastic analysis

Features of the Plastic analysis are:

Drainage behaviour The bulk modulus of water is calculated according to the elasticstiffness of soil (Undrained (A) and Undrained (B)). For all soilbelow and above the phreatic level in which the drainage type isdefined as Drained or Non-porous (or dry cluster) or when acluster has just been activated, a zero bulk modulus of water isconsidered (Kw = 0). The Undrained behaviour can be ignoredby selecting the corresponding option.

Groundwater flow Both steady-state and transient groundwater flow calculationscan be used. If the type of groundwater flow calculation is

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REFERENCE MANUAL

transient, for each step of flow, deformation is calculated. If thereis any mechanical load (for example, a load or activation ordeactivation of a cluster) only the last step of the groundwaterflow calculation is utilised.

Updated mesh Available.

Updated water pressuresAvailable.

Consolidation analysis

Features of the Consolidation analysis are:

Drainage behaviour The bulk modulus of water is calculated according to the elasticstiffness of soil (Undrained (A), Undrained (B) and Drained). Forall soil below and above the phreatic level in which the drainagetype is defined as Non-porous (or dry cluster), a zero bulkmodulus of water is considered (Kw = 0). In case a cluster hasjust been activated (below and above the phreatic level), a verysmall bulk modulus of water is assumed (Kw = 10−8 × Kw ).

Groundwater flow Both steady-state and transient groundwater flow calculationscan be used. If the type of groundwater flow calculation istransient, for each step of flow, deformation is calculated. If thereis any mechanical load (for example, a load or activation ordeactivation of a cluster) only the last step of the groundwaterflow calculation is utilised.

Updated mesh Available.

Updated water pressuresAvailable.

Boundary conditions for flowThe available options are closed or interface.

Safety

Features of the Safety are:

Drainage behaviour The bulk modulus of water is calculated according to the elasticstiffness of soil and type of drainage. If the Drainage type is set to Undrained (A) orUndrained (B) the bulk modulus of water is taken into account. Otherwise, the bulkmodulus of water will be set to zero (Kw = 0). If the option Ignore undrainedbehaviour is used the bulk modulus of water will be set to zero for all soil (Kw = 0).

Groundwater flow It is not possible to perform a groundwater flow calculation during aSafety analysis.

Updated mesh Available.

Updated water pressures Available.

Dynamic analysis

Features of the Dynamic analysis are:

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APPENDIX A — POSSIBILITIES AND LIMITATIONS OF PLAXIS 2D

Drainage behaviour The bulk modulus of water is calculated according to the elasticstiffness of soil and type of drainage. If the Drainage type is set to Undrained (A) orUndrained (B) the bulk modulus of water is taken into account. Otherwise, the bulkmodulus of water will be set to zero (Kw = 0). If the option Ignore undrainedbehaviour is used then the bulk modulus of water will be set to zero for all soil(Kw = 0).

Groundwater flow It is not possible to perform a groundwater flow calculation during adynamic analysis.

Updated mesh Not available.

Updated water pressures Not available.

Free vibration analysis

Features of the Free vibration analysis are:

General Only available after the Plastic or Consolidation types ofcalculation.

Drainage behaviour The bulk modulus of water is calculated according to the elasticstiffness of soil and type of drainage. If the Drainage type is setto Undrained (A) or Undrained (B) the bulk modulus of water istaken into account. Otherwise, the bulk modulus of water will beset to zero (Kw = 0). If the option Ignore undrained behaviour isused then the bulk modulus of water will be set to zero for all soil(Kw = 0).

Groundwater flow It is not possible to perform a groundwater flow calculation duringa Free vibration analysis.

Updated mesh Not available.

Updated water pressuresNot available.

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REFERENCE MANUAL

TableA

.1B

ulkm

odulusofw

aterin

classicalmode

Typeof

material

Plastic

(drained)P

lastic(undrained)

Consolidation

Phi/c

reductionor

dynamics

(drained)

Phi/c-reduction

ordynam

ics(undrained)

Undrained

(belowand

abovephreatic

level)

Kw

=0

Kwn

=

2·G3 (

1+ν

u1−

2ν

u−

1+ν′

1−

2ν′ )

Kwn

=

2·G3 (

1+ν

u1−

2ν

u−

1+ν′

1−

2ν′ )

Kw

=0

Kwn

=

2·G3 (

1+ν

u1−

2ν

u−

1+ν′

1−

2ν′ )

Drained

(belowand

abovephreatic

level)

Kw

=0

Kw

=0

Kwn

=

2·G3 (

1+ν

u1−

2ν

u−

1+ν′

1−

2ν′ )

Kw

=0

Kw

=0

Cluster

justbeen

activated(below

andabove

phreaticlevel)

Kw

=0

Kw

=0

Kwn

=

2·G3 (

1+ν

u1−

2ν

u−

1+ν′

1−

2ν′ )·

10−

8

Notrelevant

Notrelevant

Non-porous

ordry

clusterK

w=

0K

w=

0K

w=

0K

w=

0K

w=

0

304 Reference Manual | PLAXIS 2D 2012

APPENDIX A — POSSIBILITIES AND LIMITATIONS OF PLAXIS 2D

A.2 ADVANCED MODE

In this mode unsaturated soil modelling is available. This mode is new as of PLAXIS 2D2010. The following features are the same for all types of calculation:

Stress Use of Bishop’s stress.

Soil weight The weight of the soil is calculated by the following formulation:

γ = (1− Se)γunsat + Seγsat

where Se is the effective saturation.

Saturation The degree of saturation is calculated according to the SWCCdefined.

Groundwater flow Only unsaturated flow (steady-state only) is available.

K0-procedure

Features of the K0-procedure are:

Phreatic level Should be horizontal

Soil layers Should be horizontal. Tunnels and vertical clusters in which oneof them is deactivated are not allowed.

Plastic analysis

Note that this type of calculation is suction dependent and even for a linear-elasticmaterial it needs more calculation steps compare to the same type of calculation in theclassical mode. Features of the Plastic analysis are:

Drainage behaviour The bulk modulus of water is calculated according to the elasticstiffness of soil (Undrained (A) and Undrained (B)). For all soilbelow the phreatic level, the bulk modulus of saturated soil isconsidered. For soil above the phreatic level, the bulk modulus ofwater is reduced based on the degree of saturation. For soil inwhich the drainage type is defined as Drained or Non-porous (ordry cluster) or when a cluster has just been activated, a zero bulkmodulus of water is considered (Kw = 0). The Undrainedbehaviour can be ignored by selecting the corresponding option.

Groundwater flow Only a steady-state groundwater flow calculation can beperformed.

Updated mesh Available.

Updated water pressuresAvailable.

Consolidation analysis

Features of the Consolidation analysis are:

Drainage behaviour The bulk modulus of water is calculated according to the elasticstiffness of soil (Undrained (A), Undrained (B) and Drained). Forall soil below and above the phreatic level in which the drainage

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REFERENCE MANUAL

type is defined as Non-porous (or dry cluster), a zero bulkmodulus of water is considered (Kw = 0). In case a cluster hasjust been activated (below and above the phreatic level), a verysmall bulk modulus of water is assumed (Kw = 10−8 × Kw ).

Groundwater flow It is not possible to perform a groundwater flow calculation duringa consolidation analysis based on total pore pressure.

Updated mesh Not available.

Update water pressures Not available.

Boundary conditions for flowThe following boundary conditions are available: closed,interface, seepage (constant or time dependent), head (constantor time dependent), prescribed boundary flux/infiltration(constant or time dependent), a well and a drain. In addition, aninternal prescribed flux can be added, which is needed fornumerical modelling of vacuum consolidation.

Time dependent boundary conditions for flowThe following options are available: linear, harmonic and input bya table.

Safety

Features of the Safety are:

Drainage behaviour The bulk modulus of water is calculated according to the elasticstiffness of soil (Undrained (A) and Undrained (B)). For all soilbelow the phreatic level, the bulk modulus of saturated soil isconsidered. For soil above the phreatic level, the bulk modulus ofwater is reduced based on the degree of saturation. For soil inwhich the drainage type is defined as Drained or Non-porous (ordry cluster) or when a cluster has just been activated, a zero bulkmodulus of water is considered (Kw = 0). If the option Ignoreundrained behaviour is used the bulk modulus of water will beset to zero for all soil (Kw = 0).

Groundwater flow It is not possible to perform a groundwater flow calculation duringa Safety analysis.

Updated mesh Available

Updated water pressuresAvailable

Dynamic analysis

Features of the Dynamic analysis are:

Drainage behaviour The bulk modulus of water is calculated according to the elasticstiffness of soil (Undrained (A) and Undrained (B)). For all soilbelow the phreatic level, the bulk modulus of saturated soil isconsidered. For soil above the phreatic level, the bulk modulus ofwater is reduced based on the degree of saturation. For soil in

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APPENDIX A — POSSIBILITIES AND LIMITATIONS OF PLAXIS 2D

which the drainage type is defined as Drained or Non-porous (ordry cluster) or when a cluster has just been activated, a zero bulkmodulus of water is considered (Kw = 0). If the option Ignoreundrained behaviour is used the bulk modulus of water will beset to zero for all soil (Kw = 0).

Groundwater flow It is not possible to perform a groundwater flow calculation duringa dynamic analysis.

Updated mesh Not available.

Updated water pressuresNot available.

Free vibration analysis

Features of the Free vibration analysis are:

General : Only available after a plastic or consolidation types ofcalculation.

Drainage behaviour The bulk modulus of water is calculated according to the elasticstiffness of soil (Undrained (A) and Undrained (B)). For all soilbelow the phreatic level, the bulk modulus of saturated soil isconsidered. For soil above the phreatic level, the bulk modulus ofwater is reduced based on the degree of saturation. For soil inwhich the drainage type is defined as Drained or Non-porous (ordry cluster) or when a cluster has just been activated, a zero bulkmodulus of water is considered (Kw = 0).If the option Ignoreundrained behaviour is used the bulk modulus of water will beset to zero for all soil (Kw = 0).

Groundwater flow It is not possible to perform a groundwater flow calculation duringa dynamic analysis.

Updated mesh Not available.

Updated water pressuresNot available.

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REFERENCE MANUAL

TableA

.2B

ulkm

odulusofw

aterin

advancedm

ode

Typeof

material

Plastic

(drained)P

lastic(undrained)

Consolidation

Safety

ordynam

ics(drained)

Safety

ordynam

ics(undrained)

Undrained

(pw≤

0)

Kw

=0

Ksatwn

=

2·G3 (

1+ν

u1−

2ν

u−

1+ν′

1−

2ν′ )

Ksatwn

=

2·G3 (

1+ν

u1−

2ν

u−

1+ν′

1−

2ν′ )

Kw

=0

Ksatwn

=

2·G3 (

1+ν

u1−

2ν

u−

1+ν′

1−

2ν′ )

Undrained

(pw>

0)

Kw

=0

Kunsatw

=Ksatw

Kair

SK

air +(1−

S)K

satw

Ksatwn

=

2·G3 (

1+ν

u1−

2ν

u−

1+ν′

1−

2ν′ )

Kw

=0

Kunsatw

=Ksatw

Kair

SK

air +(1−

S)K

satw

Drained

(pw≤

0)

Kw

=0

Kw

=0

Ksatwn

=

2·G3 (

1+ν

u1−

2ν

u−

1+ν′

1−

2ν′ )

Kw

=0

Kw

=0

Drained

(pw>

0)

Kw

=0

Kw

=0

Ksatwn

=

2·G3 (

1+ν

u1−

2ν

u−

1+ν′

1−

2ν′ )

Kw

=0

Kw

=0

Cluster

justbeen

activatedK

w=

0K

w=

0K

w=

Ksatw·10

−8

Notrelevant

Notrelevant

Non-porous

ordry

clusterK

w=

0K

w=

0K

w=

0K

w=

0K

w=

0

308 Reference Manual | PLAXIS 2D 2012

APPENDIX A — POSSIBILITIES AND LIMITATIONS OF PLAXIS 2D

A.3 FLOW MODE

In this mode pure groundwater flow calculations are available. Note that the bulk modulusof water is automatically calculated according to the elastic stiffness. This leads to aconsistent elastic storage in the coupled flow deformation analysis and groundwater flowanalysis. Since in the flow mode stresses are zero, constitutive models in which elasticityis stress dependent should not be used.

Steady-state flow

Features of the steady-state flow are:

• Drainage behaviour: a groundwater flow calculation is only possible for activatedclusters with a soil material of which the Drainage type has been set to Undrained(A), Undrained (B) or Drained. In case a Non-porous material has been used or thecluster has been set to Cluster dry, a zero bulk modulus of water is considered(Kw = 0), meaning that there is no flow in such clusters.

• Updated mesh: this feature is not available.

• Updated water pressures: this feature is not available.

• Boundary conditions for flow: the following boundary conditions are available:closed, interface, seepage, head, prescribed boundary flux (infiltration), a well and adrain.

• Time dependent boundary conditions for flow: this feature is not available.

Transient flow

Features of the transient flow are:

• Drainage behaviour: the bulk modulus of water is calculated according to the elasticstiffness of soil (Undrained (A), Undrained (B) and Drained). For all soil below andabove the phreatic level in which the drainage type is defined as Non-porous (or drycluster), a zero bulk modulus of water is considered (Kw = 0). In case a cluster hasjust been activated (below and above the phreatic level), a very small bulk modulusof water is assumed (Kw = 10−8 × Kw ).

• Updated mesh: this feature is not available.

• Update water pressures: this feature is not available.

• Boundary conditions for flow: the following boundary conditions are available:closed, interface, seepage (constant or time dependent), head (constant or timedependent), prescribed boundary flux/infiltration (constant or time dependent), awell and a drain.

• Time dependent boundary conditions for flow: the following options are available:linear, harmonic and input by a table.

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REFERENCE MANUAL

Table A.3 Bulk modulus of water in flow mode

Type ofmaterial

Steady-state Transient

Undrained(pw ≤ 0)

K satwn =

2 ·G3

(1 + νu

1− 2νu− 1 + ν′

1− 2ν′

) K satwn =

2 ·G3

(1 + νu

1− 2νu− 1 + ν′

1− 2ν′

)Undrained(pw > 0)

K satwn =

2 ·G3

(1 + νu

1− 2νu− 1 + ν′

1− 2ν′

) K satwn =

2 ·G3

(1 + νu

1− 2νu− 1 + ν′

1− 2ν′

)Drained(pw ≤ 0)

K satwn =

2 ·G3

(1 + νu

1− 2νu− 1 + ν′

1− 2ν′

) K satwn =

2 ·G3

(1 + νu

1− 2νu− 1 + ν′

1− 2ν′

)Drained(pw > 0)

K satwn =

2 ·G3

(1 + νu

1− 2νu− 1 + ν′

1− 2ν′

) K satwn =

2 ·G3

(1 + νu

1− 2νu− 1 + ν′

1− 2ν′

)Cluster justbeen activated

K satwn =

2 ·G3

(1 + νu

1− 2νu− 1 + ν′

1− 2ν′

) Kw = K satw · 10−8

Non-porous ordry cluster

Kw = 0 Kw = 0

310 Reference Manual | PLAXIS 2D 2012

APPENDIX A — POSSIBILITIES AND LIMITATIONS OF PLAXIS 2D

A.4 OVERVIEW

PLAXIS 2D 2012 | Reference Manual 311

REFERENCE MANUAL

TableA

.4O

verviewpfthe

possibilitiesto

definew

aterconditions

Calculation

Classicalm

odeA

dvancedm

ode

Steady-state

TransientP

hreaticlevel

Previous

phaseS

teady-stateTransient

Phreatic

levelP

reviousphase

K0 -procedure

√√

√√

Plastic

√√

√√

√√

√

Safety

√√

Consolidation

√√

√√

√√

Dynam

ic√

√

Freevibration

√√

312 Reference Manual | PLAXIS 2D 2012

APPENDIX A — POSSIBILITIES AND LIMITATIONS OF PLAXIS 2D

Tabl

eA

.5A

vaila

bilit

yof

the

feat

ures

Upd

ated

mes

han

dU

pdat

edw

ater

pres

sure

s.N

ote

that

none

ofth

eop

tions

are

avai

labl

ein

the

flow

mod

e.

Type

ofca

lcul

atio

nC

lass

ical

mod

eA

dvan

ced

mod

e

Upd

ated

mes

hU

pdat

edw

ater

pres

sure

sU

pdat

edm

esh

Upd

ated

wat

erpr

essu

res

K0-p

roce

dure

Pla

stic

√√

√√

Saf

ety

√√

√√

Con

solid

atio

n√

√

Dyn

amic

Free

vibr

atio

n

PLAXIS 2D 2012 | Reference Manual 313

REFERENCE MANUAL

314 Reference Manual | PLAXIS 2D 2012

APPENDIX B — PROGRAM AND DATA FILE STRUCTURE

APPENDIX B — PROGRAM AND DATA FILE STRUCTURE

B.1 PROGRAM STRUCTURE

The full PLAXIS 2D program consists of various sub-programs, modules and other fileswhich are copied to various directories during the installation procedure (Section 4 in theGeneral information part). The most important files are located in the PLAXIS 2Dprogram directory. Some of these folders, files and their functions are listed below.

B.1.1 FOLDERS

Manuals The pdf version of the manuals

Markers Resources used by SendMaterial

Tools Tools for expert users

B.1.2 EXECUTABLES

batch.exe Calculations program (Chapter 5)

CodemeterChecker.exe Plaxis codemeter license update

geo.exe Input program (pre-processor) (Chapter 3)

k02d.exe K0 procedure analysis

mdbtomat.exe Convert of old material databases to the new one

PackProject.exe Pack project

plasw.exe Deformation analysis program (plastic calculation, consolidation,updated mesh)

Plaxis2DInput.exe Input program (pre-processor)

plaxout.exe Output program (post-processor) (Chapter 6)

plxmshw.exe Mesh generator

ReportGenerator.exe Report generation module

sensiana.exe Sensitivity analysis module

VirtuaLab.exe SoilTest module

vlabc_2d .exe SoilTest kernel

B.1.3 DLL FILES

CMUserMsgUs.dll Display a friendly error message in case of CodeMeter issues

fspline.dll Spline functions for retention curve

KernelLog32.dll Internal communication mechanism (32-bit)

plxzip.dll Unpack old zipped projects

timecons.dll Estimate the first minimum and maximum time steps forconsolidation

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REFERENCE MANUAL

B.2 PROJECT DATA FILES

The main file used to store information for a PLAXIS project has a structured format andis named <project>.P2D, where <project> is the project title. Besides this file, additionaldata is stored in multiple files in the sub-directory <project>.P2DAT. The files in thisdirectory may include:

d##.log Contains deformation calculation progress logs

f##.log Contains flow calculation progress logs

data.### The files having the extension ‘###’ are created by thecalculation kernel. The ‘###’ is the step number; it is at least 3digits but can be longer when there are 1000 or more steps. 1)

data.anaini Configuration of the sensitivity analysis

data.c## Contains data for curve generation. 2)

data.d## Debug calculation logs generated by the kernel during thecalculation. 2)

EMF Files Preview of the defined phases

plaxmesh.err Error message file

data.gpv Previews of the generated curves

data.gxl Information about the generated curves

data.his Information about the nodes selected for curve generation

data.sis Information about the stress points selected for curve generation

data.inp Contains project model data.

data.l## Staged construction settings2)

data.m## File containing information about the materials in the model

MSH Files Project model data. It is generated only once; directly aftergenerating the mesh. It contains all data concerning the mesh.

plaxis.msi Mesh generator input file

plaxis.mso Mesh generator output files

data.nsl Information about the selected nodes and stress points (afterCalculation)

data.opi The information of project phases for output

data.p2d Main project file

data.plxmat Contains all material sets and parameters

PLXML Files The PLXML file format is essentially a limited binaryrepresentation of XML, tweaked for the needs of the HierarchicStorages

S## Files Files containing all the monitored values for the integration points

data.log Log file of the project

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APPENDIX B — PROGRAM AND DATA FILE STRUCTURE

data.W## The files having the extension ‘W##’ contain the currentgroundwater conditions. The ‘##’ stands for the phase number inwhich the groundwater condition is first created. A project alwayshas a ‘W00’ file for the initial conditions.

1) Three digit deformation calculation step number (001, 002, . . . ). Above 999 gives anadditional digit in the file extension.2) Two digit calculation phase number (01, 02, . . . ). Above 99 gives an additional digit inthe file extension.

To create a copy of a PLAXIS project under a different name or in a different directory, itis recommended to open the project in the Input program and to save it under a differentname using the Save as option in the File menu. In this way the required file and datastructure is properly created.

During the creation of a project, before the project is explicitly saved under a specificname, intermediately generated information is stored in the TEMP directory as specifiedin the Windows® operating system using the project name XXOEGXX. The TEMPdirectory also contains some backup files (GEO.# where # is a number) as used for therepetitive undo option (Section 3.3). The structure of the GEO.# files is the same as thePLAXIS project files. Hence, these files may also be used to ‘repair’ a project of which,for any reason, the project file was damaged. This can be done by copying the mostrecent backup file to <project>.P2D in the PLAXIS work directory.

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APPENDIX C — SHORTCUTS OUTPUT PROGRAM

APPENDIX C — SHORTCUTS OUTPUT PROGRAM

Table C.1 Keyboard shortcuts

Key Action View

<Ctrl — A> Select all structures of selected type Model, Structure, Cross section

<Ctrl — C> Copy All

<Ctrl — D> Display prescribed displacements All

<Ctrl — E> Export to file All

<Ctrl — F> Display fixities All

<Ctrl — H> Display phreatic level All

<Ctrl — I> Stress points All

<Ctrl — L> Display loads All

<Ctrl — M> Materials All

<Ctrl — N> Nodes All

<Ctrl — O> Open project All

<Ctrl — P> Print All

<Ctrl — R> Reset view All

<Ctrl — S> Save view All

<Ctrl — T> Table All

<Ctrl — F4> Close window All

<Ctrl — 0> Connectivity plot All

<Ctrl — 1> Deformed mesh All

<Ctrl — 2> Total displacements All

<Ctrl — 3> Incremental displacements All

<Ctrl — 4> Total strains All

<Ctrl — 5> Incremental strains All

<Ctrl — 6> Plastic points All

<Ctrl — 7> Pore pressures All

<Ctrl — => Move Cross section forward 1/100 of the model size Cross section

<Ctrl — -> Move Cross section backward 1/100 of the model size Cross section

<Ctrl — Alt — C> Change soil colour intensity Model, Cross section

<Ctrl — Shift — A> Show all soil elements Model

<Ctrl — Shift — M> Create animation Model, Cross section, Structure

<Ctrl — Shift — N> Hide all soil elements Model

<Ctrl — Shift — Enter> Goes to structure view with selected materials Model, Structure, Cross section

<Ctrl — Shift — +> Move Cross section 1/1000 of the model size Cross section

<Ctrl — Shift — -> Move Cross section 1/1000 of the model size Cross section

<Escape> Clear selected structures Model, Cross section, Structure

<F1> Manuals All

<F2> Curves manager All

<F10> Settings All

Table C.2 Table shortcutsKey Action

<Ctrl — A> Select all

<Ctrl — F> Find value

<Ctrl — M> Jump to maximum value in column

<Ctrl — N> Jump to minimum value in column

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Table C.3 Mouse shortcuts

Key Action View

Wheel move Zoom in/out. All

Move with left mouse button down Move model. All — Beware not to start over a structure.

Press Select structures — Click onstructure

Select small group the structurebelongs to.†

Model, Cross section, Structure — Resets currentselection.

Press Select structures — <Shift> -Click on structure

Toggles selection of small group thestructure belongs to.‡

Model, Cross section, Structure — Selection of otherstructure type will be cleared.

Press Select structures — <Ctrl> — Clickon structure

Toggles selection of structure. Model, Cross section, Structure — Selection of otherstructure type will be cleared.

Press Select structures — <Alt> — Clickon structure

Toggles selection of large group thestructure belongs to.§

Model, Cross section, Structure — Selection of otherstructure type will be cleared.

Press Hide soil — <Ctrl> — Click on soil Hides soil element. Model, Forces — Won’t work if structure is selected.

Press Hide soil — <Ctrl + Shift> — Clickon soil

Hides soil cluster. Model, Forces — Won’t work if structure is selected.

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Reference Manual

2012

Build 5848

TABLE OF CONTENTS

TABLE OF CONTENTS

1 Introduction 9

2 General information 112.1 Units and sign conventions 112.2 File handling 132.3 Help facilities 13

3 Input program — General overview 153.1 Starting the Input program 15

3.1.1 New project 163.1.2 Existing project 203.1.3 Importing a geometry 203.1.4 Packing a project 21

3.2 Layout of the Input program 233.3 Menus in the Menu bar 25

3.3.1 File menu 253.3.2 Edit menu 263.3.3 View menu 263.3.4 Geometry menu 263.3.5 Loads menu 273.3.6 Materials menu 283.3.7 Mesh menu 283.3.8 Help menu 28

3.4 Geometry 293.4.1 Points and lines 293.4.2 Plates 303.4.3 Embedded pile row 323.4.4 Geogrids 363.4.5 Interfaces 373.4.6 Node-to-node anchors 403.4.7 Fixed-end anchors 403.4.8 Tunnels 413.4.9 Hinges and rotation springs 463.4.10 Drains 473.4.11 Wells 48

3.5 Loads and boundary conditions 483.5.1 Standard fixities 483.5.2 Standard earthquake boundaries 493.5.3 Standard absorbent boundaries (dynamics) 493.5.4 Set dynamic load system 493.5.5 Fixities 493.5.6 Rotation fixities (plates) 503.5.7 Absorbent boundaries 503.5.8 Prescribed displacements 503.5.9 Distributed loads 523.5.10 Point loads 533.5.11 Bending moments 54

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3.6 Design approaches 543.6.1 Definition of design approaches 553.6.2 Definition of partial factors for loads 573.6.3 Definition of partial factors for materials 58

3.7 Mesh generation 603.7.1 Basic element type 613.7.2 Global coarseness 613.7.3 Global refinement 613.7.4 Local coarseness 613.7.5 Local refinement 623.7.6 Automatic refinement 62

4 Material properties and material database 654.1 Modelling soil and interface behaviour 67

4.1.1 General tabsheet 674.1.2 Parameters tabsheet 734.1.3 Flow parameters tabsheet 904.1.4 Interfaces tabsheet 964.1.5 Initial tabsheet 102

4.2 Modelling undrained behaviour 1044.2.1 Undrained (A) 1054.2.2 Undrained (B) 1054.2.3 Undrained (C) 106

4.3 Simulation of soil tests 1064.3.1 Triaxial test 1094.3.2 Oedometer 1104.3.3 CRS 1114.3.4 DSS 1124.3.5 General 1134.3.6 Results 1134.3.7 Parameter optimisation 114

4.4 Material data sets for plates 1214.4.1 Material set 1214.4.2 Properties 122

4.5 Material data sets for geogrids 1254.5.1 Material set 1264.5.2 Properties 126

4.6 Material data sets for embedded pile rows 1274.6.1 Material set 1284.6.2 Properties 1294.6.3 Interaction properties (pile bearing capacity) 1304.6.4 Interface stiffness factor 131

4.7 Material data sets for anchors 1334.7.1 Material set 1334.7.2 Properties 134

4.8 Assigning data sets to geometry components 136

5 Calculations 1375.1 Layout of the Calculations program 137

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5.2 Menus in the menu bar 1395.3 Calculation modes 141

5.3.1 Classical mode 1415.3.2 Advanced mode 1425.3.3 Flow mode 142

5.4 Defining calculation phases 1435.4.1 Calculation tabsheets 1435.4.2 Inserting and deleting calculation phases 1445.4.3 Phase identification and ordening 145

5.5 Types of analysis 1455.5.1 Initial stress generation 1465.5.2 Plastic calculation 1495.5.3 Consolidation calculation in Classical mode 1495.5.4 Consolidation calculation in Advanced mode 1505.5.5 Safety calculation (phi/c reduction) 1505.5.6 Dynamic calculation 1535.5.7 Free vibration 1535.5.8 Groundwater flow (steady-state) 1535.5.9 Groundwater flow (transient) 1545.5.10 Plastic nil-step 1545.5.11 Updated mesh analysis 154

5.6 Load stepping procedures 1575.6.1 Automatic step size procedure 1575.6.2 Load advancement — Ultimate level 1585.6.3 Load advancement — Number of steps 1605.6.4 Automatic time stepping (consolidation) 1605.6.5 Automatic time stepping (dynamics) 161

5.7 Calculation control parameters 1615.7.1 Iterative procedure control parameters 1615.7.2 Pore pressure limits 1685.7.3 Loading input 1685.7.4 Control parameters 173

5.8 Staged construction — geometry definition 1755.8.1 Changing geometry configuration 1765.8.2 Activating and deactivating clusters or structural objects 1765.8.3 Activating or changing loads 1785.8.4 Applying prescribed displacements 1795.8.5 Reassigning material data sets 1805.8.6 Applying a volumetric strain in volume clusters 1815.8.7 Prestressing of anchors 1825.8.8 Applying contraction of a tunnel lining 1835.8.9 Definition of design calculations 1835.8.10 Staged construction with ΣMstage < 1 1845.8.11 Unfinished staged construction calculation 185

5.9 Staged construction — water conditions 1865.9.1 Water unit weight 1875.9.2 Phreatic level 1885.9.3 Closed boundary 1915.9.4 Precipitation 192

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5.9.5 Cluster pore pressure distribution 1945.9.6 Boundary conditions for flow and consolidation 1965.9.7 Special objects 2025.9.8 Water pressure generation 203

5.10 Calculation using design approaches 2065.11 Load multipliers 206

5.11.1 Standard load multipliers 2075.11.2 Other multipliers and calculation parameters 2095.11.3 Dynamic multipliers 210

5.12 Sensitivity analysis & Parameter variation 2125.12.1 Sensitivity analysis 2135.12.2 Parameter variation 2135.12.3 Defining variations of parameters 2135.12.4 Starting the analysis 2145.12.5 Sensitivity — View results 2155.12.6 Parameter variation — Calculate boundary values 2175.12.7 Viewing upper and lower values 2185.12.8 Viewing results of variations 2185.12.9 Delete results 218

5.13 Starting a calculation 2185.13.1 Previewing a construction stage 2185.13.2 Selecting points for curves 2195.13.3 Execution of the calculation process 2195.13.4 Aborting a calculation 2205.13.5 Output during calculations 2205.13.6 Selecting calculation phases for output 2255.13.7 Reset staged construction settings 2255.13.8 Adjustment to input data in between calculations 2265.13.9 Automatic error checks 226

6 Output program — General overview 2296.1 Layout of the output program 2306.2 Menus in the Menu bar 231

6.2.1 File menu 2316.2.2 View menu 2316.2.3 Project menu 2336.2.4 Geometry menu 2336.2.5 Mesh menu 2346.2.6 Deformations menu 2356.2.7 Stresses menu 2356.2.8 Forces menu 2356.2.9 Tools menu 2356.2.10 Window menu 2366.2.11 Help menu 236

6.3 Tools in the Output program 2376.3.1 Accessing the Output program 2376.3.2 Exporting output data 2376.3.3 Curves manager 2396.3.4 Store the view for reports 239

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6.3.5 Zooming the plot 2396.3.6 Relocation of the plot 2406.3.7 Scaling the displayed results 2406.3.8 Tables 2406.3.9 Selection of results 2416.3.10 Display type of results 2416.3.11 Select structures 2426.3.12 Partial geometry 2436.3.13 Viewing results in cross sections 2446.3.14 Plot annotations 2456.3.15 Miscellaneous tools 247

6.4 Display area 2506.4.1 Legend 2506.4.2 Modifying the display settings 251

6.5 Views in Output 2536.5.1 Model view 2536.5.2 Structures view 2536.5.3 Cross section view 2536.5.4 Forces view 253

6.6 Report generation 2546.6.1 Configuration of the document 256

6.7 Creating animations 256

7 Results available in Output program 2597.1 Connectivity plot 2597.2 Deformations 259

7.2.1 Deformed mesh 2597.2.2 Total displacements 2607.2.3 Phase displacements 2607.2.4 Sum phase displacements 2607.2.5 Incremental displacements 2607.2.6 Extreme total displacements 2617.2.7 Velocities 2617.2.8 Accelerations 2617.2.9 Accelerations in ‘g’ 2627.2.10 Total cartesian strains 2627.2.11 Phase cartesian strains 2627.2.12 Incremental cartesian strains 2627.2.13 Total strains 2637.2.14 Phase strains 2637.2.15 Incremental strains 263

7.3 Stresses 2647.3.1 Cartesian effective stresses 2647.3.2 Cartesian total stresses 2647.3.3 Principal effective stresses 2647.3.4 Principal total stresses 2667.3.5 State parameters 2667.3.6 Pore pressures 2687.3.7 Groundwater flow 269

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7.3.8 Plastic points 2707.3.9 Fixed end anchors 2717.3.10 Node to node anchors 2717.3.11 Wells 2727.3.12 Drains 272

7.4 Structures and interfaces 2727.4.1 Deformation in structural elements 2727.4.2 Resulting forces in Plates 2727.4.3 Resulting forces in Geogrids 2737.4.4 Resulting forces in embedded pile rows 2737.4.5 Anchors 2747.4.6 Interfaces 2747.4.7 Results in Hinges and rotation springs 2757.4.8 Structural forces in volumes 275

8 Curves 2798.1 Selecting points for curves 279

8.1.1 Mesh point selection 2798.1.2 Pre-calculation points 2808.1.3 Post-calculation points 280

8.2 Generating curves 2818.2.1 Load-displacement curves 2838.2.2 Force-displacement curves 2838.2.3 Displacement-time or force-time curves 2848.2.4 Stress and strain diagrams 2848.2.5 Curves in Dynamic calculations 284

8.3 Formatting curves 2878.3.1 Menus for curves 2888.3.2 Editing curve data in table 2898.3.3 Value indication 291

8.4 Formatting options 2918.4.1 Chart settings 2918.4.2 Curve settings 292

8.5 Regeneration of curves 2948.6 Multiple curves in one chart 294

9 References 295

Index

Appendix A — Possibilities and limitations of PLAXIS 2D 301

Appendix B — Program and Data File Structure 315

Appendix C — Shortcuts Output program 319

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INTRODUCTION

1 INTRODUCTION

The PLAXIS 2D program is a special purpose two-dimensional finite element programused to perform deformation and stability analysis for various types of geotechnicalapplications. Real situations may be modelled either by a plane strain or an axisymmetricmodel. The program uses a convenient graphical user interface that enables users toquickly generate a geometry model and finite element mesh based on a representativevertical cross section of the situation at hand. Users need to be familiar with the Windowsenvironment. To obtain a quick working knowledge of the main features of the PLAXISprogram, users should work through the example problems contained in the TutorialManual.

The Reference Manual is intended for users who want more detailed information aboutprogram features. The manual covers topics that are not covered exhaustively in theTutorial Manual. It also contains practical details on how to use the PLAXIS program fora wide variety of problem types. The user interface consists of three sub-programs(Input, Calculations and Output).

The Input program is a pre-processor,which is used to define the problem geometry and to create the finite element mesh.

The Calculations program is a separate partof the user-interface that is used to define and execute finite element calculations.

The Output program is a post-processor, which is used to inspect the resultsof calculations in a two dimensional view or in cross sections, and to plot graphs

(curves) of output quantities of selected geometry points.

The contents of this Reference Manual are arranged according to the sub-programs andtheir respective options as listed in the corresponding menus. This manual does notcontain detailed information about the constitutive models, the finite element formulationsor the non-linear solution algorithms used in the program. For detailed information onthese and other related subjects, users are referred to the various papers listed in theScientific Manual and the Material Models Manual.

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GENERAL INFORMATION

2 GENERAL INFORMATION

Before describing the specific features in the three parts of the PLAXIS 2D user interface,the information given in this chapter applies to all parts of the program.

2.1 UNITS AND SIGN CONVENTIONS

It is important in any analysis to adopt a consistent system of units. At the start of theinput of a geometry, a suitable set of basic units should be selected. The basic unitscomprise a unit for length, force and time. These basic units are defined in the Modeltabsheet of the Project properties window in the Input program. The default units aremeters [m] for length, kiloNewton [kN] for force and day [day] for time. Table 2.1 gives anoverview of all available units, the [default] settings and conversion factors to the defaultunits. All subsequent input data should conform to the selected system of units and theoutput data should be interpreted in terms of the same system. From the basic set ofunits, as defined by the user, the appropriate unit for the input of a particular parameter isgenerally listed directly behind the edit box or, when using input tables, above the inputcolumn. In all of the examples given in the PLAXIS manuals, the standard units are used.

Table 2.1 Available units and their conversion factor to the default units

Length Conversion Force Conversion Time Conversion

mm = 0.001 m N = 0.001 kN s (sec) = 1/86400 day

[m] = 1 m [kN] = 1 kN min = 1/1440 day

in (inch) = 0.0254 m MN = 1000 kN [h] = 1/24 day

ft (feet) = 0.3048 m lbf (pounds force) = 0.0044482 kN [day] = 1 day

kip (kilo pound) = 4.4482 kN

For convenience, the units of commonly used quantities in two different sets of units arelisted below:

Int. system (SI) Imperial system

Basic units: Length [m] [in]

Force [kN] [lbf]

Time [day] [sec]

Geometry: Coordinates [m] [in]

Displacements [m] [in]

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Material properties: Young’s modulus [kN/m2]=[kPa] [psi]=[lbf/in2]

Cohesion [kN/m2] [psi]

Friction angle [deg.] [deg.]

Dilatancy angle [deg.] [deg.]

Unit weight [kN/m3] [lbf/cu in]

Permeability [m/day] [in/sec]

Forces & stresses: Point loads [kN] [lbf]

Line loads [kN/m] [lbf/in]

Distributed loads [kN/m2] [psi]

Stresses [kN/m2] [psi]

Units are generally only used as a reference for the user but, to some extent, changingthe basic units in the Project properties window will automatically convert existing inputvalues to the new units. This applies to parameters in material data sets and othermaterial properties in the Input program. It does not apply to geometry related inputvalues like geometry data, loads, prescribed displacements or phreatic levels or to anyvalue outside the Input program. If it is the user’s intention to use a different system ofunits in an existing project, the user has to modify all geometrical data manually and redoall calculations.

In a plane strain analysis, the calculated forces resulting from prescribed displacementsrepresent forces per unit length in the out of plane direction (z-direction; see Figure 2.1).In an axisymmetric analysis, the calculated forces (Force − X , Force − Y ) are those thatact on the boundary of a circle subtending an angle of 1 radian. In order to obtain theforces corresponding to the complete problem therefore, these forces should bemultiplied by a factor of 2π. All other output for axisymmetric problems is given per unitwidth and not per radian.

Sign convention

The generation of a two-dimensional (2D) finite element model in the PLAXIS 2Dprogram is based on the creation of a geometry model. This geometry model is createdin the x-y -plane of the global coordinate system (Figure 2.1), whereas the z-direction isthe out-of-plane direction. In the global coordinate system the positive z-direction ispointing towards the user. In all of the output data, compressive stresses and forces,including pore pressures, are taken to be negative, whereas tensile stresses and forcesare taken to be positive. Figure 2.1 shows the positive stress directions.

Although PLAXIS 2D is a 2D program, stresses are based on the 3D Cartesiancoordinate system shown in Figure 2.1. In a plane strain analysis σzz is the out-of-planestress. In an axisymmetric analysis, x represents the radial coordinate, y represents theaxial coordinate and z represents the tangential direction. In this case, σxx represents theradial stress and σzz represents the hoop stress.

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GENERAL INFORMATION

y

z

x

σσ

σ

σ

σ

σσ

σ

σ

xx

xy

xz

yy

yxyz

zz zx

zy

Figure 2.1 Coordinate system and indication of positive stress components

2.2 FILE HANDLING

All file handling in PLAXIS is done using a modified version of the general Windows® filerequester (Figure 2.2).

Figure 2.2 PLAXIS file requester

With the file requester, it is possible to search for files in any admissible directory of thecomputer (and network) environment. The main file used to store information for aPLAXIS project has a structured format and is named <project>.P2D, where <project> isthe project title. Besides this file, additional data is stored in multiple files in thesub-directory <project>.P2DAT. It is generally not necessary to enter such a directorybecause it is not possible to read individual files in this directory.

If a PLAXIS project file (*.P2D) is selected, a small bitmap of the corresponding projectgeometry is shown in the file requester to enable a quick and easy recognition of aproject.

2.3 HELP FACILITIES

To inform the user about the various program options and features, PLAXIS 2D providesa link in the Help menu to a digital version of the Manuals. Moreover, the Help menu maybe used to generate a file with software license information as stored in the security lock(to be used for license updates and extensions). A more detailed description of the Help

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menu of the Input and Output program is given in Sections 3.3.8 and 6.2.11 respectively.Many features are available as buttons in a toolbar. When the mouse pointer ispositioned on a button for more than a second, a short description (‘hint’) appears,indicating the function of the button. For some input parameters side panels appear tohelp the user decide which value to select.

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INPUT PROGRAM — GENERAL OVERVIEW

3 INPUT PROGRAM — GENERAL OVERVIEW

To carry out a finite element analysis using the PLAXIS 2D program, the user has tocreate a two dimensional geometry model composed of points, lines and othercomponents, in the x − y -plane and specify the material properties and boundaryconditions. This is done in the Input program. The generation of an appropriate finiteelement mesh and the generation of properties and boundary conditions on an elementlevel is automatically performed by the PLAXIS mesh generator based on the input of thegeometry model. Users may also customise the finite element mesh in order to gainoptimum performance.

When a geometry model is created in the Input program it is suggested that the differentinput items are selected in the order given by the model toolbar (from left to right). Inprinciple, first draw the geometry contour, then add the soil layers, then structural objects,then construction layers, then boundary conditions and then loadings. Using thisprocedure, the model toolbar acts as a guide through the Input program and ensures thatall necessary input items are dealt with. Of course, not all input options are generallyrequired for any particular analysis. For example, some structural objects or loadingtypes might not be used when only soil loading is considered. Nevertheless, by followingthe toolbar the user is reminded of the various input items and will select the ones thatare of interest. The program will also give warning messages if some necessary inputhas not been specified. It is important to realise that the finite element mesh must beregenerated when the geometry of an existing model is changed. This is also checked bythe program. On following these procedures the user can be confident that a consistentfinite element model is obtained.

3.1 STARTING THE INPUT PROGRAM

This icon represents the Input program. At the start of the Input program the Quickselect window appears in which a choice must be made between the selection of

an existing project and the creation of a new project (Figure 3.1).

Figure 3.1 Quick select window

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3.1.1 NEW PROJECT

When the Start a new project option is selected, the Project properties window (Figure3.4) appears in which the basic model parameters of the new project can be defined. TheProject properties window contains the Project and the Model tabsheets. The Projecttabsheet (Figure 3.4) contains the project name and description, the type of model andacceleration data. The Model tabsheet (Figure 3.5) contains the basic units for length,force and time (see Section 2.1), the initial dimensions of the model contour and the gridspecifications. The default values can be replaced by the current values when selectingSet as default and clicking the OK button. A more detailed description of all theseoptions is given below.

Project

The title, directory and the file name of the project are available in the Project group boxavailable in the Project tabsheet.

Title The defined title appears as a default name for the file of theproject when it is saved.

Directory The address to the folder where the project is saved is displayed.For a new project, there is no information shown.

File name The name of the project file is displayed. For a new project, thereis no information shown.

Comments

The Comments box in the Project tabsheet gives the possibility to add some extracomments about the project.

General options

The general options of the project are available in the Project tabsheet of the Projectproperties window.

Model

PLAXIS 2D may be used to carry out two-dimensional finite element analysis. The finiteelement model is defined by selecting the corresponding option in the Model dropdown-menu in the Project tabsheet.

Plane strain: A Plane strain model is used for geometries with a (more or less) uniformcross section and corresponding stress state and loading scheme over a certain lengthperpendicular to the cross section (z-direction). Displacements and strains in z-directionare assumed to be zero. However, normal stresses in z-direction are fully taken intoaccount.

In earthquake problems the dynamic loading source is usually applied along the bottomof the model resulting in shear waves that propagate upwards. This type of problems isgenerally simulated using a plane strain model.

Axisymmetric: An Axisymmetric model is used for circular structures with a (more orless) uniform radial cross section and loading scheme around the central axis, where thedeformation and stress state are assumed to be identical in any radial direction. Note that

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INPUT PROGRAM — GENERAL OVERVIEW

for axisymmetric problems the x-coordinate represents the radius and the y -axiscorresponds to the axial line of symmetry. Negative x-coordinates cannot be used.

Single-source vibration problems are often modelled with axisymmetric models. This isbecause waves in an axisymmetric system radiate in a manner similar to that in a threedimensional system. In this case, the energy disperses leading to wave attenuations withdistance. Such effect can be attributed to the geometric damping (or radiation damping),which is by definition included in the axisymmetric model.

The selection of Plane strain or Axisymmetric results in a two dimensional finite elementmodel with only two translational degrees of freedom per node (x- and y -direction).

x

y y

x

Figure 3.2 Example of a plane strain (left) and axisymmetric problem (right)

Elements

The user may select either 6-node or 15-node triangular elements (Figure 3.4) to modelsoil layers and other volume clusters.

nodes stress points

a. 15-node triangle

nodes stress points

b. 6-node triangle

Figure 3.3 Position of nodes and stress points in soil elements

15-Node: The 15-node triangle is the default element. It provides a fourth orderinterpolation for displacements and the numerical integration involves twelve Gausspoints (stress points). The type of element for structural elements and interfaces isautomatically taken to be compatible with the soil element type as selected here.

The 15-node triangle is a very accurate element that has produced high quality stressresults for difficult problems, as for example in collapse calculations for incompressible

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soils (Nagtegaal, Parks & Rice,1974, Sloan,1981 and Sloan & Randolph,1982). The15-node triangle is particularly recommended to be used in axi-symmetric analysis. Theuse of 15-node triangles leads to more memory consumption and slower calculation andoperation performance. Therefore a more simple type of elements is also available.

6-Node: The 6-node triangle provides a second order interpolation for displacementsand the numerical integration involves three Gauss points. The type of element forstructural elements and interfaces is automatically taken to be compatible with the soilelement type as selected here.

The 6-node triangle is a fairly accurate element that gives good results in standarddeformation analyses, provided that a sufficient number of elements are used. However,care should be taken with axisymmetric models or in situations where (possible) failureplays a role, such as a bearing capacity calculation or a safety analysis by means of phi-creduction. Failure loads or safety factors are generally overpredicted using 6-nodedelements. In those cases the use of 15-node elements is preferred.

One 15-node element can be thought of a composition of four 6-node elements, since thetotal number of nodes and stress points is equal. Nevertheless, one 15-node element ismore powerful than four 6-node elements.

In addition to the soil elements, compatible plate elements are used to simulate thebehaviour of walls, plates and shells (Section 3.4.2) and geogrid elements are used tosimulate the behaviour of geogrids and wovens (Section 3.4.4). Moreover, compatibleinterface elements are used to simulate soil-structure interaction (Section 3.4.5). Finally,the geometry creation mode allows for the input of fixed-end anchors and node-to-nodeanchors (Sections 3.4.6 and 3.4.7).

Gravity and acceleration

By default, the earth gravity acceleration, g, is set to 9.8 m/s2 and the direction of gravitycoincides with the negative y -axis, i.e. an orientation of -90◦ in the x-y -plane. Gravity isimplicitly included in the unit weights given by the user (Section 4.1). In this way, thegravity is controlled by the total load multiplier for weights of materials, ΣMweight(Section 5.11.1).

In addition to the normal gravity the user may prescribe an independent acceleration tomodel dynamic forces in a pseudo-static way. The input values of the x- andy -acceleration components are expressed in terms of the normal gravity acceleration gand entered in the Project tabsheet of the Project properties window. The activation ofthe additional acceleration in calculations is controlled by the load multipliers Maccel andΣMaccel (Section 5.11.1).

In dynamic calculations, the value of the gravity acceleration, g, is used to calculate thematerial density, ρ, from the unit of weight, γ (ρ = γ/g).

Units

Units for length, force and time to be used in the analysis need to be specified. Thesebasic units are entered in the Model tabsheet of the Project properties window (Figure3.5).

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Figure 3.4 Project properties window (Project tabsheet)

The default units, as suggested by the program, are m (meter) for length, kN (kiloNewton)for force and day for time. The corresponding units for stress and unit weights are listedin the box below the basic units.

In a dynamic analysis, the time is usually measured in [seconds] rather than the defaultunit [days]. Hence, for dynamic analysis the unit of time could be changed in the Projecttabsheet of the Project properties window. However, this is not strictly necessary since inPLAXIS Time and Dynamic time are different parameters. The time interval in a dynamicanalysis is always the dynamic time and PLAXIS always uses seconds [s] as the unit ofDynamic time. In the case where a dynamic analysis and a consolidation analysis areinvolved, the unit of Time can be left as [days] whereas the Dynamic time is in seconds[s].

All input values should be given in a consistent set of units (Section 2.1). The appropriateunit of a certain input value is usually given directly behind the edit box, based on thebasic set of units.

Geometry dimensions

At the start of a new project, the user needs to specify the dimensions of the draw area insuch a way that the geometry model that is to be created will fit within the dimensions.The dimensions are entered in the Model tabsheet of the Project properties window. Thedimensions of the draw area do not influence the geometry itself and may be changedwhen modifying an existing project, provided that the existing geometry fits within themodified dimensions. Clicking on the rulers in the geometry creation mode may be usedas a shortcut to proceed to the input of the geometry dimensions in the Project propertieswindow.

Grid

To facilitate the creation of the geometry model, the user may define a grid for the drawarea. This grid may be used to snap the pointer into certain ‘regular’ positions. The grid isdefined by means of the parameters Spacing and Number of snap intervals. The Spacingis used to set up a coarse grid, indicated by the small dots on the draw area. The actualgrid is the coarse grid divided into the Number of snap intervals. The default number ofintervals is 1, which gives a grid equal to the coarse grid. The grid specification is entered

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in the Model tabsheet of the Project properties window. The View menu may be used toactivate or deactivate the grid and snapping options.

Figure 3.5 Project properties window (Model tabsheet)

3.1.2 EXISTING PROJECT

When the Input program is started, a list of the recent projects appears in the Quick selectwindow. In the case when a project other than the listed recent ones is required, the Openan existing project option should be selected. As this selection is made, the Windows®

file requester (Figure 2.2) pops up. It enables the user to browse through all availabledirectories and to select the desired PLAXIS project file (*.P2D). After the selection of anexisting project, the corresponding geometry is presented in the main window.

An existing PLAXIS 2D project can also be read by selecting the Open option in the Filemenu. In the file requester, the type of the file is, by default, set to ‘PLAXIS 2D files(*.P2D)’.

3.1.3 IMPORTING A GEOMETRY

It is possible to import tab-separated value (.txt) or comma-separated value (.csv) textfiles to import a geometry in PLAXIS. Such files need to include a table with thecoordinates of the points (preceded by the command Points; each new line starting with anumber which serves as the point’s ID, followed by the point coordinates) and lines(preceded by the command Lines; each new line starting with a number , which servesas the line’s ID, followed by the starting and ending point ID’s). Examples of such files areon given in Table 3.1 and 3.2. Note that PLAXIS only supports the English notation ofdecimal numbers using a dot.

It is possible to import a geometry composed of points and straight lines (with theAcdbLine property) from external sources in different formats like AutoCAD native(*.DWG) and interchange (*.DXF) file formats. Lines as part of polylines(AcdbPolyLine)are not imported. In the cases where the imported geometry contains curved elementsas well (like arcs), the geometry will be partly imported (only points and straight lines).

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Table 3.1 Example of a tab-separated value file (.txt)

Points

0 0.0 0.0

1 20.0 0.0

2 20.0 10.0

3 0.0 10.0

Lines

0 0 1

1 1 2

2 2 3

3 3 0

Table 3.2 Example of a comma-separated value file (.csv)

Points

0 , 0.0 , 0.0

1 , 20.0 , 0.0

2 , 20.0 , 10.0

3 , 0.0 , 10.0

Lines

0 , 0 , 1

1 , 1 , 2

2 , 2 , 3

3 , 3 , 0

Scaling of the imported geometry

When a geometry is imported the Import scale factor (Figure 3.6) pops up where ascaling factor can be defined for the imported geometry. The scale factor is relevant whenthe imported geometry is defined in a unit of length different from the one used in thePLAXIS project. The scaled geometry will be displayed when the OK button is clicked.

Figure 3.6 Import scale factor window

3.1.4 PACKING A PROJECT

The created project can be compressed using the Pack project application whichis available in the File menu of the Input program. This application can be executed

directly from the PLAXIS 2D installation folder by double clicking the corresponding file(PackProject.exe). A shortcut to the application can be created as well. In the Packproject window (Figure 3.7) the information archiving process and information can

The project to be compressed and the archive can be located using the Browse button.The options available in the Purpose box are:

Backup All the files in the project are included in the compressed projectas well as the mesh information, phase specification and theresults of all the saved calculation steps. The extension of the

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project file, indicating in which program it was created, and thearchiving date are included in the archive name.

Support Selecting this option enables including all the informationrequired to give support for the project at hand. Note thatsupport is only provided to VIP users.

Custom The user can define the information to be included in the archive.

Figure 3.7 Pack project window

The options for compression and volume size are available in the Archiveoptions window (Figure 3.8), displayed by clicking the button in the Purpose box.

Figure 3.8 Archive options window

The Content box displays the options for the information to be included in the archive isshown. The options available are:

Mesh The information related to geometry is imported when the Meshoption is selected.

Phases The options available are:Smart When a phase is selected in the tree,

the parent phase is selectedautomatically in order to provide aconsistent chain of phases.

All All the phases available in the project

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are selected.

Manual Specific phases can be selected by theuser.

Results The results to be included in the archive can be selected. Theoptions available are:All steps The results of all the calculation steps

are included in the archive.

Last step only The results of only the last calculationstep of each phase are included in thearchive.

Manual The results of specific calculation stepscan be selected by the user.

Note that when the Backup or the Support option is selected, the Content options areautomatically selected by the program.

3.2 LAYOUT OF THE INPUT PROGRAM

The general layout of the Input program for a new project is shown in Figure 3.9.

Figure 3.9 Layout of the Input program

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The main window of the Input program contains the following items:

Title bar

The name of the program and the title of the project is displayed in the title bar. Unsavedmodifications in the project are indicated by a ‘∗’ in the project name.

Menu bar

The menu bar contains drop-down menus covering the options available in the Inputprogram.

General toolbar

The general toolbar contains buttons for general actions such as disk operations,printing, zooming or selecting objects. It also contains buttons to start the othersub-programs (Calculations, Output).

Hint: If the mouse is moved over a button in a toolbar, a hint about the function ofthis button is displayed.

Mode tabs

The mode tabs are used to separate different modelling modes. The following tabs areavailable:

Geometry The geometry of the model is defined.

Calculations The calculation phases and calculation process are defined andthe project is calculated.

Model toolbar

The model toolbar contains buttons for actions that are related to the creation of ageometry model. The buttons are ordered in such a way that, in general, following thebuttons on the tool bar from the left to the right results in a fully defined model.

Draw area

The draw area is the drawing sheet on which the geometry model is created andmodified. The geometry model can be created by means of the mouse and using thebuttons available in the Model toolbar.

The physical origin is indicated by the intersection of the x− and y− axes. Each axis isdisplayed in a different colour and their positive directions are indicated by arrows.

Rulers

At both the left and the top of the draw area, rulers indicate the physical x- andy -coordinates of the geometry model. This enables a direct view of the geometrydimensions. The rulers can be switched off in the View menu. When clicking on the

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rulers the Project properties window appears in which the geometry dimensions can bechanged.

Status bar

The status bar displays information about the location of the mouse cursor in the drawarea. The cursor position is given in both in physical units (x , y -coordinates) and inscreen pixels.

Command line

If drawing with the mouse does not give the desired accuracy, the Manual input line canbe used. Values for the x- and y -coordinates can be entered here by typing the requiredvalues separated by a space (x-value <space> y -value <Enter>) or by a semicolon(x-value;y -value <Enter>). Manual input of coordinates can be given for all objects,except for Hinges and Rotation fixities.

Instead of the input of absolute coordinates, increments with respect to the previous pointcan be given by typing an @ directly in front of the value (@x-value <space> @y -value<Enter>). In addition to the input of coordinates, existing geometry points may beselected by their number.

3.3 MENUS IN THE MENU BAR

The menu bar of the Input program contains drop-down menus covering most options forhandling files, transferring data, viewing graphs, creating a geometry model, generatingfinite element meshes and entering data in general.

The menus available in the Input program are:

3.3.1 FILE MENU

New To create a new project. In case of a new project, the Projectproperties window is automatically displayed to define itsproperties.

Open To open an existing project. The file requester is displayed.

Recent projects To quickly open one of the most recent projects.

Import To import geometry data from other file types (Section 3.1.3).

Save To save the current project under the existing name. If a namehas not been given before, the file requester is presented.

Save as To save the current project under a new name. The file requesteris displayed.

Pack project To compress the current project.

Project properties To activate the Project properties window (Section 3.1.1).

Print To print the geometry model on a selected printer.

Exit To leave the Input program.

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3.3.2 EDIT MENU

Undo To restore a previous status of the geometry model (after aninput error). Repetitive use of the undo option is limited to the 10most recent actions.

Copy to clipboard To copy the view of the model displayed in the draw area toclipboard.

3.3.3 VIEW MENU

Zoom in To zoom into a rectangular area for a more detailed view.Alternatively, the mouse wheel may be used for zooming.

Zoom out To restore the view to before the most recent zoom action.

Reset view To restore the full draw area.

Table To view the table with the x- and y -coordinates of all geometrypoints. The table may be used to adjust existing coordinates.

Rulers To show or hide the rulers along the draw area.

Cross hair To show or hide the cross hair during the creation of a geometrymodel.

Grid To show or hide the grid in the draw area.

Axes To show or hide the arrows indicating the x- and y -axes.

Snap to grid To activate or deactivate the snapping into the regular grid points.

Change color scheme To change the intensity of the colours indicating the material datasets assigned to soil layers.

Point numbers To show or hide the geometry point numbers.

Chain numbers To show or hide the ‘chain’ numbers of geometry objects.’Chains’ are clusters of similar geometry objects that are drawnin one drawing action without intermediately clicking the righthand mouse button or the <Esc> key.

3.3.4 GEOMETRY MENU

Geometry line To create points and lines in the draw area.

Plate To create structural objects with a significant flexural rigidity (orbending stiffness)

Geogrid To create slender structures with a normal stiffness but with nobending stiffness.

Interface To model the soil-structure interaction.

Node-to-node anchor To create springs that are used to model ties between two points.

Fixed-end anchor To create springs that are used to model a tying of a single point.

Tunnel To create circular and non-circular tunnel cross sections whichare to be included in the geometry model.

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Hinge and rotation springTo create a plate connection that allows for a discontinuousrotation in the point of connection.

Drain To prescribe lines inside the geometry model where (excess)pore pressures are reduced.

Well To prescribe points inside the geometry model where a specificdischarge is extracted from or infiltrated into the soil.

Check consistency To check the geometry consistency. The program gives amessage indicating whether consistency issues exist. Possibleinconsistencies are overlapping lines or multiple points at thesame location.

3.3.5 LOADS MENU

Standard fixities To impose a set of general boundary conditions to the geometrymodel.

Standard earthquake boundariesTo impose standard boundary conditions for earthquake loading.

Standard absorbent boundaries (dynamics)To impose standard absorbent boundaries for single sourcevibrations.

Set dynamic load systemTo specify which of the load system(s) will be used as a dynamicload.

Total fixities To impose total fixities.

Vertical fixities To impose vertical fixities.

Horizontal fixities To impose horizontal fixities.

Rotation fixities (plates) To fix the rotational degree of freedom of a plate around the z−axis.

Absorbent boundaries To define a boundary that absorbs the increments of stressescaused by dynamic loading.

Prescribed displacementsTo impose special conditions on the model to control thedisplacement of certain points.

Distributed load — static load system ATo define distributed loads for load system A.

Distributed load — static load system BTo define distributed loads for load system B.

Point load — static load system ATo define point loads for load system A.

Point load — static load system BTo define point loads for load system B.

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Design approaches To define partial factors according to a design approach and toselect the design approaches for the current project.

Hint: Note that point loads actually represent line loads in the out-of-planedirection.

3.3.6 MATERIALS MENU

Soil & interfaces To activate the data base engine for the creation andmodification of material data sets for soil and interfaces.

Plates To activate the data base engine for the creation andmodification of material data sets for plates.

Geogrids To activate the data base engine for the creation andmodification of material data sets for geogrids.

Anchors To activate the data base engine for the creation andmodification of material data sets for anchors.

The use of the data base and the parameters contained in the data sets are described indetail in Chapter 4.

3.3.7 MESH MENU

Basic element type To display the Project tabsheet of the Project properties windowwhere the basic element type can be selected.

Global coarseness To select one of the available options for the global meshcoarseness.

Refine global To refine the mesh globally.

Refine cluster To locally refine the selected clusters.

Refine line To locally refine the mesh around selected lines.

Refine around point To locally refine the mesh around selected points.

Reset all To reset all the refinements.

Generate To generate the mesh.

The options in this menu are explained in detail in Section 3.7.

3.3.8 HELP MENU

Manuals To display the manuals.

Instruction movies To reach the PLAXIS TV website where instruction movies aredisplayed.

Update license To update the PLAXIS 2D license via e-mail.

http://www.plaxis.nl/ To reach the PLAXIS website.

Disclaimer The complete disclaimer text is displayed.

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About Information about the program version and license are displayed.

3.4 GEOMETRY

The generation of a finite element model begins with the creation of a geometry model,which is a representation of the problem of interest. A geometry model consists of points,lines and clusters. Points and lines are entered by the user, whereas clusters aregenerated by the program. In addition to these basic components, structural objects orspecial conditions can be assigned to the geometry model to simulate tunnel linings,walls, plates, soil-structure interaction or loadings.

It is recommended to start the creation of a geometry model by drawing the full geometrycontour. In addition, the user may specify material layers, structural objects, lines usedfor construction phases, loads and boundary conditions. The geometry model should notonly include the initial situation, but also situations that occur in the various calculationphases.

After the geometry components of the geometry model have been created, the usershould compose data sets of material parameters and assign the data sets to thecorresponding geometry components (Section 4). When the full geometry model hasbeen defined and all geometry components have their initial properties, the finite elementmesh can be generated (Section 3.7).

Selecting geometry components

When the Selection tool is active, a geometry component may be selectedby clicking once on that component in the geometry model. Multiple selection is

possible by holding down the <Shift> key on the keyboard while selecting the desiredcomponents.

Properties of geometry components

Most geometry components have certain properties, which can be viewed and altered inproperty windows. After double clicking a geometry component the correspondingproperty window appears. If more than one object is located on the indicated point, aselection dialog box appears from which the desired component can be selected.

3.4.1 POINTS AND LINES

The basic input item for the creation of a geometry model is the Geometry line. Thisitem can be selected from the Geometry menu as well as from the second tool bar.

When the Geometry line option is selected, the user may create points and lines in thedraw area by clicking with the mouse pointer (graphical input) or by typing coordinates atthe command line (keyboard input). As soon as the left hand mouse button is clicked inthe draw area a new point is created, provided that there is no existing point close to thepointer position. If there is an existing point close to the pointer, the pointer snaps into theexisting point without generating a new point. After the first point is created, the user maydraw a line by entering another point, etc. The drawing of points and lines continues untilthe right hand mouse button is clicked at any position or the <Esc> key is pressed.

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If a point is to be created on or close to an existing line, the pointer snaps onto the lineand creates a new point exactly on that line. As a result, the line is split into two newlines. If a line crosses an existing line, a new point is created at the crossing of both lines.As a result, both lines are split into two new lines. If a line is drawn that partly coincideswith an existing line, the program makes sure that over the range where the two linescoincide only one line is present. All these procedures accomplish that a consistentgeometry is created without double points or lines. The Check consistency option in theGeometry menu may be used to check the consistency of the geometry model.

Existing points or lines may be modified or deleted by first choosing the Selection toolfrom the tool bar. To move a point or line, select the point or the line in the cross sectionand drag it to the desired position. To delete a point or line, select the point or the line inthe cross section and press <Delete> on the keyboard. If more than one object is presentat the selected position, a delete dialog box appears from which the object(s) to bedeleted can be selected. If a point is deleted where one or more geometry lines cometogether, then all these connected geometry lines will be deleted as well.

After each drawing action the program determines the clusters that can be formed. Acluster is a closed loop of different geometry lines. In other words, a cluster is an areafully enclosed by geometry lines. The detected clusters are lightly shaded. Each clustercan be given certain material properties to simulate the behaviour of the soil in that partof the geometry (Section 4.1). The clusters are divided into soil elements during meshgeneration (Section 3.7).

3.4.2 PLATES

Plates are structural objects used to model slender structures in the ground witha significant flexural rigidity (or bending stiffness) and a normal stiffness. Plates can

be used to simulate the influence of walls, plates, shells or linings extending inz-direction. In a geometry model, plates without assigned material properties appear as’light blue lines’, whereas plates with assigned material properties appear in their materialset colour. Examples of geotechnical structures involving plates are shown in Figure 3.10.

Figure 3.10 Applications in which plates, anchors and interfaces are used

Plates can be selected from the Geometry menu or by clicking on the correspondingbutton in the tool bar. The creation of plates in the geometry model is similar to thecreation of geometry lines (Section 3.4.1). When creating plates, the correspondinggeometry lines are created simultaneously. Hence, it is not necessary to create first ageometry line at the position of a plate. Plates can be erased by selecting them in thegeometry and pressing the <Delete> key.

The material properties of plates are contained in material data sets (Section 4.2). Themost important parameters are the flexural rigidity (bending stiffness) EI and the axialstiffness EA.

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From these two parameters an equivalent plate thickness deq is calculated from theequation:

deq =√

12EIEA

Plates can be activated or de-activated in calculation phases using Staged constructionas Loading input.

Plate elements

Plates in the 2D finite element model are composed of plate elements (line elements)with three degrees of freedom per node: two translational degrees of freedom (ux , uy )and one rotational degrees of freedom (rotation in the x-y plane: φz ). When 6-node soilelements are employed then each plate element is defined by three nodes whereas5-node plate elements are used together with the 15-node soil elements (Figure 3.15).The plate elements are based on Mindlin’s plate theory (Bathe, 1982). This theory allowsfor plate deflections due to shearing as well as bending. In addition, the element canchange length when an axial force is applied. Plate elements can become plastic if aprescribed maximum bending moment or maximum axial force is reached.

Bending moments and axial forces are evaluated from the stresses at the stress points. A3-node plate element contains two pairs of Gaussian stress points whereas a 5-nodeplate element contains four pairs of stress points. Within each pair, stress points arelocated at a distance 1/6

√3deq above and below the plate centre-line.

Figure 3.15 shows a single 3-node and 5-node plate element with an indication of thenodes and stress points.

stress pointnode

3-node plate element 5-node plate element

Figure 3.11 Position of nodes and stress points in plate elements

It is important to note that a change in the ratio EI/EA will change the equivalentthickness deq and thus the distance separating the stress points. If this is done whenexisting forces are present in the plate element, it would change the distribution ofbending moments, which is unacceptable. For this reason, if material properties of aplate are changed during an analysis (for example in the framework of StagedConstruction) it should be noted that the ratio EI/EA must remain unchanged.

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3.4.3 EMBEDDED PILE ROW

Since the stress state and deformation pattern around piles is fully three-dimensional, it isimpossible to model piles realistically in a 2D model. Hence, the 2D embedded pileelement is only a simplified approach to deal with a row of piles in the out-of-planedirection in a 2D plane strain model.

The idea behind the 2D embedded pile is that the pile (represented by a Mindlin beamelement) is not ‘in’ the 2D mesh, but superimposed ‘on’ the mesh, while the soil elementmesh itself is continuous (Figure 3.12, after Sluis (2012)). A special out-of-plane interfaceconnects the beam with the underlying soil elements. The beam is supposed to representthe deformations of an out-of-plane row of individual piles, whereas displacements of thesoil elements are supposed to represent the ‘average’ soil displacement in theout-of-plane direction. The interface stiffness should be chosen such that it accounts forthe difference between the (average) soil displacement and the pile displacement whiletransferring loads from the pile onto the soil and vice versa. This requires at least theout-of-plane spacing of the piles to be taken into account in relation to the pile diameter.

Figure 3.12 Schematic representation of embedded pile (after Sluis (2012))

An embedded pile row can be utilised to model a row of long slender structuralmembers used to transmit loads to the ground at lower levels. The Embedded pile

row feature is available only for Plane strain models. The information required for anembedded pile row consists of the properties of a single pile and the spacing of the pilesin the out-of-plane direction.

Hint: Since installation effects cannot be considered, the Embedded pile rowfeature should be primarily used for pile types that cause a limiteddisturbance of the surrounding soil during installation. This may include sometypes of bored piles, but obviously not driven piles or soil displacement piles.

The feature can be selected from the Geometry menu or by clicking on the correspondingbutton in the toolbar. The creation of embedded pile rows in the geometry model is

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similar to the creation of a geometry line (Section 3.4.1). Note that one row is indicatedby one line in the model. When creating embedded pile rows, the correspondinggeometry line is created simultaneously. Hence it is not necessary to create first ageometry line at the position of an embedded pile row. It is also not necessary to createinterface elements around the embedded pile row, since special interface elements areautomatically created with the embedded pile elements. An embedded pile row can beerased by selecting the corresponding pile in the geometry and pressing the <Delete>key. Figure 3.13 is displayed as the <Delete> key is pressed and it indicates that both anembedded pile and a line have been created simultaneously. In a geometry model,embedded pile rows without assigned material properties appear as ‘pink lines’, whereasembedded pile rows with assigned material properties appear in their material set colour.

Figure 3.13 Indication of an embedded pile and a line created simultaneously

The order of drawing an embedded pile row is relevant in defining the connection of theembedded pile to the surrounding (soil or structure) and the application of the bearingcapacity. By default the first drawn point corresponds to the top point of the pile and thesecond drawn point corresponds to the tip of the pile. Note that the top point is the pointwhere the connection type may be defined. The user may redefine the top point of thepile, as well as modify the connection of the top point of the pile to the surroundinggeometry. To define the connection of the embedded pile:

• Select the embedded pile row in the model.

• In the select window select the embedded pile and press OK. The Embedded pilerow window (Figure 3.14) is displayed. Note that the connection type can only bedefined for the top point.

Figure 3.14 Embedded pile row window

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The options available are:

Free: The top of the pile is not directly coupled with the soil element inwhich the pile top is located, but the interaction through theinterface elements is still present.

Hinged: The displacement at the top point of the pile is directly coupledwith the displacement of the element in which the top point islocated, which means that they undergo exactly the samedisplacement.

Rigid: The displacement and rotation at the pile top are both coupledwith the displacement and rotation of the element in which thepile top is located, provided that this element has rotationaldegrees of freedom. This option only applies if the pile topcoincides with plates elements.

Hint: When embedded pile rows are located in a volume cluster with linear elasticmaterial behaviour, the specified values of the shaft resistance and spacingare ignored. The reason for this is that the linear elastic material is notsupposed to be soil, but part of the structure. The connection between thepile and the structure is supposed to be rigid to avoid, for example, punchingof piles through a concrete deck.

» When an embedded pile row and a structure are both active and share thesame geometry point, the node created at the top point of the embedded pileis by default rigidly connected to the structure node. However, if the structureis not active, the embedded pile node is by default connected (hinged) to thesoil node at that location.

» Note that when an interface is available, the embedded pile row is NOTconnected to the interface but to the structure or soil node at that location.

The material properties of embedded pile rows are contained in material data sets(Section 4.6). Embedded pile rows can be activated or de-activated in calculation phasesusing Staged construction as Loading input.

Embedded pile elements

Embedded piles in the 2D finite element model are composed of line elements with threedegrees of freedom per node: two translational degrees of freedom (ux , uy ) and onerotational degrees of freedom (rotation in the x-y plane: φz ). When 6-node soil elementsare employed then each embedded pile element is defined by three nodes whereas5-node embedded pile elements are used together with the 15-node soil elements(Figure 3.15). The elements are based on Mindlin’s beam theory (Bathe, 1982). Thistheory allows for deflections due to shearing as well as bending. In addition, the elementcan change length when an axial force is applied. Figure 3.15 shows a single 3-node and5-node embedded pile element with an indication of the nodes and stress points.

Bending moments and axial forces are evaluated from the stresses at the stress points. A3-node embedded pile element contains two pairs of Gaussian stress points whereas a5-node embedded pile element contains four pairs of stress points. Within each pair,

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stress pointnode

3-node plate element 5-node plate element

Figure 3.15 Position of nodes and stress points in embedded pile elements

stress points are located at a distance 1/6

√3deq above and below the embedded pile

centre-line.

The interaction between the pile and the surrounding soil may involve a skin resistance aswell as a foot resistance. Therefore, special out-of-plane interface elements (line-to-lineinterface along the shaft and point-to-point interface at the base) are used to connect thepile elements to the surrounding soil elements. The interface elements involve springs inthe longitudinal and transverse pile direction and a slider in the longitudinal direction.

Figure 3.16 Embedded pile interaction with soil (after Sluis (2012))

Pile forces (structural forces) are evaluated at the embedded pile element integrationpoints and extrapolated to the beam element nodes. These forces can be viewedgraphically and tabulated in the Output program. Details about the embedded pileelement formulations are given in the Material Models Manual.

Embedded pile row properties

The material properties of embedded pile rows are contained in Embedded pile rowsmaterial data sets (Section 4.6). In the material dataset geometric features of the pile,material properties, spacing of the piles in the out of plane direction, skin friction andbearing capacity of the pile as well as the interface stiffness factor can be defined.

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3.4.4 GEOGRIDS

Geogrids are slender structures with a normal stiffness but with no bendingstiffness. Geogrids can only sustain tensile forces and no compression. These

objects are generally used to model soil reinforcements. Examples of geotechnicalstructures involving geotextiles are presented in Figure 3.17.

Figure 3.17 Applications in which geogrids are used

Geogrids can be selected from the Geometry menu or by clicking on the correspondingbutton in the tool bar. The creation of geogrids in the geometry model is similar to thecreation of geometry lines (Section 3.4.1). In a geometry model geogrids withoutassigned material properties appear as ‘light yellow lines’, whereas geogrids withassigned properties appear in their material colour. When creating geogrids,corresponding geometry lines are created simultaneously. The only material property of ageogrid is an elastic normal (axial) stiffness EA, which can be specified in the materialdata base (Section 4.5). Geogrids can be erased by selecting them in the geometry andpressing the <Delete> key. Geogrids can be activated or de-activated in calculationphases using Staged construction as Loading input.

Geogrid elements

Geogrids are composed of geogrid elements (line elements) with two translationaldegrees of freedom in each node (ux , uy ). When 15-node soil elements are employedthen each geogrid element is defined by five nodes whereas 3-node geogrid elementsare used in combination with 6-node soil lements. Axial forces are evaluated at theNewton-Cotes stress points. These stress points coincide with the nodes. The locationsof the nodes and stress points in geogrid elements are indicated in Figure 3.18.

nodesa. 3-node geogrid element

stress pointnodes

b. 5-node geogrid element

Figure 3.18 Position of nodes and stress points in geogrid elements

Modelling ground anchors

Geogrids may be used in combination with node-to-node anchors to simulate a groundanchor. In this case the geogrid is used to model the grouted anchor section and thenode-to-node anchor is used to model the ungrouted part of the anchor (free length)(Section 3.4.6).

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3.4.5 INTERFACES

Each interface has assigned to it a ‘virtual thickness’ which is an imaginarydimension used to define the material properties of the interface. The higher the

virtual thickness is, the more elastic deformations are generated. In general, interfaceelements are supposed to generate very little elastic deformations and therefore thevirtual thickness should be small. On the other hand, if the virtual thickness is too small,numerical ill-conditioning may occur. The virtual thickness is calculated as the Virtualthickness factor times the global element size. The global element size is determined bythe global coarseness setting for the mesh generation (Section 3.7.2). The default valueof the Virtual thickness factor is 0.1. This value can be changed by double clicking on thegeometry line and selecting the interface from the selection dialog box. In general, careshould be taken when changing the default factor. However, if interface elements aresubjected to very large normal stresses, it may be required to reduce the Virtual thicknessfactor. Further details of the significance of the virtual thickness are given in Section4.1.4.

The creation of an interface in the geometry model is similar to the creation of a geometryline. The interface appears as a dashed line at the right hand side of the geometry line(considering the direction of drawing) to indicate at which side of the geometry line theinteraction with the soil takes place. The side at which the interface will appear is alsoindicated by the arrow on the cursor pointing in the direction of drawing. To place aninterface at the other side, it should be drawn in the opposite direction. Note thatinterfaces can be placed at both sides of a geometry line. This enables a full interactionbetween structural objects (walls, plates, geogrids, etc.) and the surrounding soil. To beable to distinguish between the two possible interfaces along a geometry line, theinterfaces are indicated by a plus-sign (+) or a minus-sign (-). This sign is just foridentification purposes; it does not have a physical meaning and it has no influence onthe results. Interfaces can be erased by selecting them in the geometry and pressing the<Delete> key.

A typical application of interfaces would be in a region which is intermediate betweensmooth and fully rough. The roughness of the interaction is modelled by choosing asuitable value for the strength reduction factor in the interface (Rinter ). This factor relatesthe interface strength (wall friction and adhesion) to the soil strength (friction angle andcohesion). Instead of entering Rinter as a direct interface property, this parameter isspecified together with the soil strength parameters in a material data set for soil andinterfaces. For detailed information about the interface material properties, see Section4.1.4.

Interfaces can be activated or de-activated in calculation phases using Stagedconstruction as Loading input.

Interface elements

Interfaces are composed of interface elements. Figure 3.19 shows how interfaceelements are connected to soil elements. When using 15-node soil elements, thecorresponding interface elements are defined by five pairs of nodes, whereas for 6-nodesoil elements the corresponding interface elements are defined by three pairs of nodes.In the figure, the interface elements are shown to have a finite thickness, but in the finiteelement formulation the coordinates of each node pair are identical, which means that theelement has a zero thickness.

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nodesa. 6-node soil element

stress pointnodes

b. 15-node soil element

Figure 3.19 Distribution of nodes and stress points in interface elements and their connection to soilelements

The stiffness matrix for interface elements is obtained by means of Newton Cotesintegration. The position of the Newton Cotes stress points coincides with the node pairs.Hence, five stress points are used for a 10-node interface element whereas three stresspoints are used for a 6-node interface element.

Interface properties

The basic property of an interface element is the associated material data set for soil andinterfaces. This property is contained in the interface properties window, which can beentered by double clicking an interface in the geometry model and selecting the positiveor negative interface element or interface chain from the selection window. Alternatively,the right-hand mouse button may be clicked, then the Properties option should beselected and finally the positive or negative interface element or interface chain may beselected from the right-hand mouse button menu. As a result, the Interface windowappears showing the associated Material set. By default, the Material set is set to<Cluster material> indicating that the material of the associated cluster has beenassigned. However, any other existing material data set for soil and interfaces can beselected in the Material set drop down menu to change the associated material data set.

In addition, the interface properties window shows the Virtual thickness factor. This factoris used to calculate the Virtual thickness of interface elements (see Page 37). Thestandard value of the Virtual thickness factor is 0.1. Care should be taken when changingthe standard value. The standard value can be restored using the Standard button.

In a consolidation analysis or a groundwater flow analysis, interface elements can beused to block the flow perpendicular to the interface, for example to simulate animpermeable screen. In fact, when interfaces are used in combination with plates, theinterface is used to block the flow since plate elements are fully permeable. In situationswhere interfaces are used in a mesh where they should be fully permeable, it is possibleto de-activate the interface (see Sections 5.9.8, 5.9.6 and 5.8.1).

Interfaces around corner points

Figure 3.20 and Figure 3.21 show that problems of soil-structure interaction may involvepoints that require special attention. Corners in stiff structures and an abrupt change inboundary condition may lead to high peaks in the stresses and strains. Volume elementsare not capable of reproducing these sharp peaks and will, as a result, producenon-physical stress oscillations. This problem can be solved by making use of interface

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elements as shown in Figure 3.21.

Figure 3.20 Inflexible corner point, causing poor quality stress results

Figure 3.21 Flexible corner point with improved stress results

Figure 3.21 shows that the problem of stress oscillation may be prevented by specifyingadditional interface elements inside the soil body. These elements will enhance theflexibility of the finite element mesh and will thus prevent non-physical stress results.However, these elements should not introduce an unrealistic weakness in the soil.Therefore special attention should be made to the properties of these interface elements(Section 4.1.4).

It is advised to extend the interface beyond the end (ends) of the plate in the soil. Thisavoids the end (ends) of the plate becoming fixed to the soil. Figure 3.22 displays theeffect of extending the interface in the mesh. A possible result of not extending theinterface may be an unrealistic end bearing capacity or unrealistic contact stresses.

a. Not extended interface b. Extended interface

Figure 3.22 Effect of the interface extension in the mesh

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Additional theoretical details on this special use of interface elements is provided byGoodman, Taylor & Brekke (1968) and van Langen & Vermeer (1991).

3.4.6 NODE-TO-NODE ANCHORS

Node-to-node anchors are springs that are used to model ties between two points.This type of anchors can be selected from the Geometry menu or by clicking on the

corresponding button in the tool bar. Typical applications include the modelling of acofferdam as shown in Figure 3.10. It is not recommended to draw a geometry line at theposition where a node-to-node anchor is to be placed. However, the end points ofnode-to-node anchors must always be connected to geometry lines, but not necessarilyto existing geometry points. In the latter case a new geometry point is automaticallyintroduced. The creation of node-to-node anchors is similar to the creation of geometrylines (Section 3.4.1) but, in contrast to other types of structural objects, geometry linesare not simultaneously created with the anchors. Hence, node-to-node anchors will notdivide clusters nor create new ones.

A node-to-node anchor is a two-node elastic spring element with a constant springstiffness (normal stiffness). This element can be subjected to tensile forces (for anchors)as well as compressive forces (for struts). Both the tensile force and the compressiveforce can be limited to allow for the simulation of anchor or strut failure. The propertiescan be entered in the material data base for anchors (Section 4.7). Node-to-nodeanchors can be activated, de-activated or prestressed in a calculation phase usingStaged construction as Loading input.

3.4.7 FIXED-END ANCHORS

Fixed-end anchors are springs that are used to model a tying of a single point.This type of anchor can be selected from the Geometry menu or by clicking on the

corresponding button in the tool bar. An example of the use of fixed-end anchors is themodelling of struts (or props) to sheet-pile walls, as shown in Figure 3.10. Fixed-endanchors must always be connected to existing geometry lines, but not necessarily toexisting geometry points. A fixed-end anchor is visualised as a rotated T (—|). The lengthof the plotted T is arbitrary and does not have any particular physical meaning. Bydefault, a fixed-end anchor is pointing in the positive x-direction, i.e. the angle in thex ,y -plane is zero. By double clicking in the middle of the T the Fixed-end anchor windowappears in which the angle can be changed. The angle is defined in the anticlockwisedirection, starting from the positive x-direction towards the y -direction. In addition to theangle, the equivalent length of the anchor may be entered in the Fixed-end anchorwindow. The equivalent length is defined as the distance between the anchor connectionpoint and the fictitious point in the longitudinal direction of the anchor where thedisplacement is assumed to be zero.

A fixed-end anchor is a one-node elastic spring element with a constant spring stiffness(or normal stiffness). The other end of the spring (defined by the equivalent length andthe direction) is fixed. The properties can be entered in the material database for anchors(Section 4.7).

Fixed-end anchors can be activated, de-activated or prestressed in a calculation phaseusing Staged construction as Loading input.

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3.4.8 TUNNELS

The Tunnel option can be used to create circular and non-circular tunnel crosssections which are to be included in the geometry model. A tunnel cross section is

composed of arcs and lines, optionally supplied with a lining and an interface. A tunnelcross section can be stored as an object on the hard disk (i.e. as a file with the extension.TNL) and included in other projects. The tunnel option is available from the Geometrymenu or from the tool bar.

Tunnel designer

Once the tunnel option has been selected, the Tunnel designer window appears. TheTunnel designer contains the following items (Figure 3.23):

Figure 3.23 Tunnel designer with standard tunnel shape

Tunnel menu Menu with options to open and save a tunnel object and to settunnel attributes.

Tool bar Bar with buttons as shortcuts to set tunnel attributes.

Display area Area in which the tunnel cross section is plotted.

Rulers The rulers indicate the dimension of the tunnel cross section inlocal coordinates. The origin of the local coordinate system isused as a reference point for the positioning of the tunnel in thegeometry model.

Section group box Box containing shape parameters and attributes of individualtunnel sections. Use the buttons to select other sections.

Other parameters See further.

Standard buttons To accept (OK ) or to cancel the created tunnel.

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Basic tunnel shape

Once the tunnel option has been selected, the following toolbar buttons can be used toselect a basic tunnel shape:

A Whole tunnel should be used if the full tunnel cross section is included in thegeometry model.

A half tunnel should be used if the geometry model includes only one symmetric half ofthe problem where the symmetry line of the geometry model corresponds to thesymmetry line of the tunnel. Depending on the side of the symmetry line that is used inthe geometry model the user should select the right half of a tunnel or the left half.

Half a tunnel — Left half

Half a tunnel — Right half

Hint: A half tunnel can also be used to define curved sides of a larger structure,such as an underground storage tank. The remaining linear parts of thestructure can be added in the draw area using geometry lines or plates.

Type of tunnel

Before creating the tunnel cross section the type of tunnel must be selected.

None: Select this option when you want to create an internal geometry contourcomposed of different sections and have no intention to create a tunnel. Each section isdefined by a line, an arc or a corner. The outline consists of two lines if you enter apositive value for the Thickness parameter. The two lines will form separate clusters witha corresponding thickness when inserting the outline in the geometry model.

Bored tunnel: Select this option to create a circular tunnel that includes a homogeneoustunnel lining (composed of a circular shell) an outside and an inside interface. The tunnelshape consists of different sections that can be defined with arcs. Since the tunnel liningis circular, each section has the radius that is defined in the first section. The tunneloutline consists of two lines if you enter a positive value for the Thickness parameter.This way a thick tunnel lining can be created that is composed of volume elements.

The tunnel lining (shell) is considered to be homogeneous and continuous. As a result,assigning material data and the activation or deactivation of the shell in the framework ofstaged construction can only be done for the lining as a whole (and not individually foreach section). If the shell is active, a contraction of the tunnel lining (shrinkage) can bespecified to simulate the volume loss due to the tunnel boring process (Section 5.8.8).

NATM tunnel: The tunnel lining (shell) is considered to be discontinuous. As a result,assigning material data and the activation or deactivation of lining parts in the frameworkof staged construction is done for each section individually. It is not possible to apply acontraction of the shell (shrinkage) for NATM tunnels. To simulate the deformations dueto the excavation and construction in NATM tunnels other calculation methods areavailable (Sections 5.8.6 and 5.8.10).

The tunnel lining (shell) is considered to be discontinuous. As a result, assigning materialdata and the activation or deactivation of lining parts in the framework of staged

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construction is done for each section individually. It is not possible to apply a contractionof the shell (shrinkage) for NATM tunnels. To simulate the deformations due to theexcavation and construction in NATM tunnels other calculation methods are available(Sections 5.8.6 and 5.8.10).

Geometrical features of tunnel sections

The creation of a tunnel cross section starts with the definition of the inner tunnelboundary, which is composed of sections. Each section is either an Arc (part of a circle,defined by a centre point, a radius and an angle), or a Line increment (defined by astarting point and a length). In addition, sharp corners can be defined, i.e. a suddentransition in the inclination angle of two adjacent tunnel sections. When entering thetunnel designer, a standard circular tunnel is presented composed of 6 sections (3sections for half a tunnel).

The first section starts with a horizontal tangent at the lowest point on the local y -axis(highest point for a left half), and runs in the anti-clockwise direction. The position of thisfirst start point is determined by the Center coordinates and the Radius (if the first sectionis an Arc) or by the Starting point coordinates (if the first section is a Line). The end pointof the first section is determined by the Angle (in the case of an arc) or by the Length (inthe case of a line).

The start point of a next section coincides with the end point of the previous section. Thestart tangent of the next section is equal to the end tangent of the previous section. Ifboth sections are arcs, the two sections have the same radial (normal of the tunnelsection), but not necessarily the same radius (Figure 3.24). Hence, the centre point of thenext section is located on this common radial and the exact position follows from thesection radius.

If the tangent of the tunnel outline in the connection point is discontinuous, a sharp cornermay be introduced by selecting the Corner option for the next section. In this case asudden change in the tangent can be specified by the Angle parameter. The radius andthe angle of the last tunnel section are automatically determined such that the end radialcoincides again with the y -axis.

For a whole tunnel the start point of the first section should coincide with the end point ofthe last section. This is not automatically guaranteed. The distance between the startpoint and the end point (in units of length) is defined as the closing error. The closingerror is indicated on the status line of the tunnel designer. A well-defined tunnel crosssection must have a zero closing error. When a significant closing error exists, it isadvisable to carefully check the section data.

The number of sections follows from the sum of the section angles. For whole tunnels thesum of the angles is 360 degrees and for half tunnels this sum is 180 degrees. Themaximum angle of a section is 90.0 degrees. The automatically calculated angle of thelast section completes the tunnel cross section and it cannot be changed. If the angle ofan intermediate section is decreased, the angle of the last section is increased by thesame amount, until the maximum angle is reached. Upon further reduction of theintermediate section angle or by reducing the last section angle, a new section will becreated. If the angle of one of the intermediate tunnel sections is increased, the angle ofthe last tunnel section is automatically decreased. This may result in elimination of thelast section.

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R2

R2

R1

R1 commonradial

Figure 3.24 Detail of connection point between two tunnel sections

When the creation of the tunnel cross section is finished, it can be saved as a tunnelobject on the hard disk by using the Save as option from the File menu in the Tunneldesigner window.

Symmetric tunnel: The option Symmetric is only relevant for whole tunnels. When thisoption is selected, the tunnel is made fully symmetric. In this case the input proceduresare similar to those used when entering half a tunnel (right half). The left half of thetunnel is automatically made equal to the right half.

Circular tunnel: When changing the radius of one of the tunnel sections, the tunnelceases to be circular. To enforce the tunnel to be circular, the Circular option may beselected. If this option is selected, all tunnel sections will be arcs with the same radius. Inthis case the radius can only be entered for the first tunnel section. This option isautomatically selected when the type of tunnel is a bored tunnel.

Structural features of tunnel sections

Beside the geometric features, structural features can be assigned as well to the tunnelsections. The available structural features for tunnel sections are:

Shell To model the boring machine in shield tunneling or shotcretelining in NATM. Note that final lining can be modelled by defininga thickness greater than 0.

Outside interface To model the interaction of the tunnel lining with the surroundingsoil in the selected section.

Inside interface To model for example the interaction between the shotcrete andthe final lining in the selected section.

Load To assign loads to the selected segment. When this option isselected, the options to define the distribution, the referencepoint (for varying loads), and the necessary numerical values (σ,σref are displayed. More description on load options is given asfollows.

Hint: Selecting the For all segments option enables assigning all the selectedoptions and the defined values to all the segments in the tunnel.

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Load options for tunnel segments

The information required to define a load assigned to a segment in the tunnel consists ofload distribution, load value and the point of reference (in case of linear loads).

The distribution options for loads are:

Perpendicular: To create a uniformly distributed load perpendicular to theselected segment. The value of the load (σn) needs to bespecified.

Perpendicular, vertical increment:To create a load perpendicular to the selected segment varyingin y direction by defining the components and the magnitude ofthe load at the reference point and its increment in y direction.The values of the reference load (σn,ref ) and the load increment(σn,inc) as well as the reference point need to be specified.

X direction: To create a uniformly distributed horizontal load. The value of theload (σx ) needs to be specified.

X direction, vertical increment:To create a linearly distributed horizontal load varying iny -direction. The values of the reference load (σx ,ref ) and the loadincrement (σx ,inc) as well as the reference point need to bespecified.

X direction, horizontal increment:To create a linearly distributed horizontal load varying inx-direction. The values of the reference load (σn,ref ) and the loadincrement (σn,inc) as well as the reference point need to bespecified.

Y direction: To create a uniformly distributed vertical load. The value of theload (σy ) needs to be specified.

Y direction, vertical increment:To create a linearly distributed vertical load varying in y -direction.The values of the reference load (σy ,ref ) and the load increment(σy ,inc) as well as the reference point need to be specified.

Y direction, horizontal increment:To create a linearly distributed vertical load varying in y -direction.The values of the reference load (σy ,ref ) and the load increment(σy ,inc) as well as the reference point need to be specified.

The reference point to be considered when linear loads are defined can be specified byselecting the corresponding option in the drop down menu.

The options available for the reference point are:

Top of the tunnel: To specify the highest point in the tunnel cross section as thereference point.

Bottom of the tunnel: To specify the lowest point in the tunnel cross section as thereference point.

Start point of segment: To specify the start point of the segment as the reference point.

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End point of segment: To specify the end point of the segment as the reference point.

Hint: The coordinates of the reference point are displayed under the drop downmenu containing the available options. The location of the coordinated iscalculated according to the coordinate system displayed in the plot shown inthe Tunnel designer window.

Including tunnel in geometry model

After clicking on the OK button in the Tunnel designer the window is closed and the maininput window is displayed again. A tunnel symbol is attached to the cursor to emphasizethat the reference point for the tunnel must be selected. The reference point will be thepoint where the origin of the local tunnel coordinate system is located. When thereference point is entered by clicking with the mouse in the geometry model or byentering the coordinates in the manual input line, the tunnel is included in the geometrymodel, taking into account eventual crossings with existing geometry lines or objects.

Editing an existing tunnel

An existing tunnel can be edited by double clicking its reference point or one of the othertunnel points. As a result, the Tunnel designer window reappears showing the existingtunnel cross section. Desired modifications can now be made. On clicking the OK buttonthe ‘old’ tunnel is removed and the ‘new’ tunnel is directly included in the geometry modelusing the original reference point. Note that previously assigned material sets of a liningmust be reassigned after modification of the tunnel.

Moving an existing tunnel

An existing tunnel can be moved in the geometry by dragging the tunnel reference point.Note that this is only possible if the tunnel reference point does not coincide with anotherpoint.

3.4.9 HINGES AND ROTATION SPRINGS

A hinge is a plate connection that allows for a discontinuous rotation in the point ofconnection (joint). By default, in a geometry point where plate ends come together,

the rotation is continuous and the point contains only one rotational degree of freedom. Inother words, the default plate connection is rigid (clamped). If it is desired to create ahinge connection (a joint where plate ends can rotate freely with respect to each other) ora rotation spring (a joint where the rotation of plate ends with respect to each otherrequires a finite torque), the option Hinges and rotation springs can be selected from theGeometry menu or by clicking the corresponding button in the tool bar.

When this option is selected and an existing geometry point is clicked where at least twoplates come together, the Hinges and rotation springs window appears presenting adetailed view of the joint with all connected plates. For each individual plate end it can beindicated whether the connection is a hinge or a clamp. A hinge is indicated by an opencircle whereas a clamp is indicated by a solid circle.

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Figure 3.25 Example of a joint in the hinges and rotation springs window

After selecting a particular plate connection by clicking on the corresponding circle, theconnection can be toggled from a clamp into a hinge or vice versa by clicking again onthe circle. For each hinge, an additional rotational degree of freedom is introduced inorder to allow for an independent rotation.

In reality, plate connections may allow for rotations, but this generally requires a torque.To simulate such a situation, PLAXIS enables the input of rotation springs andcorresponding relative rotation spring stiffnesses between two plates. This option is onlyuseful if at least one of the two individual plate connections is a hinge (otherwise theconnection between the two plates is rigid). To define rotation springs in a joint, the jointis surrounded by large circle sections in which rotation springs can be activated. Possiblelocations of rotation springs are indicated by small circles (comparable with the hinges)on the large circle sections. In the case of a straight plate there are no large circlesaround the joint. In that case the central circle represents the rotation spring. Afterselecting a particular rotation spring by clicking on the corresponding circle, the rotationspring can be toggled on and off by clicking again on the circle.

When a rotation spring is created, the properties of the rotation spring must be entereddirectly in the right part of the window. The properties of a rotation spring include thespring stiffness and the maximum torque that it can sustain. The spring stiffness isdefined as the torque per radian (in the unit of Force times Length per Radian per Lengthout of plane).

In the project geometry, a hinge and a rotation spring are indicated by a white and a cyancircle respectively. To modify the hinges and rotation spring properties in a plateconnection, the Hinge and rotation spring button is clicked in the toolbar and theconnection is clicked in the model. The modification can be done in the appearing Hingesand rotation springs window.

3.4.10 DRAINS

Drains are used to prescribe lines inside the geometry model where (excess)pore pressures are reduced. Together with the creation of a drain, the input of a

groundwater head is required. This option is only relevant for consolidation analyses orgroundwater flow calculations. In such calculations, the pore pressure in all nodes of thedrain is reduced such that it is equivalent to the given head. Pore pressures lower thanthe equivalent to the given head are not affected by the drain.

The Drain option can be selected from the Geometry menu or by clicking on the

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corresponding button in the tool bar. The creation of a drain in the geometry model issimilar to the creation of a geometry line (Section 3.4.1). In a geometry model drainsappear as blue dashed lines.

Drains can be activated or de-activated in calculation phases when the Loading input isdefined as Staged construction. Drains can be activated by clicking on them in the Waterconditions mode. Active drains are indicated by a blue colour. A description of theproperties of the drains is given in Section 5.9.7.

3.4.11 WELLS

Wells are used to prescribe points inside the geometry model where a specificdischarge is extracted from or infiltrated into the soil. This option is only relevant for

groundwater flow calculations. The Well option can be selected from the Geometry menuor by clicking on the corresponding button in the tool bar. The creation of a well in thegeometry model is similar to the creation of a fixed-end anchor, but it is not restricted toexisting geometry lines. In a geometry model wells appear as a blue circles attached tosmall black lines.

After creating a well, the discharge of the well can be specified by double clicking the wellin the geometry model. This may require zooming into the area where the well is located.As a result, the Well window appears. In this window the discharge can be specified as apositive value in the unit of volume per unit time per unit of width out of plane. In addition,it can be selected whether the well is used to apply Extraction from the soil or to applyInfiltration in the soil. In the case of an Extraction well, the minimum groundwater headmust be specified in [m] with respect to the global system of axes. The default Equal towell location means that the extraction is automatically stopped if the groundwater leveldrops below the well level.

Wells can be activated or de-activated in calculation phases using Staged construction asLoading input. A description of the properties of the wells is given in Section 5.9.7.

3.5 LOADS AND BOUNDARY CONDITIONS

The Loads menu contains the options to introduce boundary conditions, prescribeddisplacements and loads in the geometry model. Loads and prescribed displacementscan be applied at the model boundaries as well as inside the model.

3.5.1 STANDARD FIXITIES

On selecting Standard fixities from the Loads menu or by clicking the correspondingbutton in the tool bar PLAXIS automatically imposes a set of general boundary

conditions to the geometry model. These boundary conditions are generated accordingto the following rules:

• Vertical geometry lines for which the x-coordinate is equal to the lowest or highestx-coordinate in the model obtain a horizontal fixity (ux = 0).

• Horizontal geometry lines for which the y -coordinate is equal to the lowesty -coordinate in the model obtain a full fixity (ux = uy = 0).

• Plates that extend to the boundary of the geometry model obtain a fixed rotation in

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the point at the boundary (φz = 0) if at least one of the displacement directions ofthat point is fixed.

Standard fixities can be used as a convenient and fast input option for many practicalapplications.

3.5.2 STANDARD EARTHQUAKE BOUNDARIES

PLAXIS has a convenient default setting to generate standard boundary conditions forearthquake loading. This option can be selected from the Loads menu. On selectingStandard earthquake boundaries, the program will automatically generate absorbentboundaries at the left-hand and right-hand vertical boundaries and prescribeddisplacements with ux = 0.01 m and uy = 0.00 m at the bottom boundary (see alsobelow).

3.5.3 STANDARD ABSORBENT BOUNDARIES (DYNAMICS)

An absorbent boundary is aimed to absorb the increments of stresses on the boundariescaused by dynamic loading, that otherwise would be reflected inside the soil body.

For single-source vibrations, PLAXIS has a default setting for generating appropriateabsorbent boundaries. This option can be selected from the Loads menu. For planestrain models, the standard absorbent boundaries are generated at the left-hand, theright-hand and the bottom boundary. For axisymmetric models, the standard absorbentboundaries are only generated at the bottom and the right-hand boundaries.

For manual setting, however, the input of an absorbent boundary is similar to the input offixities (Section 3.5.5).

3.5.4 SET DYNAMIC LOAD SYSTEM

In PLAXIS 2D, the input of a dynamic load is similar to that of a static load. Here, thestandard external load options (point loads and distributed loads in system A and B andprescribed displacements) can be used. In the Input program, the user must specifywhich of the load system(s) will be used as a dynamic load. This can be done using theSet dynamic load system option in the Loads menu. Load systems that are set asdynamic, cannot be used for static loading. Load systems that are not set as dynamic,are considered to be static.

3.5.5 FIXITIES

Fixities are prescribed displacements equal to zero. These conditions can be applied togeometry lines as well as to geometry points. Fixities can be selected from the Loadsmenu. The following options can be selected:

Total fixities Displacements in both x and y directions are equal to zero(ux = uy = 0).

Vertical fixities Displacements in y directions are equal to zero (uy = 0).

Horizontal fixities Displacements in x directions are equal to zero (ux = 0).

To introduce a sharp transition in different prescribed displacements or betweenprescribed displacements and fixities (for example to model a trap-door problem; Figure

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3.26), it is necessary to introduce an interface at the point of transition perpendicular tothe geometry line. As a result, the thickness of the transition zone between the twodifferent displacements is zero. If no interface is used then the transition will occur withinone of the elements connected to the transition point. Hence, the transition zone will bedetermined by the size of the element. The transition zone will therefore be unrealisticallywide.

Figure 3.26 Modelling of a trap-door problem using interfaces

Only one type of boundary conditions can be applied to individual points. In points wherefixities as well as loads are defined, the fixities have priority over the loads. In pointswhere fixities as well as prescribed displacements are defined, the prescribeddisplacements have priority over fixities.

3.5.6 ROTATION FIXITIES (PLATES)

Rotations fixities are used to fix the rotational degree of freedom of a plate aroundthe z-axis. Rotation fixities can be selected from the Loads menu or by clicking on

the corresponding button in the tool bar. Rotation fixities must always act on plates, butnot necessarily on existing geometry points. In the latter case a new geometry point isautomatically introduced.

Existing rotation fixities can be eliminated by selecting the rotation fixity in the geometrymodel and pressing the <Delete> key on the keyboard.

3.5.7 ABSORBENT BOUNDARIES

An absorbent boundary is aimed to absorb the increments of stresses on the boundariescaused by dynamic loading, that otherwise would be reflected inside the soil body.

3.5.8 PRESCRIBED DISPLACEMENTS

Prescribed displacements are special conditions that can be imposed on the modelto control the displacements of certain points. Prescribed displacements can be

selected from the Loads menu or by clicking on the corresponding button in the tool bar.The input of Prescribed displacements in the geometry model is similar to the creation ofgeometry lines (Section 3.4.1). By default, the input values of prescribed displacementsare set such that the vertical displacement component is one unit in the negative verticaldirection (uy = −1) and the horizontal displacement component is free.

The input values of prescribed displacements can be changed by double clicking thecorresponding geometry line and selecting Prescribed displacements from the selectiondialog box. As a result, the Prescribed displacements window appears in which the input

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Figure 3.27 Input window for prescribed displacements

values of the prescribed displacements of both end points of the geometry line can bechanged (Figure 3.5.8). The distribution is always linear along the line. The input valuemust be in the range [-9999, 9999]. In the case that one of the displacement directions isprescribed whilst the other direction is free, one can use the check boxes in the Freedirections group to indicate which direction is free. The Perpendicular button can be usedto impose a prescribed displacement of one unit perpendicular to the correspondinggeometry line. For internal geometry lines, the displacement is perpendicular to the rightside of the geometry line (considering that the line goes from the first point to the secondpoint). For geometry lines at a model boundary, the displacement direction is towards theinside of the model.

On a geometry line where both prescribed displacements and loads are applied, theprescribed displacements have priority over the loads during the calculations, except ifthe prescribed displacements are not activated. On a geometry line where bothprescribed displacements and full fixities are applied, the prescribed displacements havepriority over the fixities during the calculations, except if the prescribed displacements arenot activated.

Although the input values of prescribed displacements can be specified in the geometrymodel, the actual values that are applied during a calculation may be changed in theframework of Staged construction (Section 3.4.1). Moreover, an existing composition ofprescribed displacements may be increased globally by means of the load multipliersMdisp and ΣMdisp (Section 5.11.1).

During calculations, the reaction forces corresponding to prescribed displacements in x-and y -direction are calculated and stored as output parameters (Force-X, Force-Y ).

Hint: Prescribed displacements should be interpreted as specified totaldisplacements at the end of the phase instead of additional phasedisplacements.

Prescribed displacements in dynamics

A special method for introducing dynamic loads in a model is by means of prescribeddisplacements. Earthquakes are usually modelled by means of prescribed horizontaldisplacements. When the Standard earthquake boundaries in the Loads menu is

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selected the horizontal displacement component is defined automatically by PLAXIS.

To define the prescribed displacement for an earthquake manually:

• Enter a prescribed displacement in the geometry model (usually at the bottom).

• Double click on the prescribed displacement.

• Select Prescribed displacement in the window that appears.

• Change the x-values of both geometry points to 1 (or 0.01 when working withstandard SMC files with unit of length in meters, or 0.0328 with unit of length in feet)and the y -values to 0. Now the given displacement is one unit in horizontal direction.

• Optionally, the same input value can be entered for both x- and y-values to allow for(independent) horizontal and vertical motions (see Section 5.11.3 for the applicationof dynamic loads).

• In the Loads menu, set the dynamic load system to Prescribed displacements.

3.5.9 DISTRIBUTED LOADS

The creation of a distributed load in the geometry model is similar to the creationof a geometry line (Section 3.4.1). Two load systems (A and B) are available for a

combination of distributed loads or point loads. The load systems A and B can beactivated independently. Distributed loads for load system A or B can be selected fromthe Loads menu or by clicking on the corresponding button in the tool bar.

The input values of a distributed load are given in force per area (for example kN/m2).Distributed loads may consist of a x- and/or y -component. By default, when applyingloads to the geometry boundary, the load will be a unit pressure perpendicular to theboundary. The input value of a load may be changed by double clicking thecorresponding geometry line and selecting the corresponding load system from theselection dialog box. As a result, the Distributed load window is opened in which the twocomponents of the load can be specified for both end points of the geometry line in thegeometry model. The distribution is always linear along the line.

Figure 3.28 Input window for distributed loads

Although the global input values of distributed loads can be specified in the geometrymodel, the actual value that is applied in a calculation may be changed in the frameworkof Staged construction (Section 5.8.3). Moreover, an existing composition of loads maybe increased globally by means of the load multipliers MloadA (or ΣMloadA) for loadsystem A and MloadB (or ΣMloadB) for load system B (Section 5.11.1).

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On a geometry line where both prescribed displacements and distributed loads areapplied, the prescribed displacements have priority over the distributed loads during thecalculations, provided that the prescribed displacements are active. Hence, it is notuseful to apply distributed loads on a line with fully prescribed displacements. When onlyone displacement direction is prescribed whilst the other direction is free, it is possible toapply a distributed load in the free direction.

3.5.10 POINT LOADS

This option may be used to create point loads, which are actually line loads in theout-of-plane direction. The input values of point loads are given in force per unit of

width (for example kN/m). In axisymmetric models, point loads are in fact line loads on acircle section of 1 radian. In that case the input value of is still given in force per unit ofwidth, except when the point load is located at x = 0. In the latter case (axisymmetry;point load in x = 0) the point load is a real point load and the input value is given in theunit of force (for example kN, though the input window still shows kN/m). Note that thisforce is acting on a circle section of 1 radian only. To derive the input value from a realsituation, the real point force must be divided by 2π to get the input value of the pointforce at the centre of the axisymmetric model.

The creation of a point or line load in the geometry model is similar to the creation of ageometry point (Section 3.4.1). Two load systems (A and B) are available for acombination of distributed loads and line loads or point loads. The load systems A and Bcan be activated independently. Point loads for load system A or B can be selected fromthe Loads menu or by clicking on the corresponding button in the tool bar.

The input values of a point load (or line load) are given in force per unit of length (forexample kN/m). Point loads may consist of a x- and/or y -component. By default, whenapplying point loads, the load will be one unit in the negative y -direction. The input valueof a load may be changed by double clicking the corresponding point and selecting thecorresponding load system from the selection dialog box. As a result, the Point loadwindow is opened in which the two components of the load can be specified (Figure3.5.10).

Figure 3.29 Input window for point loads

A bending moment can be specified in the Point load window as well. For moreinformation on Bending moments see Section 3.5.11.

Although the input values of point loads can be specified in the geometry model, theactual value that is applied in a calculation may be changed in the framework of Stagedconstruction. Moreover, an existing composition of loads may be increased globally bymeans of the load multipliers MloadA (or ΣMloadA) for load system A and MloadB (orΣMloadB) for load system B (Section 5.11.1).

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On a part of the geometry where both prescribed displacements and point loads areapplied, the prescribed displacements have priority over the point loads during thecalculations, provided that the prescribed displacements are active. Hence, it is notuseful to apply point loads on a line with fully prescribed displacements. When only onedisplacement direction is prescribed whilst the other direction is free, it is possible toapply a point load in the free direction.

3.5.11 BENDING MOMENTS

Bending moments can be assigned as a value at a specific point in a plate. The bendingmoment can be defined by clicking the Point load button in the toolbar and clicking on thelocation on the plate where the bending moment is to be assigned. The value of thebending moment can be specified in the corresponding cell in the Point load window(Figure 3.5.11). A positive value indicates a counter clockwise bending moment whereasa negative sign indicates a clockwise one.

Figure 3.30 Definition of bending moment

Hint: Note that the Bending moment option is not accessible in the Point loadwindow (Figure 3.5.10) when the point is not located on a plate.

Although the input values of bending moment can be specified in the geometry model,the actual value that is applied in a calculation may be changed in the framework ofStaged construction. Moreover, an existing composition of loads may be increasedglobally by means of the load multipliers MloadA (or ΣMloadA) for load system A andMloadB (or ΣMloadB) for load system B (Section 5.11.1).

On a part of the geometry where both a rotation fixity and a bending moment are applied,the rotation fixity has priority over the bending moment during the calculations, providedthat the rotation fixity is active. Hence, it is not useful to apply bending moment on a pointwith a rotation fixity.

3.6 DESIGN APPROACHES

PLAXIS 2D has a facility to deal with partial factors for loads and model parameters. Thisfacility is called ‘Design approaches’ and enables PLAXIS 2D to be used for designcalculations in the framework of the Eurocode, LRFD or other design methods based onpartial factors.

The main idea is that a project is first analyzed for a Serviceability Limit State (SLS)situation, without using Design approaches. The input values of loads and the model

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parameters are supposed to be representative or characteristic values. The result wouldbe a cautious estimate of deformations, stresses and structural forces.

If satisfactory results have been obtained for the serviceability state, one may considerusing Design approaches to deal with Ultimate Limit State (ULS) design. In order toperform design calculations, new phases need to be defined in addition to theserviceability state calculations. There are two main schemes to perform designcalculations in relation to serviceability calculations (Bauduin, Vos & Simpson (2000)).

Scheme 1:

0. Initial phase

1. Phase 1 (SLS) → 4. Phase 4 (ULS)

2. Phase 2 (SLS) → 5. Phase 5 (ULS)

3. Phase 3 (SLS) → 6. Phase 6 (ULS)

In this scheme, the design calculations (ULS) are performed for each serviceability statecalculation separately. This means that Phase 4 starts from Phase 1, Phase 5 starts fromPhase 2, etc. Note that in this case a partial factor on a stiffness parameter is only usedto calculate additional displacements as a result of stress redistribution due to thefactored (higher) loads and the factored (reduced) strength parameters.

Scheme 2:

0. Initial phase → 4. Phase 4 (ULS)

1. Phase 1 (SLS) 5. Phase 5 (ULS)

2. Phase 2 (SLS) 6. Phase 6 (ULS)

3. Phase 3 (SLS)

In this scheme, the design calculations (ULS) start from the initial situation and areperformed subsequently. This means that Phase 4 starts from the Initial phase, Phase 5starts from Phase 4, etc.

It is the responsibility of the geotechnical engineer to consider all the different conditionsthat effect the design. Engineering judgment plays a vital role in the determination ofdifferent combinations to be considered in the design.

3.6.1 DEFINITION OF DESIGN APPROACHES

Different design approaches, i.e. coherent sets of partial factors, can be defined for loadsand model parameters according to the applicable design methods (for example:Eurocode 7 — DA 3). After defining such a coherent set of partial factors by the user, itmay then be exported (stored) under an appropriate name in a global data base, afterwhich it can be imported and re-used in other projects. Hence, once complete sets ofpartial factors have been defined and stored, it is a relatively small effort to make designcalculations in addition to serviceability calculations.

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Figure 3.31 Design approaches window

• To add a new design approach click the corresponding option under the designapproaches list. The New design approach window pops up where the name of thenew design approach can be defined (Figure 3.32). The new approach is added inthe list when OK is clicked in the New design approach window.

Figure 3.32 New design approach window

• To delete a design approach from the list select the design in the list and click thecorresponding button under the list.

• To create a copy of a predefined design approach select the design approach in thelist and click the Copy button.

• To import design approaches from other projects or from the global repository ofdesign approaches. Click the corresponding button under the list. As a result, theImport/Export to global repository window appears.The global repository is adatabase of the design approaches contained in other projects, simplifying theirreuse. The address to the location of the global repository is given under the list ofthe global design approaches. A different repository can be selected by clicking theSelect button and selecting the new repository. Global design approaches can beremoved from the depository by selecting them first in the list and by clicking Deletebutton.

Within a design approach, distinction is made between partial factors for loads (actions)and partial factors for model parameters (providing resistances). Design approachesavailable in the model can be defined and managed in the Design approaches window

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Figure 3.33 Import design approach window

that appears when the corresponding option, available in the Loads menu is selected.The Design approaches window consists of two parts. In the upper part of the window alist of the design approaches is displayed. By default no design approaches areavailable. The buttons available under the design approaches list enable adding anddeleting of the approaches in the list as well as importing and exporting designapproaches between different projects.

3.6.2 DEFINITION OF PARTIAL FACTORS FOR LOADS

Loads to be considered in the design approaches for a geotechnical project are:

• Distributed loads

• Point loads

• Prescribed displacements

Different partial factors may apply to different loads or groups of loads. This can bearranged by assigning Labels to individual loads or groups of loads. Considering partialfactors for loads, distinction can be made between different load cases, for examplepermanent unfavourable, permanent favourable, variable unfavourable, variablefavourable, etc.

To change a label, double click it and type the new label. Up to 10 labels and theircorresponding partial factors can be defined. The partial factors for loads are used as amultiplication factor to the reference values of the loads.

Hint: The partial factors for loads are defined such that the design value of aparameter is the reference value multiplied with the partial factor.

By default, the first load case (permanent unfavourable) is assigned to external loads inthe model, but this may be changed when defining a design calculation. Other labels canbe assigned to loads in the Staged construction tabsheet, as part of the definition of acalculation phase. However, the partial factors corresponding to the load labels are onlyapplied when the calculation is performed according to the selected design approach(see Section 5.8.9); otherwise reference values of loads are used.

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3.6.3 DEFINITION OF PARTIAL FACTORS FOR MATERIALS

The partial factors for materials for a selected design approach in the list can be definedin the corresponding tabsheet in the Design approaches window. A list of all the availablematerial models for soil and the materials for structural elements, for which partial factorsare supported is displayed (Figure 3.34).

Figure 3.34 Partial factors for materials tabsheet

Considering partial factors for model parameters, a first distinction is made between thedifferent material models, because different models have different sets of parameters. If aproject contains Mohr-Coulomb material as well as Hardening Soil material, separate setsof partial factors are needed for MC and for HS, even when the parameters to be factoredhappen to be the same (e.g. ϕ’ and c’).

A further distinction can be made between different cases of how the parameters or thematerial model are used. For example, when using the Mohr-Coulomb model, soilstrength may be defined in terms of effective strength (using ϕ’ and c’, i.e. the Drained orUndrained A approach) or in terms of undrained strength (using su , i.e. the Undrained Bor Undrained C approach), for which different partial factors may apply. Hence, separatesets of partial factors may be defined for a case named ‘Effective strength’ (= defaultcase) and a case named ‘Undrained strength’.

To add a case:

• Click the Add case button. The corresponding window pops up (Figure 3.35).

Figure 3.35 Add materialcase window

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• Specify the name of the new case and select the material set and the materialmodel from the corresponding drop-down menus. Note that the Model option is notapplicable for the structural elements.

• Click OK to add the new material case. Note that a new column is added for thenew material case, where the selected material model is indicated by a greenbutton. The window for the soil material set pops up where the partial factors can bedefined for the material parameters.

Hint: The partial factors for materials are defined such that the design value of aparameter is the reference value divided by the partial factor.

» In the case of a partial factor on the friction angle ϕ or the dilatancy angle ψ,the partial factor is applied to tanϕ and tanψ respectively.

» By default, all partial factors are set to 1.0.

In addition to partial factors for soil model parameters, partial factors for structural modelparameters may be defined as well. After creating the different material cases, theyshould be assigned to the materials in the current project, listed in the table namedaccordingly (Figure 3.36). The first two columns in the table give the name of the materialdataset and the material model respectively. The cells in the third column aretransformed into drop-down menus where the material cases available in the selecteddesign approach are listed. Clicking on the options will assign the material case to theselected material in the model. Make sure all material data sets have been assigned acorresponding material case other than the default ‘none’.

Figure 3.36 Assignment of material cases

Subsequently, the material data sets can be opened via the material data base to view(and modify, if necessary!) the actual values of model parameters that will be used whendesign calculations are performed.

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To complete the definition of a design calculation it is necessary to proceed to the Stagedconstruction tabsheet (Section 5.8.9) where the design approach to be used for a specificphase is selected and the loads in the model are labelled. Make sure that the requiredload labels with corresponding partial factors are properly assigned to the external loadsin the model.

When using Design approaches in combination with advanced soil models, these modelswill continue to behave as advanced models, maintaining all their features, such asstress-dependent stiffness behaviour and hardening effects. This is different than whenusing a Safety analysis with advanced models (Section 5.5.5), since in the latter caseadvanced models loose their advanced features and basically switch to Mohr-Coulomb.When comparing a Safety analysis to a target value of ΣMsf with a Design approachesanalysis using the same partial factor for c and tanϕ, it should be realized that the resultscould be different because of this reason.

3.7 MESH GENERATION

When the geometry model is fully defined and material properties have been assigned toall clusters and structural objects, the geometry has to be divided into finite elements inorder to perform finite element calculations. A composition of finite elements is called amesh. The basic type of element in a mesh is the 15-node triangular element or the6-node triangular element, as described in Section 3.1.1. In addition to these elements,there are special elements for structural behaviour (plates, embedded pile rows, geogridsand anchors), as described in Section 3.4.2 to 3.4.7. PLAXIS 2D allows for a fullyautomatic mesh generation of finite element meshes. The generation of the mesh isbased on a robust triangulation procedure.

Although PLAXIS 2D automatically applies local mesh refinements (Section 3.7.6),meshes that are automatically generated by PLAXIS may not be accurate enough toproduce acceptable numerical results. Please note that the user remains responsible tojudge the accuracy of the finite element meshes and may need to consider further globaland local refinement options.

The required input for the mesh generator is a geometry model composed of points, linesand clusters, of which the clusters (areas enclosed by lines) are automatically generatedduring the creation of the geometry model. Geometry lines and points may also be usedto influence the position and distribution of elements.

The generation of the mesh is started by clicking on the mesh generationbutton in the tool bar or by selecting the Generate option from the Mesh menu. The

generation is also activated directly after the selection of a refinement option from theMesh menu.

After the mesh generation the Output program is started and a plot of the mesh isdisplayed. Although interface elements have a zero thickness, the interfaces in the meshare drawn with a certain thickness to show the connections between soil elements andinterfaces. This so-called Connectivity plot is also available as a regular output option(Section 7.1). The scale factor (Section 6.3.7) may be used to reduce the graphicalthickness of the interfaces. To return to the Input program, the green Close arrow mustbe clicked.

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3.7.1 BASIC ELEMENT TYPE

On selecting Basic element type from the Mesh menu, the Project properties window isopened. The user may select either 15-Node or 6-Node triangular elements (Figure 3.3)as the basic type of element to model soil layers and other volume clusters. The type ofelement for structures and interfaces is automatically taken to be compatible with thebasic type of soil element.

3.7.2 GLOBAL COARSENESS

The mesh generator requires a general meshing parameter which represents the averageelement size, le. In PLAXIS this parameter is calculated from the outer geometrydimensions (xmin, xmax , ymin, ymax ) and a Global coarseness setting as defined in theMesh menu:

le =nc

12

√(xmax − xmin)(ymax − ymin)

Distinction is made between five levels of global coarseness: Very coarse, Coarse,Medium, Fine and Very fine. By default, the global coarseness is set to Medium. Theglobal element size and the number of generated triangular elements depends on thisglobal coarseness setting. A rough estimate is given below (based on a generationwithout local refinement):

Very coarse: nc = 2.0 Around 70 elements

Coarse: nc = 1.4 Around 150 elements

Medium: nc = 1.0 Around 200 elements

Fine: nc = 0.7 Around 500 elements

Very fine: nc = 0.5 Around 1000 elements

The exact number of elements depends on the shape of the geometry and optional localrefinement settings. The number of elements is not influenced by the Type of elementsparameter, as set in the Project properties window. Note that a mesh composed of15-node elements gives a much finer distribution of nodes and thus much more accurateresults than a similar mesh composed of an equal number of 6-node elements. On theother hand, the use of 15-node elements is more time consuming than using 6-nodeelements.

3.7.3 GLOBAL REFINEMENT

A finite element mesh can be refined globally by selecting the Refine global option fromthe Mesh menu. When selecting this option, the global coarseness parameter isincreased one level (for example from Medium to Fine) and the mesh is automaticallyregenerated.

3.7.4 LOCAL COARSENESS

In areas where large stress concentrations or large deformation gradients are expected, itis desirable to have a more accurate (finer) finite element mesh, whereas other parts ofthe geometry might not require a fine mesh. Such a situation often occurs when thegeometry model includes edges or corners or structural objects. For these cases PLAXIS

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uses local coarseness parameters in addition to the global coarseness parameter. Thelocal coarseness parameter is the Local element size factor, which is contained in eachgeometry point. These factors give an indication of the relative element size with respectto the average element size as determined by the Global coarseness parameter. Bydefault, the Local element size factor is set to 1.0 at all geometry points. Automaticrefinement will be applied where necessary (see Section 3.7.6). To reduce the length ofan element to half the global element size, the Local element size factor should be set to0.5.

The local element size factor can be changed by double clicking the correspondinggeometry point. Alternatively, when double clicking a geometry line, one can set the localelement size factor for both points of the geometry line simultaneously. Values in therange from 0.05 to 5.0 are acceptable.

3.7.5 LOCAL REFINEMENT

Instead of specifying local element size factors, a local refinement can be achieved byselecting clusters, lines or points and selecting a local refinement option from the Meshmenu.

When selecting one or more clusters, the Mesh menu allows for the option Refine cluster .Similarly, when selecting one or more geometry lines, the Mesh menu provides the optionRefine line. When selecting one or more points, the option Refine around point isavailable.

Using one of the options for the first time will give a local element size factor of 0.5 for allselected geometry points or all geometry points that are included in the selected clustersor lines. Repetitive use of the local refinement option will result in a local element sizefactor which is half the current factor, however, the minimum and maximum value arerestricted to the range [0.05, 5.0]. After selecting one of the local refinement options, themesh is automatically regenerated.

3.7.6 AUTOMATIC REFINEMENT

To supply a good quality mesh for every geometry which also takes into account thenecessary mesh refinement around structural elements, loads and prescribeddisplacements, PLAXIS will apply automatic mesh refinements. These automaticrefinements in terms of an implicit local element size multiplication factor will be applied incase of:

• structural elements, loads and prescribed displacements: the Local element sizefactor will be multiplied by 0.25, except when prescribed displacements or loadshave been applied along a whole edge of the geometry. The implicit multiplicationfactors can be compensated in the Input program by setting the Local element sizefactor manually to 4.0.

• the distance between points and/or lines is rather close, which requires a smallerelement size to avoid large aspect ratios.

• an angle between geometry lines other than a multiple of 900, to allow for moreaccurate stresses around geometry discontinuities. The Local element size factorwill be multiplied according to Figure 3.37.

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Figure 3.37 The implicit Local element size multiplication factor as a function of the angle betweentwo lines.

Note that the Local element size factors are implicitly applied, and are not visible to theuser. In order to ‘compensate’ implicitly applied Local element size factors, an inverseLocal element size factor can be given manually to the corresponding geometry point(e.g. a Local element size factor of 4 will compensate the implicit factor of 0.25 for loadssuch that the global coarseness is retained).

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4 MATERIAL PROPERTIES AND MATERIAL DATABASE

In PLAXIS, soil properties and material properties of structures are stored in materialdata sets. There are four different types of material sets grouped as data sets for soil andinterfaces, data sets for plates, data sets for geogrids, data sets for embedded pile rowsand data sets for anchors. All data sets are stored in the material database. From thedatabase, the data sets can be assigned to the soil clusters or to the correspondingstructural objects in the geometry model.

The material database can be activated by selecting one of the options from theMaterials menu or by clicking the Materials button in the tool bar. As a result, the

Material sets window appears showing the contents of the project material database. Thewindow can be extended to show the global database by clicking the Show global buttonin the upper part of the window. The Material sets window displaying the material definedin the current project and the ones available in a selected global database is shown inFigure 4.1.

Figure 4.1 Material sets window showing the project and the global database

The database of a new project is empty. The global database can be used to storematerial data sets in a global folder and to exchange data sets between different projects.

At both sides of the window (Project materials and Global materials) there are twodrop-down menus and a tree view. The Set type can be selected from the drop-downmenu on the left hand side. The Set type parameter determines which type of materialdata set is displayed in the tree view (Soil and interfaces, Plates, Embedded pile rows,Geogrids, Anchors).

The data sets in the tree view are identified by a user-defined name. The data sets forSoil and interfaces can be ordered in groups according to the material model, thematerial type or the name of the data set by selecting this order in the Group orderdrop-down menu. The None option can be used to discard the group ordering.

The small buttons between the two tree views can be used to copy individual data setsfrom the project database to the selected global database or vice versa.

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To copy the selected project material set to the global database.

To copy all the project material sets of the specified type to the global database.

To copy the selected global material set to the project database.

The location of the selected global database is shown below its tree view. The buttonsbelow the tree view of the global database enable actions in the global database.

Select To select an existing global database.

Delete To delete a selected material data set from the selected globaldatabase.

By default, the global database for soil and interface data contains the data sets of all thetutorials and it is contained in the file ‘SoilMat.matdb’. This file is compatible with otherPLAXIS database files for soil and interfaces and is stored in the installation folder ofPLAXIS 2D. Material data sets for structural elements will be contained in separate files.Similarly, the global data bases for plates, geogrids and anchors are contained in the files’PlateMat2D.matdb’, ‘GeogridMat.matdb’, ‘EmbeddedPile2DMat.matdb’ and’AnchorMat2D.matdb’ respectively.

Note that besides the global material files (*.matdb), it is possible to select projectmaterial files (*.plxmat) and legacy project material files (*.mat) as global database.

In addition, databases with data sets of standard sheet-pile wall profiles are availablefrom the Plaxis Knowledge Base(http://kb.plaxis.nl/downloads/material-parameter-datasets-sheetpiles-and-beams).

Hint: A new global database can be created by clicking the Select button, definingthe name of the new global database and clicking Open.

The project data base can be managed using the buttons below the tree view of theproject database.

New To create a new data set in the project. As a result, a newwindow appears in which the material properties or modelparameters can be entered. The first item to be entered isalways the Identification, which is the user-defined name of thedata set. After completing a data set, it will appear in the treeview, indicated by its name as defined by the Identification.

Edit To modify the selected data set in the project material database.

SoilTest To perform standard soil lab tests. A separate window will openwhere several basic soil tests can be simulated and thebehaviour of the selected soil material model with the givenmaterial parameters can be checked (Section 4.3).

Copy To create a copy of a selected data set in the project materialdatabase.

Delete To delete a selected material data set from the project materialdatabase.

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4.1 MODELLING SOIL AND INTERFACE BEHAVIOUR

The material properties and model parameters for soil clusters are entered in materialdata sets (Figure 4.2). The properties in the data sets are divided into five tabsheets:General, Parameters , Flow parameters, Interfaces and Initial.

4.1.1 GENERAL TABSHEET

The General tabsheet contains the type of soil model, the drainage type and the generalsoil properties such as unit weights. Several data sets may be created to distinguishbetween different soil layers. A user may specify any identification title for a data set inthe General tabsheet of the Soil window. It is advisable to use a meaningful name sincethe data set will appear in the database tree view by its identification.

For easy recognition in the model, a colour is given to a certain data set. This colour alsoappears in the database tree view. PLAXIS 2D selects a unique default colour for a dataset, but this colour may be changed by the user. Changing the colour can be done byclicking on the colour box in the General tabsheet.

Figure 4.2 General tabsheet of the Soil window

Material model

Soil and rock tend to behave in a highly non-linear way under load. This non-linearstress-strain behaviour can be modelled at several levels of sophistication. Clearly, thenumber of model parameters increases with the level of sophistication. PLAXIS supportsdifferent models to simulate the behaviour of soil and other continua. The models andtheir parameters are described in detail in the Material Models Manual. A shortdiscussion of the available models is given below:

Linear elastic model: This model represents Hooke’s law of isotropic linear elasticity.The linear elastic model is too limited for the simulation of soil behaviour. It is primarilyused for stiff structures in the soil.

Mohr-Coulomb model (MC): This well-known linear elastic perfectly-plastic model isused as a first approximation of soil behaviour in general. It is recommended to use thismodel for a first analysis of the problem considered. A constant average stiffness is

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estimated for the soil layer. Due to this constant stiffness, computations tend to berelatively fast and a first estimate of deformations can be obtained.

Hardening Soil model (HS): This is an advanced model for the simulation of soilbehaviour. The Hardening Soil model is an elastoplastic type of hyperbolic model,formulated in the framework of shear hardening plasticity. Moreover, the model involvescompression hardening to simulate irreversible compaction of soil under primarycompression. This second-order model can be used to simulate the behaviour of sandsand gravel as well as softer types of soil such as clays and silts.

Hardening Soil model with small-strain stiffness (HSsmall): This is an elastoplastictype of hyperbolic model, similar to the Hardening Soil model. Moreover, this modelincorporates strain dependent stiffness moduli, simulating the different reaction of soilsfrom small strains (for example vibrations with strain levels below 10-5) to large strains(engineering strain levels above 10-3).

Soft Soil model (SS): This is a Cam-Clay type model that can be used to simulate thebehaviour of soft soils like normally consolidated clays and peat. The model performsbest in situations of primary compression.

Soft Soil Creep model (SSC): This is a second order model formulated in theframework of viscoplasticity. The model can be used to simulate the time-dependentbehaviour of soft soils like normally consolidated clays and peat. The model includeslogarithmic primary and secondary compression.

Jointed Rock model (JR): This is an anisotropic elastic-perfectly plastic model whereplastic shearing can only occur in a limited number of shearing directions. This modelcan be used to simulate the anisotropic behaviour of stratified or jointed rock.

Modified Cam-Clay model (MCC): This well-known critical state model can be used tosimulate the behaviour of normally consolidated soft soils. The model assumes alogarithmic relationship between the volumetric strain and the mean effective stress.

NGI-ADP model (NGI-ADP): The NGI-ADP model may be used for capacity,deformation and soil-structure interaction analysis involving undrained loading of clay.Distinct anisotropic stress strengths may be defined for different stress paths.

Hoek-Brown model (HB): This well-known elastic perfectly-plastic model is used tosimulate the isotropic behaviour of rock. A constant stiffness is used for the rock mass.Shear failure and tension failure are described by a non-linear stress curve.

Sekiguchi-Ohta model (Inviscid): The Sekiguchi-Ohta model (Inviscid) is a Cam-Claytype effective stress model for time-independent behaviour of clay-type soils.

Sekiguchi-Ohta model (Viscid): The Sekiguchi-Ohta model (Viscid) is a Cam-Claytype effective stress model for time-dependent behaviour (creep) behaviour of clay-typesoils.

User-defined soil models (UDSM): With this option it is possible to use otherconstitutive models than the standard PLAXIS models. For a detailed description of thisfacility, reference is made to the Material Models Manual. Links to existing User-definedsoil models are available on the Plaxis Knowledge Base (http://kb.plaxis.nl/models).

Drainage type

In principle, all model parameters in PLAXIS are meant to represent the effective soilresponse, i.e. the relation between the stresses and strains associated with the soil

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skeleton. An important feature of soil is the presence of pore water. Pore pressuressignificantly influence the soil response. To enable incorporation of the water-skeletoninteraction in the soil response PLAXIS offers a choice of different types of drainage:

Drained behaviour: Using this setting no excess pore pressures are generated. This isclearly the case for dry soils and also for full drainage due to a high permeability (sands)and/or a low rate of loading. This option may also be used to simulate long-term soilbehaviour without the need to model the precise history of undrained loading andconsolidation.

Undrained behaviour: This setting is used for saturated soils in cases where porewater cannot freely flow through the soil skeleton. Flow of pore water can sometimes beneglected due to a low permeability (clays) and/or a high rate of loading. All clusters thatare specified as undrained will indeed behave undrained, even if the cluster or a part ofthe cluster is located above the phreatic level.

Distinction is made between three different methods of modelling undrained soilbehaviour. Method A is an undrained effective stress analysis with effective stiffness aswell as effective strength parameters. This method will give a prediction of the porepressures and the analysis can be followed by a consolidation analysis. The undrainedshear strength (su) is a consequence of the model rather then an input parameter. It isrecommended to check this shear strength with known data. To consider this type ofanalysis, the Undrained (A) option should be selected in the Drainage type drop-downmenu.

Method B is an undrained effective stress analysis with effective stiffness parameters andundrained strength parameters. The undrained shear strength su is an input parameter.This method will give a prediction of pore pressures. However, when followed by aconsolidation analysis, the undrained shear strength (su) is not updated, since this is aninput parameter. To consider this type of analysis, the Undrained (B) option should beselected in the Drainage type drop-down menu.

Method C is an undrained total stress analysis with all parameters undrained. Thismethod will not give a prediction of pore pressures. Therefore it is not useful to perform aconsolidation analysis. The undrained shear strength (su) is an input parameter. Toconsider this type of analysis, the Undrained (C) option should be selected in theDrainage type drop-down menu.

More information about modelling undrained behaviour can be found in Section 4.2 andthe Material Models Manual.

Non-porous behaviour: Using this setting neither initial nor excess pore pressures willbe taken into account in clusters of this type. Applications may be found in the modellingof concrete or structural behaviour. Non-porous behaviour is often used in combinationwith the Linear elastic model. The input of a saturated weight is not relevant fornon-porous materials or intact rock.

In a consolidation analysis it is the permeability parameter in the Flow tabsheet thatdetermines the drainage capacity of a layer rather than the drainage type. Still, thedrainage type has influence on the applied compressibility of water in a consolidationanalysis. For more information see Appendix A.

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Saturated and unsaturated weight (γsat and γunsat )

The saturated and the unsaturated weight refer to the total unit weight of the soil skeletonincluding the fluid in the pores. The unsaturated weight γunsat applies to all materialabove the phreatic level and the saturated weight γsat applies to all material below thephreatic level. The unit weights are entered as a force per unit volume.

For non-porous material only the unsaturated weight is relevant, which is just the total unitweight. For porous soils the unsaturated weight is obviously smaller than the saturatedweight. For sands, for example, the saturated weight is generally around 20 kN/m3

whereas the unsaturated weight can be significantly lower, depending on the degree ofsaturation.

Note that soils in practical situations are never completely dry. Hence, it is advisable notto enter the fully dry unit weight for γunsat . For example, clays above the phreatic levelmay be almost fully saturated due to capillary action. Other zones above the phreaticlevel may be partially saturated. However, the steady-state pore pressures above thephreatic level are always set equal to zero. In this way tensile capillary stresses aredisregarded. However, excess pore stresses (both pressure and suction) may occurabove the phreatic line as a result of undrained behaviour A or B. The latter does notaffect the unit weight of the soil.

In the Advanced mode (Section 5.3.2), the actual unit weight for the soil that is used inthe calculations depends on the effective degree of saturation Se as calculated in theprevious calculation step.

γ = (1− Se)γunsat + Seγsat (4.1)

where

Se = (S − Smin)/(Smax − Smin) (4.2)

S is the actual degree of saturation, Smin is the minimum degree of saturation and Ssat isthe maximum degree of saturation.

Weights are activated by means of Gravity loading or K0 procedure in the Calculationmode, which is always the first calculation phase (Initial phase) (see Section 5.5.1).

Advanced general properties

Additional properties for advanced modelling features can be defined in the Advancedsubtree in the General tabsheet (Figure 4.2).

Void ratio (einit , emin, emax ): The void ratio, e, is related to the porosity, n(e = n/(1− n)). This quantity is used in some special options. The initial value einit is thevalue in the initial situation. The actual void ratio is calculated in each calculation stepfrom the initial value and the volumetric strain ∆εv . These parameters are used tocalculate the change of permeability when input is given for the ck value (in the Flowtabsheet). In addition to einit , a minimum value emin and a maximum value emax can beentered. These values are related to the maximum and minimum density that can bereached in the soil. When the Hardening Soil model or Hardening Soil model withsmall-strain stiffness is used with a certain (positive) value of dilatancy, the mobiliseddilatancy is set to zero as soon as the maximum void ratio is reached (this is termed

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dilatancy cut-off). For other models this option is not available. To avoid the dilatancycut-off in the Hardening Soil model or Hardening Soil model with small-strain stiffnessthe option may be deselected in the Advanced general properties subtree.

Rayleigh α and β: Material damping in dynamic calculations is caused by the viscousproperties of soil, friction and the development of irreversible strains. All plasticity modelsin PLAXIS 2D can generate irreversible (plastic) strains, and may thus cause materialdamping. However, this damping is generally not enough to model the dampingcharacteristics of real soils. For example, most soil models show pure elastic behaviourupon unloading and reloading which does not lead to damping at all. There is one modelin PLAXIS that includes viscous behaviour, which is the Soft Soil Creep model. Using themodel in dynamic calculations may lead to viscous damping, but also the Soft Soil Creepmodel hardly shows any creep strain in load / reload cycles. There is also one model inPLAXIS that includes hysteretic behaviour in loading / reload cycles, which is the HSsmall model (Chapter 7 of the Material Models Manual). When using this model, theamount of damping that is obtained depends on the amplitude of the strain cycles.Considering very small vibrations, even the HS small model does not show materialdamping, whereas real soils still show a bit of viscous damping. Hence, additionaldamping is needed to model realistic damping characteristics of soils in dynamiccalculations. This can be done by means of Rayleigh damping.

Rayleigh damping is a numerical feature in which a damping matrix C is composed byadding a portion of the mass matrix M and a portion of the stiffness matrix K :

C = αM + βK

The parameters α and β are the Rayleigh coefficients. α is the parameter thatdetermines the influence of mass in the damping of the system. The higher α is, the morethe lower frequencies are damped. β is the parameter that determines the influence ofstiffness in the damping of the system. The higher β is, the more the higher frequenciesare damped. In PLAXIS 2D, these parameters can be specified for each material data setfor soil and interfaces as well as for material data sets for plates. In this way, the (viscous)damping characteristics can be specified for each individual material in the finite elementmodel. The values for α and β can be specified in the corresponding cells in theParameters tabsheet of the Soil window.

Figure 4.3 Damping parameters in the General tabsheet

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Despite the considerable amount of research work in the field of dynamics, little has beenachieved yet for the development of a commonly accepted procedure for dampingparameter identification. Instead, for engineering purposes, some measures are made toaccount for material damping. A commonly used engineering parameter is the dampingratio ξ. The damping ratio is defined as ξ = 1 for critical damping, i.e. exactly the amountof damping needed to let a single degree-of-freedom system that is released from aninitial excitation u0, smoothly stop without rebouncing.

Considering Rayleigh damping, a relationship can be established between the dampingratio ξ and the Rayleigh damping parameters α and β:

α + β ω2 = 2ω ξ and ω = 2π f

where ω is the angular frequency in rad/s and f is the frequency in Hz (1/s).

u

t

Critically damped (ξ = 1)

Underdamped (ξ < 1)

Overdamped (ξ > 1)

Figure 4.4 Role of damping ratio ξ in free vibration of a single degree-of-freedom system

Solving this equation for two different target frequencies and corresponding targetdamping ratios gives the required Rayleigh damping coefficients:

α = 2ω1ω2ω1ξ2 − ω2ξ1

ω21 − ω2

2and β = 2

ω1ξ1 − ω2ξ2

ω21 − ω2

2

For example, when it is desired to have a target damping of 8% at the target frequenciesf = 1.5 Hz and 8.0 Hz, the corresponding Rayleigh damping ratios are α = 1.2698 andβ = 0.002681. From Figure 4.5 it can be seen that within the range of frequencies asdefined by the target frequencies the damping is less than the target damping, whereasoutside this range the damping is more than the target damping.

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0.1

0.1

0.2

0.3

0.4

0.5

1.5 8.0

10

10 100

8%

Dam

ping

ratio

(-)

Frequency (Hz)

Influence of β Influence of α

Damping curve

Figure 4.5 Rayleigh damping parameter influence

The damping parameters (α and β) can be automatically calculated by the program whenthe target damping ratio (ξ) and the target frequencies (f) are specified in the panedisplayed in the General tabsheet when one of the cells corresponding to the dampingparameters is clicked (Figure 4.6). A graph shows the damping ratio as a function of thefrequency.

Figure 4.6 Input of ξ and f

4.1.2 PARAMETERS TABSHEET

The Parameters tabsheet contains the stiffness and strength parameters of the selectedsoil model. These parameters depend on the selected soil model as well as on theselected drainage type.

Linear Elastic model (LE): The Parameters tabsheet for the Linear Elastic model(drained behaviour) is shown in Figure 4.7.

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Hint: Optional drainage types when the Linear Elastic model is selected are:Drained, Undrained (A), Undrained (C), and Non-porous.

» In the case of Undrained (A) or Non-porous drainage types, the sameparameters are used as for drained behaviour.

» In the case of Undrained (C) drainage type, an undrained Young’s modulus(Eu) and undrained Poisson’s ratio (νu) are used.

The model involves two elastic stiffness parameters, namely the effective Young’smodulus E ‘ and the effective Poisson’s ratio ν ‘.

E ‘ : Effective Young’s modulus [kN/m2]

ν ‘ : Effective Poisson’s ratio [-]

During the input for the Linear Elastic model the values of the shear modulus G and theoedometer modulus Eoed are presented as auxiliary parameters (alternatives).

G : Shear modulus, where G = E ‘2(1 + ν ‘)

[kN/m2]

Eoed : Oedometer modulus, where Eoed = E ‘(1− ν ‘)(1 + ν ‘)(1− 2ν ‘)

[kN/m2]

Figure 4.7 Parameters tabsheet for the Linear Elastic model (drained behaviour)

Note that the alternatives are influenced by the input values of E ‘ and ν ‘. Entering aparticular value for one of the alternatives G or Eoed results in a change of the Young’smodulus E ‘.

It is possible for the Linear Elastic model to specify a stiffness that varies linearly withdepth. Therefore, the increment of stiffness per unit of depth, E ‘inc , can be defined.Together with the input of E ‘inc the input of yref becomes relevant. For any y -coordinateabove yref the stiffness is equal to E ‘ref . For any y -coordinate below yref the stiffness is

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given by:

E ‘(y ) = E ‘ +(yref − y )E ‘inc y < yref (4.3)

The Linear Elastic model is usually inappropriate to model the highly non-linear behaviourof soil, but it is of interest to simulate structural behaviour, such as thick concrete walls orplates, for which strength properties are usually very high compared with those of soil.For these applications, the Linear Elastic model will often be selected together withNon-porous type of material behaviour in order to exclude pore pressures from thesestructural elements.

Hint: When embedded piles penetrate a volume cluster with linear elastic materialbehaviour, the specified value of the shaft resistance is ignored. The reasonfor this is that the linear elastic material is not supposed to be soil, but part ofthe structure. The connection between the pile and the structure is supposedto be rigid to avoid, for example, punching of piles through a concrete deck.

Beside the parameters related to strength and stiffness of the soil, the velocities of wavepropagation in soil can be defined in the Parameters tabsheet of the Soil window whenthe Dynamics module of the program is available. These velocities are:

Vs : Shear wave velocity, where Vs =√

G/ρ [m/s]

Vp : Compression wave velocity, where Vp =√

Eoed/ρ [m/s]

Note that ρ = γ/g.

Hint: Note that the wave velocities are influenced by the input values of E ‘ and ν ‘.Entering a particular value for one of the wave velocities results in a changeof the Young’s modulus.

» Velocities of wave propagation in soil can be defined only for models withstress independent stiffness.

Mohr-Coulomb model (MC): The linear-elastic perfectly-plastic model withMohr-Coulomb failure contour (in short the Mohr-Coulomb model) requires a total of fiveparameters (two stiffness parameters and three strength parameters), which aregenerally familiar to most geotechnical engineers and which can be obtained from basictests on soil samples.

The stiffness parameters of the Mohr-Coulomb model (drained behaviour) are:

E ‘ : Effective Young’s modulus [kN/m2]

ν ‘ : Effective Poisson’s ratio [-]

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Figure 4.8 Parameters tabsheet for the Mohr-Coulomb model (drained behaviour)

Hint: Optional drainage types when Mohr-Coulomb model is selected are:Drained, Undrained (A), Undrained (B), Undrained (C), and Non-porous.

» In the case of Undrained (A) or Non-porous drainage types, the sameparameters are used as for drained behaviour.

» In the case of Undrained (B) drainage type, ϕ = ϕu = 0, ψ = 0 and theundrained shear strength su is used instead of the effective cohesion (c’).

» In the case of Undrained (C) drainage type all parameters are undrained. i.e.Eu , νu and su as undrained Young’s modulus, undrained Poisson’s ratio andundrained shear strength respectively, and ϕ = ψ = 0.

Instead of using the Young’s modulus as a stiffness parameter, alternative stiffnessparameters can be entered. These parameters, the relations and their standard units arelisted below:

G : Shear modulus, where G = E ‘2(1 + ν ‘)

[kN/m2]

Eoed : Oedometer modulus, where Eoed = E ‘(1− ν ‘)(1 + ν ‘)(1− 2ν ‘)

[kN/m2]

Note that the alternatives are influenced by the input values of E ‘ and ν ‘. Entering aparticular value for one of the alternatives G or Eoed results in a change of the Young’smodulus E ‘.

Stiffness varying with depth can be defined in Mohr-Coulomb model by entering a valuefor E ‘inc which is the increment of stiffness per unit of depth. Together with the input ofE ‘inc the input of yref becomes relevant. For any y -coordinate above yref the stiffness isequal to E ‘ref . For any y -coordinate below yref the stiffness is given by:

E ‘(y ) = E ‘ +(yref − y )E ‘inc y < yref (4.4)

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The strength parameters for the Mohr-Coulomb model are:

c’ref : Effective cohesion [kN/m2]

ϕ’ : Effective friction angle [◦]

ψ : Dilatancy angle [◦]

A cohesion varying with depth can be defined in Mohr-Coulomb model by entering avalue for c’inc which is the increment of effective cohesion per unit of depth. Together withthe input of c’inc the input of yref becomes relevant. For any y -coordinate above yref thecohesion is equal to c’ref . For any y -coordinate below yref the cohesion is given by:

c'(y ) = c’ref +(yref − y )c’inc y < yref (4.5)

In some practical problems an area with tensile stresses may develop. This is allowedwhen the shear stress is sufficiently small. However, the soil surface near a trench in claysometimes shows tensile cracks. This indicates that soil may also fail in tension insteadof in shear. Such behaviour can be included in a PLAXIS analysis by selecting theTension cut-off option. When selecting the Tension cut-off option the allowable tensilestrength (σt ,soil ) may be entered. For the Mohr-Coulomb model model the default value ofthe tension cut-off is zero.

Beside the parameters related to strength and stiffness of the soil, the velocities of wavepropagation in soil can be defined in the Parameters tabsheet of the Soil window. Thesevelocities are:

Vs : Shear wave velocity, where Vs =√

G/ρ [m/s]

Vp : Compression wave velocity, where Vp =√

Eoed/ρ [m/s]

Note that ρ = γ/g.

Hint: Note that the wave velocities are influenced by the input values of E ‘ and ν ‘.Entering a particular value for one of the wave velocities results in a changeof the Young’s modulus.

» Velocities of wave propagation in soil can be defined only for models withstress independent stiffness.

Hardening Soil model (HS): The Parameters tabsheet for the Hardening Soil model isshown in Figure 4.9.

Hint: Optional drainage types when Hardening Soil model is selected are:Drained, Undrained (A), and Undrained (B).

» In the case of Undrained (A) drainage type, the same parameters are usedas for drained behaviour.

» In the case of Undrained (B) drainage type, ϕ = ϕu = 0 , ψ = 0 and theundrained shear strength su is used instead of the effective cohesion (c’).

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Figure 4.9 Parameters tabsheet for the Hardening Soil model (drained behaviour)

The stiffness parameters of the Hardening Soil model are:

E ref50 : Secant stiffness in standard drained triaxial test [kN/m2]

E refoed : Tangent stiffness for primary oedometer loading [kN/m2]

E refur : Unloading / reloading stiffness (default E ref

ur = 3E ref50 ) [kN/m2]

m : Power for stress-level dependency of stiffness [-]

Instead of entering the basic parameters for soil stiffness, alternative parameters can beentered. These parameters are listed below:

Cc : Compression index [-]

Cs : Swelling index or reloading index [-]

einit : Initial void ratio [-]

In addition, advanced parameters can be defined for stiffness (it is advised to use thedefault setting):

νur : Poisson’s ratio for unloading-reloading (default ν = 0.2) [-]

pref : Reference stress for stiffnesses (default pref = 100kN/m2)

[kN/m2]

K nc0 : K0-value for normal consolidation (default K nc

0 =1− sinϕ)

[-]

The strength parameters of the present hardening model coincide with those of thenon-hardening Mohr-Coulomb model:

c’ref : Effective cohesion [kN/m2]

ϕ’ : Effective angle of internal friction [◦]

ψ : Angle of dilatancy [◦]

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In addition, advanced parameters can be defined for strength:

c’inc : As in Mohr-Coulomb model (default cinc = 0) [kN/m3]

Rf : Failure ratio qf / qa (default Rf = 0.9) [-]

σtension : Tensile strength (default σtension = 0 stress units) [kN/m2]

In some practical problems an area with tensile stresses may develop. This is allowedwhen the shear stress is sufficiently small. However, the soil surface near a trench in claysometimes shows tensile cracks. This indicates that soil may also fail in tension insteadof in shear. Such behaviour can be included in a PLAXIS analysis by selecting theTension cut-off option. When selecting the Tension cut-off option the allowable tensilestrength may be entered. For the Hardening Soil model the default value of the tensioncut-off is zero.

Hardening Soil model with small-strain stiffness (HSsmall): Compared to thestandard HS model, the HS small model requires two additional stiffness parameters asinput: γ0.7 and Gref

0 . The Parameters tabsheet for the HS small model is shown in Figure4.10.

Hint: Optional drainage types when Hardening Soil model with small-strainstiffness is selected are: Drained, Undrained (A), and Undrained (B).

» In the case of Undrained (A) drainage type, the same parameters are usedas for drained behaviour.

» In the case of Undrained (B) drainage type, ϕ = ϕu = 0, ψ = 0 and theundrained shear strength su is used instead of the effective cohesion (c’).

Figure 4.10 Parameters tabsheet for the HS small model (drained behaviour)

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All other parameters, including the alternative stiffness parameters, remain the same asin the standard Hardening Soil model. In summary, the input stiffness parameters of theHS small model are listed below:

Parameters for stiffness:

E ref50 : Secant stiffness in standard drained triaxial test [kN/m2]

E refoed : Tangent stiffness for primary oedometer loading [kN/m2]

E refur : unloading / reload stiffness at engineering strains

(ε ≈ 10−3 to 10−2)[kN/m2]

m : Power for stress-level dependency of stiffness [-]

Alternative parameters for stiffness:

Cc : Compression index [-]

Cs : Swelling index or reloading index [-]

einit : Initial void ratio [-]

Advanced parameters for stiffness:

νur : Poisson’s ratio for unloading-reloading (default ν = 0.2) [-]

pref : Reference stress for stiffnesses (default pref = 100kN/m2)

[kN/m2]

K nc0 : K0-value for normal consolidation (default K nc

0 =1− sinϕ)

[-]

Parameters for strength:

c’ref : Effective cohesion [kN/m2]

ϕ’ : Effective angle of internal friction [◦]

ψ : Angle of dilatancy [◦]

Advanced parameters for strength:

c’inc : As in Mohr-Coulomb model (default c’inc = 0) [kN/m3]

Rf : Failure ratio qf / qa (default Rf = 0.9) [-]

σtension : Tensile strength (default σtension = 0 stress units) [kN/m2]

Parameters for small strain stiffness:

γ0.7 : shear strain at which Gs = 0.722G0 [-]

Gref0 : reference shear modulus at very small strains

(ε < 10−6)[kN/m2]

Hysteretic damping

The elastic modulus ratio is plotted as a function of the shear strain (γ) in a side panewhen specifying the small-strain stiffness parameters (Modulus reduction curve). The HSsmall model shows typical hysteretic behaviour when subjected to cyclic shear loading. Indynamic calculations this leads to hysteretic damping. The damping ratio is plotted as afunction of the cyclic shear strain γc . Details are given in Brinkgreve, Kappert & Bonnier(2007).

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Figure 4.11 Effect of small strain stiffness parameters on dumping

Hint: Note that the Modulus reduction curve and the Damping curve are based onfully elastic behaviour. Plastic strains as a result of hardening or local failuremay lead to significant lower stiffness and higher damping.

Soft Soil model (SS): The Parameters tabsheet for the Soft Soil model is shown inFigure 4.12.

Hint: Optional drainage types when Soft Soil model is selected are: Drained andUndrained (A).

» In the case of Undrained (A) drainage type, the same parameters are usedas for drained behaviour.

The parameters for stiffness are:

λ∗ : Modified compression index [-]

κ∗ : Modified swelling index [-]

Alternative parameters can be used to define stiffness:

Cc : Compression index [-]

Cs : Swelling index or reloading index [-]

einit : Initial void ratio [-]

The parameters for strength are:

c’ref : Effective cohesion [kN/m2]

ϕ’ : Effective friction angle [◦]

ψ : Dilatancy angle [◦]

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Figure 4.12 Parameters tabsheet for the Soft Soil model (drained behaviour)

Advanced parameters (use default settings):

νur : Poisson’s ratio for unloading / reloading (defaultνur = 0.15)

[-]

K nc0 : Coefficient of lateral stress in normal consolidation

(default K nc0 = 1− sinϕ)

[-]

M : K nc0 — related parameter [-]

Soft Soil Creep model (SSC): The Parameters tabsheet for the Soft Soil Creep modelis shown in Figure 4.13.

Hint: Optional drainage types when Soft Soil Creep model is selected are: Drainedand Undrained (A).

» In the case of Undrained (A) drainage type, the same parameters are usedas for drained behaviour.

The parameters for stiffness are:

λ∗ : Modified compression index [-]

κ∗ : Modified swelling index [-]

The parameter taking time effect into account is:

µ∗ : Modified creep index [-]

Alternative parameters can be used to define stiffness:

Cc : Compression index [-]

Cs : Swelling index or reloading index [-]

Cα : Secondary compression index [-]

einit : Initial void ratio [-]

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Figure 4.13 Parameters tabsheet for the Soft Soil Creep model (drained behaviour)

The parameters for strength are:

c’ref : Cohesion [kN/m2]

ϕ’ : Friction angle [◦]

ψ : Dilatancy angle [◦]

Advanced parameters (use default settings):

νur : Poisson’s ratio for unloading / reloading (defaultνur = 0.15)

[-]

K nc0 : Coefficient of lateral stress in normal consolidation

(default K nc0 = 1− sinϕ)

[-]

M : K nc0 — related parameter [-]

Jointed Rock model (JR): The Parameters tabsheet for the Jointed Rock model isshown in Figure 4.14.

Hint: Optional drainage types when Jointed Rock model is selected are: Drainedand Non-porous.

» In the case of Non-porous drainage type, the same parameters are used asfor drained behaviour.

Parameters for stiffness:

E1 : Young’s modulus for rock as a continuum [kN/m2]

ν1 : Poisson’s ratio for rock as a continuum [-]

Anisotropic elastic parameters ‘Plane 1’ direction (e.g. stratification direction):

E2 : Young’s modulus in ‘Plane 1’ direction [kN/m2]

G2 : Shear modulus in ‘Plane 1’ direction [kN/m2]

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Figure 4.14 Parameters tabsheet for the Jointed Rock model (drained behaviour)

ν2 : Poisson’s ratio in ‘Plane 1’ direction [-]

Parameters for strength:

Strength parameters in joint directions (Plane i=1, 2, 3):

ci : Cohesion [kN/m2]

ϕi : Friction angle [◦]

ψi : Dilatancy angle [◦]

σt ,i : Tensile strength [kN/m2]

Definition of joint directions (Plane i=1, 2, 3):

n : Number of joint directions (1 ≤ n ≤ 3) [-]

α1,i : Dip angle [◦]

α2,i : Dip direction [◦]

Modified Cam-Clay model (MCC): This is a critical state model that can be used tosimulate the behaviour of normally consolidated soft soils. The model assumes alogarithmic relationship between the volumetric strain and the mean effective stress. TheParameters tabsheet for the Modified Cam-Clay model is shown in Figure 4.15.

Hint: Optional drainage types when Modified Cam-Clay model is selected are:Drained and Undrained (A).

» In the case of Undrained (A) drainage type, the same parameters are usedas for drained behaviour.

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Figure 4.15 Parameters tabsheet for the Modified Cam-Clay model (drained behaviour)

Parameters for stiffness:

λ : Cam-Clay compression index [-]

κ : Cam-Clay swelling index [-]

ν : Poisson’s ratio [-]

einit : Initial void ratio for loading/unloading [-]

Parameters for strength:

M : Tangent of the critical state line [-]

K nc0 : Coefficient of lateral stress in normal consolidation

derived from M . The relationship between M and K nc0

is given in Section 9.7 of the Material Models Manual

[-]

NGI-ADP model (NGI-ADP): The NGI-ADP model may be used for capacity,deformation and soil-structure interaction analysis involving undrained loading of clay.The Parameters tabsheet for the NGI-ADP model is shown in Figure 4.16.

Hint: Optional drainage types when NGI-ADP model is selected are: Drained,Undrained (B) and Undrained (C).

» In the case of Undrained (B) drainage type, the same parameters are usedas for drained behaviour.

Parameters for stiffness:

Gur/sAu : Ratio unloading/reloading shear modulus over (plane

strain) active shear strength[-]

γCf : Shear strain in triaxial compression (|γC