plaxis tutorial manual

PLAXIS 3D

Tutorial Manual

2013

Build 6448

TABLE OF CONTENTS

TABLE OF CONTENTS

1 Foundation in overconsolidated clay 71.1 Case A: Rigid foundation 81.2 Case B: Raft foundation 201.3 Case C: Pile-Raft foundation 27

2 Excavation in sand 332.1 Geometry 342.2 Mesh generation 392.3 Performing calculations 392.4 Viewing the results 42

3 Loading of a suction pile 473.1 Geometry 473.2 Mesh generation 503.3 Performing calculations 513.4 Viewing the results 52

4 Construction of a road embankment 534.1 Geometry 534.2 Mesh generation 574.3 Performing calculations 584.4 Viewing the results 614.5 Safety analysis 644.6 Using drains 67

5 Phased excavation of a shield tunnel 695.1 Geometry 695.2 Mesh generation 785.3 Performing calculations 795.4 Viewing the results 86

6 Rapid drawdown analysis 876.1 Geometry 876.2 Mesh generation 896.3 Performing calculations 906.4 Viewing the results 95

7 Dynamic analysis of a generator on an elastic foundation 977.1 Geometry 977.2 Mesh generation 1007.3 Performing calculations 1017.4 Viewing the results 104

8 Free vibration and earthquake analysis of a building 1078.1 Geometry 1078.2 Mesh generation 1138.3 Performing calculations 1138.4 Viewing the results 115

PLAXIS 3D 2013 | Tutorial Manual 3

TUTORIAL MANUAL

Appendix A - Menu tree 119

Appendix B - Calculation scheme for initial stresses due to soil weight 123

4 Tutorial Manual | PLAXIS 3D 2013

INTRODUCTION

INTRODUCTION

PLAXIS is a finite element package that has been developed specifically for the analysisof deformation and stability in geotechnical engineering projects. The simple graphicalinput procedures enable a quick generation of complex finite element models, and theenhanced output facilities provide a detailed presentation of computational results. Thecalculation itself is fully automated and based on robust numerical procedures. Thisconcept enables new users to work with the package after only a few hours of training.

Though the various tutorials deal with a wide range of interesting practical applications,this Tutorial Manual is intended to help new users become familiar with PLAXIS 3D. Thetutorials should therefore not be used as a basis for practical projects.

Users are expected to have a basic understanding of soil mechanics and should be ableto work in a Windows environment. It is strongly recommended that the tutorials arefollowed in the order that they appear in the manual.

The Tutorial Manual does not provide theoretical background information on the finiteelement method, nor does it explain the details of the various soil models available in theprogram. The latter can be found in the Material Models Manual, as included in the fullmanual, and theoretical background is given in the Scientific Manual. For detailedinformation on the available program features, the user is referred to the ReferenceManual. In addition to the full set of manuals, short courses are organised on a regularbasis at several places in the world to provide hands-on experience and backgroundinformation on the use of the program.


TUTORIAL MANUAL


FOUNDATION IN OVERCONSOLIDATED CLAY

1 FOUNDATION IN OVERCONSOLIDATED CLAY

In this chapter a first application of PLAXIS 3D is considered, namely the settlement of afoundation in clay. This is the first step in becoming familiar with the practical use of theprogram.

The general procedures for the creation of a geometry, the generation of a finite elementmesh, the execution of a finite element calculation and the evaluation of the output resultsare described here in detail. The information provided in this tutorial will be utilised in thefollowing tutorials. Therefore, it is important to complete this first tutorial beforeattempting any further tutorial examples.

18.0 m

75.0 m

75.0 mBuilding

Clay

x

x

y

z

z = 0z = -2

z = -40

40.0 m

Figure 1.1 Geometry of a square building on a raft foundation

GEOMETRY

This exercise deals with the construction and loading of a foundation of a square buildingin a lightly overconsolidated lacustrine clay. Below the clay layer there is a stiff rock layerthat forms a natural boundary for the considered geometry. The rock layer is not includedin the geometry; instead an appropriate boundary condition is applied at the bottom of theclay layer. The purpose of the exercise is to find the settlement of the foundation.

The building consists of a basement level and 5 floors above the ground level (Figure1.1). To reduce calculation time, only one-quarter of the building is modelled, usingsymmetry boundary conditions along the lines of symmetry. To enable any possible


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mechanism in the clay and to avoid any influence of the outer boundary, the model isextended in both horizontal directions to a total width of 75 m.

The model is considered in three different cases:

Case A: The building is considered very stiff and rough. The basement is simulated bymeans of non-porous linear elastic volume elements.

Case B: The structural forces are modelled as loads on a raft foundation.

Case C: Embedded piles are included in the model to reduce settlements.

1.1 CASE A: RIGID FOUNDATION

In this case, the building is considered to be very stiff. The basement is simulated byterms of non-porous linear elastic volume elements. The total weight of the basementcorresponds to the total permanent and variable load of the building. This approach leadsto a very simple model and is therefore used as a first exercise, but it has somedisadvantages. For example it does not give any information about the structural forces inthe foundation.

Objectives:

Starting a new project.

Creation of soil stratigraphy using a single borehole.

Creation of material data sets.

Creation of volumes using Create surface and Extrude tools.

Assigning material.

Local mesh refinement.

Generation of mesh.

Generating initial stresses using the K0 procedure.

Defining a Plastic calculation.

1.1.1 GEOMETRY INPUT

Start the PLAXIS 3D program. The Quick select dialog box will appear in which youcan select an existing project or create a new one (Figure 1.2).

Click Start a new project. The Project properties window appears, consisting ofProject and Model tabsheets.

Project properties

The first step in every analysis is to set the basic parameters of the finite element model.This is done in the Project properties window. These properties include the description ofthe problem, the basic units and the size of the draw area.



Figure 1.2 Quick select dialog box

To enter the appropriate properties for the foundation calculation follow these steps:

In the Project tabsheet, enter "Tutorial 1" as the Title of the project and type"Settlements of a foundation" in the Comments box (Figure 1.3).

Figure 1.3 Project tabsheet of the Project properties window

Proceed to the Model tabsheet by clicking either the Next button or the Model tab(Figure 1.4).

Keep the default units in the Units box (Length = m; Force = kN; Time = day ).

The General box indicates a fixed gravity of 1.0 G, in the vertical direction downward(-z). The value of the acceleration of gravity (1.0 G) can be specified in the Earthgravity box. This should be kept to the default value of 9.810 m/s2 for this exercise.In the water box the unit weight of water can be defined. Keep this to the defaultvalue of 10 kN/m3.

Define the limits for the soil contour as xmin = 0, xmax = 75, ymin = 0 and ymax = 75 inthe Contour group box.

Click the OK button to confirm the settings.

Hint: In case of a mistake or for any other reason that the project properties needto be changed, you can access the Project properties window by selectingthe corresponding option in the File menu.


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Figure 1.4 Model tabsheet of the Project properties window

Definition of soil stratigraphy

When you click the OK button the Project properties window will close and the Soil modeview will be shown. Information on the soil layers is entered in boreholes.

Boreholes are locations in the draw area at which the information on the position of soillayers and the water table is given. If multiple boreholes are defined, PLAXIS 3D willautomatically interpolate between the boreholes, and derive the position of the soil layersfrom the borehole information.

Hint: PLAXIS 3D can also deal with layers that are discontinuous, i.e. only locallypresent in the model area. See Section 4.2.2 of the Reference Manual formore information.

In the current example, only one soil layer is present, and only a single borehole isneeded to define the soil stratigraphy. In order to define the borehole, follow these steps:

Click the Create borehole button in the side toolbar to start defining the soilstratigraphy. Click on position (0 0 0) in the geometry. A borehole will be located at(x , y ) = (0 0). The Modify soil layers window will appear.

In the Modify soil layers window add a soil layer by clicking on the Add button. Keepthe top boundary of the soil layer at z = 0 and set the bottom boundary to z = 40m.

Set the Head value in the borehole column to 2 m (Figure 1.5).The creation of material data sets and their assignment to soil layers is described in thefollowing section.

1.1.2 MATERIAL DATA SETS

In order to simulate the behaviour of the soil, a suitable material model and appropriatematerial parameters must be assigned to the geometry. In PLAXIS soil properties arecollected in material data sets and the various data sets are stored in a materialdatabase. From the database, a data set can be assigned to one or more clusters. Forstructures (like beams, plates, etc.) the system is similar, but different types of structures



Figure 1.5 Modify soil layers window

have different parameters and therefore different types of data sets.

PLAXIS 3D distinguishes between material data sets for Soils and interfaces, Plates,Geogrids, Beams, Embedded Piles and Anchors. Before the mesh can be generatedmaterial data sets have to be assigned to all soil volumes and structures.

Open the Material sets window by clicking the Materials button in the Modify soillayers window.

Hint: In the case that the Modify soil layers window was closed by mistake, it canbe re-opened by double-clicking the borehole in the draw area or by selectingthe Modify soil layers option from the Soil menu.

Click the New button in the lower part of the Material sets window. The Soil windowwill appear. It contains five tabsheets: General, Parameters, Flow parameters,Interfaces and Initial.

In the Material set box of the General tabsheet (Figure 1.6), write "Lacustrine Clay"in the Identification box.

Select Mohr-Coulomb as the material model from the Material model drop-downmenu and Drained from the Drainage type drop-down menu.

Enter the unit weights in the General properties box according to the material dataas listed in Table 1.1. Keep the unmentioned Advanced parameters as their defaultvalues.

Click the Next button or click the Parameters tab to proceed with the input of modelparameters. The parameters appearing on the Parameters tabsheet depend on theselected material model (in this case the Mohr-Coulomb model). The Mohr-Coulomb


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Figure 1.6 General tabsheet of the Soil and interfaces data set window

Table 1.1 Material properties

Parameter Name Lacustrine clay Building Unit

General

Material model Model Mohr-Coulomb Linear elastic Drainage type Type Drained Non-porous Unit weight above phreatic level unsat 17.0 50 kN/m3

Unit weight below phreatic level sat 18.0 kN/m3Parameters

Young's modulus (constant) E ' 1 104 3 107 kN/m2Poisson's ratio ' 0.3 0.15 Cohesion (constant) c'ref 10 kN/m2Friction angle ' 30.0 Dilatancy angle 0.0 Initial

K0 determination Automatic Automatic Lateral earth pressure coefficient K0 0.5000 1.000

model involves only five basic parameters (E ', ', c',','). See the Material ModelsManual for a detailed description of the different soil models and their correspondingparameters.

Enter the model parameters E ', ', c'ref , ' and of Lacustrine clay according toTable 1.1 in the corresponding boxes of the Parameters tabsheet (Figure 1.7).



Figure 1.7 Parameters tabsheet of the Soil and interfaces data set window

No consolidation will be considered in this exercise. As a result, the permeability ofthe soil will not influence the results and the Flow parameters window can beskipped.

Since the geometry model does not include interfaces, the Interfaces tab can beskipped.

Click the Initial tab and check that the K0 determination is set to Automatic. In thatcase K0 is determined from Jaky's formula: K0 = 1 sin.

Click the OK button to confirm the input of the current material data set. The createddata set appears in the tree view of the Material sets window.

Drag the set Lacustrine clay from the Material sets window (select it and hold downthe left mouse button while moving) to the graph of the soil column on the left handside of the Modify soil layers window and drop it there (release the left mousebutton).

Hint: Notice that the cursor changes shape to indicate whether or not it is possibleto drop the data set. Correct assignment of the data set to the soil layer isindicated by a change in the colour of the layer.

The building is modelled by a linear elastic non-porous material. To define this data set,follow these steps:

Click the New button in the Material sets window.

In the Material set box of the General tabsheet, write "Building" in the Identificationbox.

Select Linear elastic as the material model from the Material model drop-downmenu and Non-porous from the Drainage type drop-down menu.


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Enter the unit weight in the General properties box according to the material data setas listed in Table 1.1. This unit weight corresponds to the total permanent andvariable load of the building.

Click the Next button or click the Parameters tab to proceed with the input of themodel parameters. The linear elastic model involves only two basic parameters (E ', ').

Enter the model parameters of Table 1.1 in the corresponding edit boxes of theParameters tabsheet.

Click the OK button to confirm the input of the current material data set. The createddata set will appear in the tree view of the Material sets window, but it is not directlyused.

Click the OK button to close the Material sets window.

Click the OK button to close the Modify soil layers window.

Hint: PLAXIS 3D distinguishes between a project database and a global databaseof material sets. Data sets may be exchanged from one project to anotherusing the global database. The global database can be shown in the Materialsets window by clicking the Show global button. The data sets of all tutorialsin the Tutorial Manual are stored in the global database during the installationof the program.

1.1.3 DEFINITION OF STRUCTURAL ELEMENTS

The structural elements are created in the Structures mode of the program. Click theStructures button to proceed with the input of structural elements. To model the building:

Click the Create surface button. Position the cursor at the coordinate (0 0 0). Checkthe cursor position displayed in the cursor position indicator. As you click, the firstsurface point of the surface is defined.

Define three other points with coordinates (0 18 0), (18 18 0), (18 0 0) respectively.Press the right mouse button or to finalize the definition of the surface. Notethat the created surface is still selected and displayed in red.

Click the Extrude object button to create a volume from the surface.

Change the z value to -2 in the Extrude window (Figure 1.8). Click the Apply buttonto close the window.

Click the Select button. Select the created surface using the right mouse button.Select Delete from the appearing menu. This will delete the surface but the buildingvolume is retained.

The building volume, as well as the corresponding material data sets have now beencreated.



Figure 1.8 Extrude window

1.1.4 MESH GENERATION

The model is complete. In order to proceed to the Mesh mode click the Mesh tab.PLAXIS 3D allows for a fully automatic mesh generation procedure, in which thegeometry is divided into volume elements and compatible structure elements, ifapplicable. The mesh generation takes full account of the position of the geometryentities in the geometry model, so that the exact position of layers, loads and structures isaccounted for in the finite element mesh. A local refinement will be considered in thebuilding volume. To generate the mesh, follow these steps:

Click the Refine mesh button in the side toolbar and click the created buildingvolume to refine the mesh locally. It will colour green.

Figure 1.9 The indication of the local refinement in the model

Click the Generate mesh button in the side toolbar or select the Generate meshoption in the Mesh menu. Change the Element distribution to Coarse in the Meshoptions window (Figure 1.10) and click OK to start the mesh generation.

As the mesh is generated, click the View mesh button. A new window is openeddisplaying the generated mesh (Figure 1.11).

Click the Close button to go back to the Mesh mode of the Input program.


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Figure 1.10 Mesh options window

Figure 1.11 Generated mesh in the Output window

Hint: By default, the Element distribution is set to Medium. The Elementdistribution setting can be changed in the Mesh options window. In addition,options are available to refine the mesh globally or locally (Section 7.1 ofReference Manual).

The finite element mesh has to be regenerated if the geometry is modified. The automatically generated mesh may not be perfectly suitable for the

intended calculation. Therefore it is recommended that the user inspects themesh and makes refinements if necessary.

1.1.5 PERFORMING CALCULATIONS

Once the mesh has been generated, the finite element model is complete. Click Stagedconstruction to proceed with the definition of calculation phases.

Initial conditions

The 'Initial phase' always involves the generation of initial conditions. In general, the initialconditions comprise the initial geometry configuration and the initial stress state, i.e.effective stresses, pore pressures and state parameters, if applicable. The initial waterlevel has been entered already in the Modify soil layers window. This level is taken intoaccount to calculate the initial effective stress state. It is therefore not needed to enter theWater levels mode.



When a new project has been defined, a first calculation phase named "Initial phase", isautomatically created and selected in the Phases explorer (Figure 1.12). All structuralelements and loads that are present in the geometry are initially automatically switchedoff; only the soil volumes are initially active.

Figure 1.12 Phases explorer

In this tutorial lesson the properties of the Initial phase will be described. This part of thetutorial gives an overview of the options to be defined even though the default values ofthe parameters are used.

The Phases window (Figure 1.13) is displayed by clicking the Edit phase button orby double clicking on the phase in the Phases explorer.

Figure 1.13 The Phases window for Initial phase

By default the K0 procedure is selected as Calculation type in the General subtreeof the Phases window. This option will be used in this project to generate the initialstresses.

The Staged construction option is selected as the Loading type. This is the onlyoption available for the K0 procedure.

The Phreatic option is selected by default as the Pore pressure calculation type.

The other default options in the Phases window will be used as well in this tutorial.Click OK to close the Phases window.

In the Model explorer extend the Model conditions subtree.

Extend the Water subtree. The water level generated according to the Head valueassigned to boreholes in the Modify soil layers window (BoreholeWaterLevel_1) isautomatically assigned to GlobalWaterLevel.

Make sure that all the soil volumes in the project are active and the materialassigned to them is Lacustrine clay.


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Hint: The K0 procedure may only be used for horizontally layered geometries witha horizontal ground surface and, if applicable, a horizontal phreatic level.See Section 7.3 of the Reference Manual for more information on the K0procedure.

Construction stage

After the definition of the initial conditions, the construction of the building can bemodelled. This will be done in a separate calculation phase, which needs to be added asfollows:

Click the Add button in the Phases explorer. A new phase, named Phase_1 will beadded in the Phases explorer.

Double-click Phase_1 to open the Phases window.

In the ID box of the General subtree, write (optionally) an appropriate name for thenew phase (for example "Building").

The current phase starts from Initial phase, which contains the initial stress state.The default options and values assigned are valid for this phase (Figure 1.14).

Figure 1.14 The Phases window for Building phase

Click OK to close the Phases window.

Right-click the building volume as created in Section 1.1.3. From the Set materialoption in the appearing menu select the Building option. The 'Building' data set hasnow been assigned to the building volume.

Hint: Calculation phases may be added, inserted or deleted using the Add, Insertand Delete buttons in the Phases explorer or in the Phases window.

Execution of calculation

All calculation phases (two phases in this case) are marked for calculation (indicated by ablue arrow). The execution order is controlled by the Start from phase parameter.



Click the Calculate button to start the calculation process. Ignore the warning thatno nodes and stress points have been selected for curves. During the execution of acalculation, a window appears which gives information about the progress of theactual calculation phase (Figure 1.15).

Figure 1.15 Active task window displaying the calculation progress

The information, which is continuously updated, shows, amongst others, the calculationprogress, the current step number, the global error in the current iteration and the numberof plastic points in the current calculation step. It will take a few seconds to perform thecalculation. When a calculation ends, the window is closed and focus is returned to themain window.

The phase list in the Phases explorer is updated. A successfully calculated phase isindicated by a check mark inside a green circle.

Save the project before viewing results.

Viewing calculation results

Once the calculation has been completed, the results can be displayed in the Outputprogram. In the Output program, the displacement and stresses in the full threedimensional model as well as in cross sections or structural elements can be viewed.The computational results are also available in tabular form. To view the current results,follow these steps:

Select the last calculation phase (Building) in the Phases explorer tree.

Click the View calculation results button in the side toolbar to open the Outputprogram. The Output program will, by default, show the three dimensional deformedmesh at the end of the selected calculation phase. The deformations are scaled toensure that they are clearly visible.


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Select Total Displacements |u| from the Deformations menu. The plot showscolour shadings of the total displacements (Figure 1.16).

A legend is presented with the displacement values at the colour boundaries. Whenthe legend is not present, select the Legend option from the View menu to display it.

In the Output window click the Iso surfaces button to display the areas having thesame displacement.

Figure 1.16 Shadings of Total displacements at the end of the last phase

Hint: In addition to the Total displacements, the Deformations menu allows for thepresentation of Incremental displacements and Phase displacements.

The incremental displacements are the displacements that occurred in onecalculation step (in this case the final step). Incremental displacements maybe helpful in visualising failure mechanisms.

Phase displacements are the displacements that occurred in one calculationphase (in this case the last phase). Phase displacements can be used toinspect the impact of a single construction phase, without the need to resetdisplacements to zero before starting the phase.

1.2 CASE B: RAFT FOUNDATION

In this case, the model is modified so that the basement consists of structural elements.This allows for the calculation of structural forces in the foundation. The raft foundationconsists of a 50 cm thick concrete floor stiffened by concrete beams. The walls of thebasement consist of 30 cm thick concrete. The loads of the upper floors are transferredto the floor slab by a column and by the basement walls. The column bears a load of



11650 kN and the walls carry a line load of 385 kN/m, as sketched in Figure 1.17.

12.0 m12.0 m

6.0 m6.0 m

385 kN/m385 kN/m

11650 kN

5.3 kN/m2

Figure 1.17 Geometry of the basement

In addition, the floor slab is loaded by a distributed load of 5.3 kN/m2. The properties ofthe clay layer will be modified such that stiffness of the clay will increase with depth.

Objectives:

Saving project under a different name.

Modifying existing data sets.

Defining a soil stiffness that increases with depth.

Modelling of plates and defining material data set for plates.

Modelling of beams and defining material data set for beams.

Assigning point loads.

Assigning line loads.

Assigning distributed loads to surfaces.

Deleting phases.

Activation and deactivation of soil volumes.

Activation and deactivation of structural elements.

Activation of loads.

Zooming in Output.

Drawing cross sections in Output.

Viewing structural output.

Geometry input

The geometry used in this exercise is the same as the previous one, except thatadditional elements are used to model the foundation. It is not necessary to create a newmodel; you can start from the previous model, store it under a different name and modifyit. To perform this, follow these steps:

Start the PLAXIS 3D program. The Quick select dialog box will appear in which theproject of case A should be selected.

Select the Save project as option in the File menu to save the project under a


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different name (e.g. "Tutorial 1b").

The material set for the clay layer has already been defined. To modify this material set totake into account the stiffness of the soil increasing with depth, follow these steps:

Open the Material sets window by clicking the Show materials button.

Make sure that the option Soil and interfaces is selected as Set type.

Select the Lacustrine clay material set and click the Edit button.

In the Parameters tabsheet, change the stiffness of the soil E ' to 5000 kN/m2.

Enter a value of 500 in the E 'inc box in the Advanced parameters. Keep the defaultvalue of 0.0 m for zref . Now the stiffness of the soil is defined as 5000 kN/m2 atz = 0.0 m and increases with 500 kN/m2 per meter depth.

Click OK to close the Soil window.

Click OK to close the Material sets window.

Definition of structural elements

Proceed to the Structures mode to define the structural elements that compose thebasement.

Click the Selection button.

Right-click the volume representing the building. Select the Decompose intosurfaces option from the appearing menu.

Delete the top surface by selecting it and pressing the key.

Select the volume representing the building. Click the visualisation toggle in theSelection explorer to hide the volume.

Right-click the bottom surface of the building. Select the Create plate option fromthe appearing menu.

Assign plates to the two vertical basement surfaces that are inside the model.Delete the remaining two vertical surfaces at the model boundaries.

Hint: Multiple entities can be selected by holding the button pressed whileclicking on the entities.

A feature can be assigned to multiple similar objects the same way as to asingle selection.

Open the material data base and set the Set type to Plates.

Create data sets for the basement floor and for the basement walls according toTable 1.2.

Drag and drop the data sets to the basement floor and the basement wallsaccordingly. It may be needed to move the Material sets window by clicking at itsheader and dragging it.




Figure 1.18 Location of plates in the project

Table 1.2 Material properties of the basement floor and basement walls

Parameter Name Basement floor Basement wall Unit

Thickness d 0.5 0.3 mWeight 15 15.5 kN/m3

Type of behaviour Type Linear, isotropic Linear, isotropic Young's modulus E1 3 107 3 107 kN/m2Poisson's ratio 12 0.15 0.15

Hint: When specifying a unit weight, please consider the fact that the element itselfdoes not occupy any volume and overlaps with the soil elements. Hence, itmight be considered to subtract the unit soil weight from the real unit weightof the plate, beam or embedded pile material in order to compensate for theoverlap. For partially overlapping plates, beams or embedded piles thereduction of the unit weight should be proportional.

Right-click the bottom of the surface of the building volume and select the Createsurface load option from the appearing menu. The actual value of the load can beassigned in the Structures mode as well as when the calculation phases will bedefined (Phase definition mode). In this example, the value will be assigned in thePhase definition modes.

Click the Create line button in the side toolbar.

Select the Create line load option from the additional tools displayed.

Click the command input area, type "0 18 0 18 18 0 18 0 0 " and press .Line loads will now be defined on the basement walls. The defined values are thecoordinates of the three points of the lines. Click the right mouse button to stopdrawing line loads.

Click the Create line button in the side toolbar.

Select the Create beam option from the additional tools displayed.

Click on (6 6 0) to create the first point of a vertical beam. Keep the keypressed and move the mouse cursor to (6 6 -2). Note that while the key ispressed the cursor will move only vertically. As it can be seen in the cursor positionindicator, the z coordinate changes, while x and y coordinates will remain the same.Click on (6 6 -2) to define the second point of the beam. To stop drawing click the


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right mouse button.

Create horizontal beams from (0 6 -2) to (18 6 -2) and from (6 0 -2) to (6 18 -2).

Hint: By default, the cursor is located at z=0. To move in the vertical direction,keep the key pressed while moving the mouse.

Open the material data base and set the Set type to Beams.

Create data sets for the horizontal and for the vertical beams according to Table 1.3.Assign the data set to the corresponding beam elements by drag and drop.

Table 1.3 Material properties of the basement column and basement beams

Parameter Name Basement column Basement beam Unit

Cross section area A 0.49 0.7 m2

Volumetric weight 24.0 6.0 kN/m3

Type of behaviour Type Linear Linear Young's modulus E 3 107 3 107 kN/m2Moment of Inertia I3 0.020 0.058 m4

I2 0.020 0.029 m4

Click the Create load button in the side toolbar.

Select the Create point load option from the additional tools displayed. Click at (6 60) to add a point load at the top of the vertical beam.

Proceed to the Mesh tabsheet to generate the mesh.

Mesh generation

Click the Generate mesh. Keep the Element distribution as Coarse.

Inspect the generated mesh.

As the geometry has changed, all calculation phases have to be redefined.

1.2.1 PERFORMING CALCULATIONS

Proceed to the Staged construction mode.

Initial conditions

As in the previous example, the K0 procedure will be used to generate the initialconditions.

All the structural elements should be inactive in the Initial Phase.

No excavation is performed in the Initial Phase. So, the basement volume should beactive and the material assigned to it should be Lacustrine clay.

Construction stages

Instead of constructing the building in one calculation stage, separate calculation phaseswill be used. In Phase 1, the construction of the walls and the excavation is modelled. InPhase 2, the construction of the floor and beams is modelled. The activation of the loads



is modelled in the last phase (Phase 3).

The calculation type for the phases representing the construction stages is set bydefault to Plastic.

Rename the Phase_1 to "Excavation".

Deactivate the soil volume located over the foundation by selecting it and by clickingon the checkbox in front of it in the Selection explorer.

In the Model explorer click the checkbox in front of the plates corresponding to thebasement walls to activate them.

In the Phases explorer click the Add phase button. A new phase (Phase_2) isadded. Double-click Phase_2. The Phases window pops up.

Rename the phase by defining its ID as "Construction". Keep the default settings ofthe phase and close the Phases window.

In the Model explorer click the checkbox in front of the plate corresponding to thebasement floor to activate it.

In the Model explorer click the checkbox in front of the beams to activate all thebeams in the project.

Add a new phase following the Construction phase. Rename it to "Loading".

In the Model explorer click the checkbox in front of the Surface loads to activate thesurface load on the basement floor. Set the value of the zcomponent of the load to5.3. This indicates a load of 5.3 kN/m2, acting in the negative zdirection.

In the Model explorer, click the checkbox in front of Line loads to activate the lineloads on the basement walls. Set the value of the zcomponent of each load to385. This indicates a load of 385 kN/m, acting in the negative zdirection.

In the Model explorer click the checkbox in front of Point loads to activate the pointload on the basement column. Set the value of the zcomponent of the load to11650. This indicates a load of 11650 kN, acting in the negative zdirection.Click the Preview phase button to check the settings for each phase.

As the calculation phases are completely defined, calculate the project. Ignore thewarning that no nodes and stress points have been selected for curves.

Save the project after the calculation.

Viewing calculation results

Select Construction option in the Phases explorer.

Click the View calculation results button to open the Output program. The deformedmesh at the end of this phase is shown.

Select the last phase in the Displayed step drop-down menu to switch to the resultsat the end of the last phase.

In order to evaluate stresses and deformations inside the geometry, select theVertical cross section tool. A top view of the geometry is presented and the Crosssection points window appears. As the largest displacements appear under thecolumn, a cross section here is most interesting.


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Enter (0.0 6.0) and (75.0 6.0) as the coordinates of the first point (A) and the secondpoint (A') respectively in the Cross section points window.

Click OK. A vertical cross section is presented. The cross section can be rotated inthe same way as a regular 3D view of the geometry.

Select Total displacements uz from the Deformations menu (Figure 1.19). Themaximum and minimum values of the vertical displacements are shown in thecaption. If the title is not visible, select this option from the View menu.

Figure 1.19 Cross section showing the total vertical displacement

Press and to move the cross section. Return to the three dimensional view of the geometry by selecting this window from

the list in the Window menu.

Double-click the floor. A separate window will appear showing the displacements ofthe floor. To look at the bending moments in the floor, select M11 from the Forcesmenu.

Click the Shadings button. The plot in Figure 1.20 will be displayed.

To view the bending moments in tabulated form, click the Table option in the Toolsmenu. A new window is opened in which a table is presented, showing the values ofbending moments in each node of the floor.



Figure 1.20 Bending moments in the basement floor

1.3 CASE C: PILE-RAFT FOUNDATION

As the displacements of the raft foundation are rather high, embedded piles will be usedto decrease these displacements. These embedded piles represent bored piles with alength of 20 m and a diameter of 1.5 m.

Objectives:

Using embedded piles.

Defining material data set for embedded piles.

Creating multiple copies of entities.

Geometry input

The geometry used in this exercise is the same as the previous one, except for the pilefoundation. It is not necessary to create a new model; you can start from the previousmodel, store it under a different name and modify it. To perform this, follow these steps:

Start the PLAXIS 3D program. The Quick select dialog box will appear in which theproject of Case B should be selected.

Select the Save project as option in the File menu to save the project under adifferent name (e.g. "Tutorial 1c").

Definition of embedded pile

Proceed to the Structures mode.

Click the Create line button at the side tool bar and select the Create embedded pilefrom the additional tools that appear.


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Define a pile from (6 6 -2) to (6 6 -22).

Open the material data base and set the Set type to Embedded piles.

Create a data set for the embedded pile according to Table 1.4. The value for thecross section area A and the moments of inertia I2, I3 and I23 are automaticallycalculated from the diameter of the massive circular pile. Confirm the input byclicking OK.

Table 1.4 Material properties of embedded pile

Parameter Name Pile foundation Unit

Young's modulus E 3 107 kN/m2Unit weight 6.0 kN/m3

Pile type - Predefined Predefined pile type - Massive circular pile Diameter Diameter 1.5 mSkin resistance Type Linear Maximum traction allowed at the top of theembedded pile

Ttop,max 200 kN/m

Maximum traction allowed at the bottom ofthe embedded pile

Tbot ,max 500 kN/m

Base resistance Fmax 1 104 kN

Drag and drop the Pile data to the embedded pile in the draw area. The embeddedpile will change colour to indicate that the material set has been assignedsuccessfully.


Hint: A material set can also be assigned to an embedded pile by right-clicking iteither in the draw area or in the Selection explorer and the Model explorerand selecting the material from the Set material option in the displayed menu.

Click the Select button and select the embedded pile.

Click the Create array button.

In the Create array window, select the 2D, in xy plane option for shape.

Keep the number of columns as 2. Set the distance between the columns to x = 12and y = 0.

Keep the number of rows as 2. Set the distance between the rows to x = 0 andy = 12 (Figure 1.21).

Press OK to create the array. A total of 2x2 = 4 piles will be created.

Mesh generation

As the geometry model is complete now, the mesh can be generated.

Create the mesh. Keep the Element distribution as Coarse.

View the mesh.

Click the eye button in front of the Soil subtree in the Model explorer to hide the soil.The embedded piles can be seen (Figure 1.22).



Figure 1.21 Create array window

Close the mesh preview.

Figure 1.22 Partial geometry of the model in the Output

Performing calculations

After generation of the mesh, all construction stages must be redefined. Even though inpractice the piles will be constructed in another construction stage than construction ofthe walls, for simplicity both actions will be done in the same construction stage in thistutorial. To redefine all construction stages, follow these steps:

Switch to the Staged construction mode.

Check if the K0 procedure is selected as Calculation type for the initial phase. Make


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sure that all the structural elements are inactive and all soil volumes are active. Thematerial assigned to it is Lacustrine clay.

Select the Excavation phase in the Phases explorer.

Make sure that the basement soil is excavated and the basement walls are active.

Activate all the embedded piles.

In the Phases explorer select the Construction phase. Make sure that all thestructural elements are active.

In the Phases explorer select the Loading phase. Make sure that all the structuralelements and loads are active.

Calculate the project.

Save the project after the calculation is finished.

Select the Loading phase and view the calculation results.

Double-click the basement floor. Select the M11 option from the Forces menu. Theresults are shown in Figure 1.23.

Figure 1.23 Bending moments in the basement floor

Select the view corresponding to the deformed mesh in the Window menu.

Click the Hide soil button in the side toolbar.

To view the embedded piles press and keep it pressed while clicking on thesoil volume in order to hide it.

Click the Select structures button. To view all the embedded piles, press+ keys and double click on one of the piles.

Select the option N in the Forces menu to view the axial loads in the embeddedpiles. The plot is shown in Figure 1.24.



Figure 1.24 Resulting axial forces (N) in the embedded piles


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EXCAVATION IN SAND

2 EXCAVATION IN SAND

This tutorial describes the construction of an excavation pit in soft clay and sand layers.The pit is a relatively small excavation of 12 by 20 m, excavated to a depth of 6.5 m belowthe surface. Struts, walings and ground anchors are used to prevent the pit to collapse.After the full excavation, an additional surface load is added on one side of the pit.

50.0 m

80.0 m

(30 20) (50 20)

(30 32) (50 32)

Strut

Ground anchors

(34 19) (41 19)

(34 12) (41 12)

4.0 m

4.0 m

4.0 m

5.0 m5.0 m5.0 m5.0 m

Figure 2.1 Top view of the excavation pit

The proposed geometry for this exercise is 80 m wide and 50 m long, as shown in Figure2.1. The excavation pit is placed in the center of the geometry. Figure 2.2 shows a crosssection of the excavation pit with the soil layers. The clay layer is considered to beimpermeable.

Objectives:

Using the Hardening Soil model

Modelling of ground anchors

Using interface features

Defining over-consolidation ratio (OCR)

Prestressing a ground anchor

Changing water conditions

Selection of stress points to generate stress/strain curves

Viewing plastic points


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z = 0z = -1

z = -4

z = -9.5

z = -11

z = -20

Fill

Sand

Sand

Soft clay

Sheet pile walls

(62 24 -9)(18 24 -9)

Figure 2.2 Cross section of the excavation pit with the soil layers

2.1 GEOMETRY

To create the geometry model, follow these steps:

Project properties

Start a new project.

Enter an appropriate title for the project.

Define the limits for the soil contour as xmin = 0, xmax = 80, ymin = 0 and ymax = 50.

2.1.1 DEFINITION OF SOIL STRATIGRAPHY

In order to define the soil layers, a borehole needs to be added and material propertiesmust be assigned. As all soil layers are horizontal, only a single borehole is needed.

Create a borehole at (0.0 0.0). The Modify soil layers window pops up.

Add 4 layers with bottom levels at -1, -9.5, -11, -20. Set the Head in the boreholecolumn to -4 m.

Open the Material sets window.

Create a new data set under Soil and interfaces set type.

Identify the new data set as "Fill".

From the Material model drop-down menu, select Hardening Soil model. In contrastwith the Mohr-Coulomb model, the Hardening Soil model takes into account thedifference in stiffness between virgin-loading and unloading-reloading. For adetailed description of the Hardening Soil model, see the Chapter 6 in the MaterialModels Manual.

Define the saturated and unsaturated unit weights according to Table 2.1.

In the Parameters tabsheet, enter values for E ref50 , Erefoed , E

refur , m, c'ref , 'ref , and

'ur according to Table 2.1. Note that Poisson's ratio is an advanced parameter.

As no consolidation will be considered in this exercise, the permeability of the soilwill not influence the results. Therefore, the default values can be kept in the Flowparameters tabsheet.


EXCAVATION IN SAND

Table 2.1 Material properties for the soil layers

Parameter Name Fill Sand Soft Clay Unit

General

Material model Model Hardening Soilmodel

Hardening Soilmodel

Hardening Soilmodel

Drainage type Type Drained Drained Undrained A Unit weight above phreatic level unsat 16.0 17.0 16.0 kN/m3

Unit weight below phreatic level sat 20.0 20.0 17.0 kN/m3

Parameters

Secant stiffness for CD triaxialtest

E ref50 2.2 104 4.3 104 2.0 103 kN/m2

Tangent oedometer stiffness E refoed 2.2 104 2.2 104 2.0 103 kN/m2Unloading/reloading stiffness E refur 6.6 104 1.29 105 1.0 104 kN/m2Power for stress leveldependency of stiffness

m 0.5 0.5 1.0

Cohesion c'ref 1 1 5 kN/m2

Friction angle ' 30.0 34.0 25.0

Dilatancy angle 0.0 4.0 0.0

Poisson's ratio 'ur 0.2 0.2 0.2 Interfaces

Interface strength Manual Manual Manual Interface reduction factor Rinter 0.65 0.7 0.5 Initial

K0 determination Automatic Automatic Automatic Lateral earth pressure coefficient K0 0.5000 0.4408 0.7411 Over-consolidation ratio OCR 1.0 1.0 1.5 Pre-overburden pressure POP 0.0 0.0 0.0

In the Interfaces tabsheet, select Manual in the Strength box and enter a value of0.65 for the parameter Rinter . This parameter relates the strength of the interfaces tothe strength of the soil, according to the equations:

ci = Rinter csoil and tani = Rinter tani tansoilHence, using the entered Rinter -value gives a reduced interface friction and interfacecohesion (adhesion) compared to the friction angle and the cohesion in the adjacentsoil.

Hint: When the Rigid option is selected in the Strength drop-down, the interfacehas the same strength properties as the soil (Rinter = 1.0). Note that a value of Rinter < 1.0, reduces the strength as well as the stiffnessof the interface (Section 6.1.4 of the Reference Manual).

In the Initial tabsheet, define the OCR-value according to Table 2.1.

Click OK to close the window.

In the same way, define the material properties of the "Sand" and "Soft Clay"materials as given by Table 2.1.

After closing the Material sets window, click the OK button to close the Modify soillayers window.

In the Soil mode right click on the upper soil layer. In the appearing right hand


TUTORIAL MANUAL

mouse button menu, select the Fill option in the Set material menu.

In the same way assign the Soft Clay material to the soil layer between y = 9.5 mand y = 11.0 m.

Assign the Sand material to the remaining two soil layers.

Proceed to the Structures mode to define the structural elements.

Hint: The Tension cut-off option is activated by default at a value of 0 kN/m2. Thisoption is found in the Advanced options on the Parameters tabsheet of theSoil window. Here the Tension cut-off value can be changed or the optioncan be deactivated entirely.


The creation of sheet pile walls, walings, struts and surface loads and ground anchors isdescribed below.

Create a surface between (30 20 0), (30 32 0), (50 32 0) and (50 20 0).

Extrude the surface to z = 1, z = 6.5 and z = 11. Right-click on the deepest created volume (between z = 0 and z = 11) and select

the Decompose into surfaces option from the appearing menu.

Delete the top surfaces (2 surfaces). An extra surface is created as the volume isdecomposed.

Hide the excavation volumes (do not delete). The eye button in the Model explorerand the Selection explorer trees can be used to hide parts of the model and simplifythe view. A hidden project entity is indicated by a closed eye.

Click the Create structure button.

Create beams (walings) around the excavation circumference at level z = 1m.Press the key and keep it pressed while moving the mouse cursor in the zdirection. Stop moving the mouse as the z coordinate of the mouse cursor is 1in the cursor position indicator. Note that as you release the key, the zcoordinate of the cursor location does not change. This is an indication that you candraw only on the xy -plane located at z = 1.

Click on (30 20 -1), (30 32 -1), (50 32 -1), (50 20 -1), (30 20 -1) to draw the walings.Click on the right mouse button to stop drawing walings.

Create a beam (strut) between (35 20 -1) and (35 32 -1). Press to enddefining the strut.

Create data sets for the walings and strut according to Table 2.2 and assign thematerials accordingly.

Copy the strut into a total of three struts at x = 35 (existing), x = 40, and x = 45.


EXCAVATION IN SAND

Table 2.2 Material properties for the beams

Parameter Name Strut Waling Unit

Cross section area A 0.007367 0.008682 m2

Unit weight 78.5 78.5 kN/m3

Material behaviour Type Linear Linear Young's modulus E 2.1 108 2.1 108 kN/m2Moment of Inertia I3 5.073 105 1.045 104 m4

I2 5.073 105 3.66 104 m4

Modelling ground anchors

In PLAXIS 3D ground anchors can be modelled using the Node-to-node anchor and theEmbedded pile options as described in the following:

First the ungrouted part of the anchor is created using the Node-to-node anchorfeature. Start creating a node-to-node anchor by selecting the corresponding buttonin the options displayed as you click on the Create structure button.

Click on the command line and type "30 24 -1 21 24 -7 " . Press and to create the ungrouted part of the first ground anchor.

Create a node-to-node anchor between the points (50 24 -1) and (59 24 -7).

The grouted part of the anchor is created using the Embedded pile option. Createembedded piles between (21 24 -7) and (18 24 -9) and between (59 24 -7) and (6224 -9).

Create a data set for the embedded pile and a data set for the node-to-node anchoraccording to Table 2.3 and Table 2.4 respectively. Assign the data sets to thenode-to-node anchors and to the embedded piles.

Table 2.3 Material properties for the node-to-node anchors

Parameter Name Node-to-node anchor Unit

Material type Type Elastic Axial stiffness EA 6.5105 kN

Table 2.4 Material properties for the embedded piles (grout body)

Parameter Name Grout Unit

Young's modulus E 3 107 kN/m2Unit weight 24 kN/m3

Pile type Predefined Predefined pile type Massive circular pile Diameter Diameter 0.14 mSkin friction distribution Type Linear Skin resistance at the top of theembedded pile

Ttop,max 200 kN/m

Skin resistance at the bottom of theembedded pile

Tbot ,max 0.0 kN/m

Base resistance Fmax 0.0 kN

Hint: The colour indicating the material set assigned to the entities in project canbe changed by clicking on the Colour box of the selected material set andselecting a colour from the Colour part of the window.


TUTORIAL MANUAL

The remaining grouted anchors will be created by copying the defined grouted anchor.

Click on the Select button and click on all the elements composing both of theground anchors keeping the key pressed.

Use the Create array function to copy both ground anchors (2 embedded piles + 2node-to-node anchors) into a total of 4 complete ground anchors located at y = 24and y = 28 by selection the 1D, in y direction option in the Shape drop-down menuand define the Distance between columns as 4 m.

Multi-select all parts of the ground anchors (8 entities in total). While all parts areselected and the key is pressed, click the right mouse button and select theGroup from the appearing menu.

In the Model explorer tree, expand the Groups subtree by clicking on the (+) in frontof the groups.

Click the Group_1 and rename it to "GroundAnchors".

Hint: The name of the entities in the project should not contain any space orspecial character except "_" .

To define the sheet pile walls and the corresponding interfaces, follow these steps:

Select all four vertical surfaces created as the volume was decomposed. Keepingthe key pressed, click the right mouse button and select the Create plateoption from the appearing menu.

Create a data set for the sheet pile walls (plates) according to Table 2.5. Assign thedata sets to the four walls.

As all the surfaces are selected, assign both positive and negative interfaces tothem using the options in the right mouse button menu.

Hint: The term 'positive' or 'negative' for interfaces has no physical meaning. Itonly enables distinguishing between interfaces at each side of a surface.

Table 2.5 Material properties of the sheet pile walls

Parameter Name Sheet pile wall Unit

Thickness d 0.379 mWeight 2.55 kN/m3

Type of behaviour Type Linear, non-isotropic Young's modulus E1 1.46 107 kN/m2

E2 7.3 105 kN/m2Poisson's ratio 0.0 Shear modulus G12 7.3 105 kN/m2

G13 1.27 106 kN/m2G23 3.82 105 kN/m2

Non-isotropic (different stiffnesses in two directions) sheet pile walls are defined. Thelocal axis should point in the correct direction (which defines which is the 'stiff' or the 'soft'direction). As the vertical direction is generally the stiffest direction in sheet pile walls,


EXCAVATION IN SAND

local axis 1 shall point in the zdirection.In the Model explorer tree expand the Surfaces subtree, set AxisFunction to Manualand set Axis1z to 1. Do this for all the pile wall surfaces.Create a surface load defined by the points: (34 19 0), (41 19 0), (41 12 0), (34 120). The geometry is now completely defined.

Hint: The first local axis is indicated by a red arrow, the second local axis isindicated by a green arrow and the third axis is indicated by a blue arrow.More information related to the local axes of plates is given in the ReferenceManual.

2.2 MESH GENERATION

Proceed to the Mesh mode.

Create the mesh. Set the Element distribution to Coarse.

View the mesh. Hide the soil in the model to view the embedded piles.

2.3 PERFORMING CALCULATIONS

The calculation consists of 6 phases. The initial phase consists of the generation of theinitial stresses using the K0 procedure. The next phase consists of the installation of thesheet piles and a first excavation. Then the walings and struts will be installed. In phase3, the ground anchors will be activated and prestressed. Further excavation will beperformed in the phase after that. The last phase will be the application of the additionalload next to the pit.

Click on the Staged construction tab to proceed with definition of the calculationphases.

The initial phase has already been introduced. Keep its calculation type as K0procedure. Make sure all the soil volumes are active and all the structural elementsare inactive.

Add a new phase (Phase_1). The default values of the parameters will be used forthis calculation phase.

Deactivate the first excavation volume (from z = 0 to z = 1). In the Model explorer, activate all plates and interfaces by clicking on the checkbox

in front of them. The active elements in the project are indicated by a green checkmark in the Model explorer.

Add a new phase (Phase_2). The default values of the parameters will be used forthis calculation phase.

In the Model explorer activate all the beams.

Add a new phase (Phase_3). The default values of the parameters will be used for


TUTORIAL MANUAL

this calculation phase.

In the Model explorer activate the GroundAnchors group.

Select one of the node-to-node anchors.

In the Selection explorer expand the node-to node anchor features.

Click Adjust prestress and change this into True. Enter a prestress force of 200 kN(Figure 2.3).

Do the same for all the other node-to-node anchors.

Figure 2.3 Node-to-node anchor in the Selection explorer

Add another phase (Phase_4). The default values of the parameters will be used forthis calculation phase.

Proceed to the Water levels mode.

Select the soil volume to be excavated in this phase (between z = 1 andz = 6.5).In the Selection explorer expand the soil entity and subsequently expand theWaterConditions feature. Click on the Conditions and select the Dry option from thedrop-down menu.

Figure 2.4 Water conditions in the Selection explorer

Hide the soil around the excavation.

Select the soil volume below the excavation (between z = 6.5 and z = 9.5).In Selection explorer expand the soil entity and subsequently expand theWaterConditions feature.

Click Conditions and select Head from the drop-down menu. Enter zref = 6.5 m.Select the soft clay volume below the excavation.


EXCAVATION IN SAND

Set the water conditions to Interpolate.

Proceed to Staged construction mode.

Deactivate the volume to be excavated (between z = 1 and z = 6.5).Preview this calculation phase.

Click the Vertical cross section button in the Preview window and define the crosssection by drawing a line across the excavation.

Select the psteady option from the Stresses menu.

Display the contour lines for steady pore pressure distribution. Make sure that theLegend option is checked in View menu. The steady state pore pressure distributionis displayed in Figure 2.5. Scroll the wheel button of the mouse to zoom in or out toget a better view.

Figure 2.5 Preview of the steady state pore pressures in Phase_4 in a cross section

Click on the Close button to return to the Input program.

Add another phase (Phase_5). The default values of the parameters will be used forthis calculation phase.

Activate the surface load and set z = 20kN/m2.

Defining points for curves

Before starting the calculation process, some stress points next to the excavation pit andloading are selected to plot a stress strain curve later on.

Click the Select points for curves button. The model and Select points window willbe displayed in the Output program.

Define (37.5 19 -1.5) as Point-of-interest coordinates.

Click the Search closest button. The number of the closest node and stress pointwill be displayed.

Click the checkbox in front of the stress point to be selected. The selected stresspoint will be shown in the list.

Select also stress points near the coordinates (37.5 19 -5), (37.5 19 -6) and (37.5 19-7) and close the Select points window.


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Click the Update button to close the Output program.

Start the calculation process.

Save the project when the calculation is finished.

Hint: Instead of selecting nodes or stress points for curves before starting thecalculation, points can also be selected after the calculation when viewingthe output results. However, the curves will be less accurate since only theresults of the saved calculation steps will be considered.

To plot curves of structural forces, nodes can only be selected after thecalculation.

Nodes or stress points can be selected by just clicking them. When movingthe mouse, the exact coordinates of the position are given in the cursorlocation indicator bar at the bottom of the window.

2.4 VIEWING THE RESULTS

After the calculations, the results of the excavation can be viewed by selecting acalculation phase from the Phases tree and pressing the View calculation results button.

Select the final calculation phase (Phase_5) and click the View calculation resultsbutton. The Output program will open and will show the deformed mesh at the endof the last phase.

The stresses, deformations and three dimensional geometry can be viewed byselecting the desired output from the corresponding menus. For example, choosePlastic points from the Stresses menu to investigate the plastic points in the model.

In the Plastic points window, Figure 2.6, select all the options except the Elasticpoints and the Show only inaccurate points options. Figure 2.7 shows the plasticpoints generated in the model at the end of the final calculation phase.

Figure 2.6 Plastic points window

Start selecting structures. Click at a part of the wall to select it. Press simultaneously on the keyboard to select all wall elements. The selected wallelements will colour red.


EXCAVATION IN SAND

Figure 2.7 Plastic points at the end of the final phase

While holding the key or key on the keyboard, double click at one ofthe wall elements to see the deformations plane of the total displacements |u| in allwall elements.

To generate a curve, select the Curves manager option from the Tools menu or clickthe corresponding button in the toolbar.

All pre-selected stress points are shown in the Curve points tabsheet of the Curvesmanager window.

Create a new chart.

Select point K from the drop-down menu for xaxis of the graph. Select 1 underTotal strains.

Select point K from the drop-down menu for yaxis of the graph. Select '1 underPrincipal effective stresses (Figure 2.8).

Invert the sign of both axis by checking the corresponding boxes.

Click OK to confirm the input.

The graph will now show the major principal strain against the major principal stress.Both values are zero at the beginning of the initial conditions. After generation of theinitial conditions, the principal strain is still zero whereas the principal stress is not zeroanymore. To plot the curves of all selected stress points in one graph, follow these steps:

Select Add curve From current project from right mouse button menu. Generate curves for point L, M and N in the same way.

The graph will now show the stress-strain curves of all four stress points (Figure 2.9). Tosee information about the markers, make sure the Value indication option is selectedfrom the View menu and hold the mouse on a marker for a while. Information about thecoordinates in the graph, the number of the point in the graph, the number of the phaseand the number of the step is given. Especially the lower stress points show aconsiderable increase in the stress when the load is applied in the last phase.


TUTORIAL MANUAL

Figure 2.8 Curve generation window

Figure 2.9 Stress - Strain curve

Hint: To re-enter the Curve generation window (in the case of a mistake, a desiredregeneration or a modification), the Curve settings option from the Formatmenu can be selected. As a result the Curves settings window appears, onwhich the Regenerate button should be clicked.

The Chart settings option in the Format menu may be used to modify thesettings of the chart.

To create a stress path plot for stress point K follow these steps:

Create a new chart.

In the Curves generation window, select point K from the drop-down menu of thexaxis of the graph and 'yy under Cartesian effective stresses.


EXCAVATION IN SAND

Select point K from the drop-down menu of the yaxis of the graph. Select 'zzunder Cartesian effective stresses.

Click OK to confirm the input (Figure 2.10).

Figure 2.10 Vertical effective stress ('zz ) versus horizontal effective stress ('yy ) at stress point Klocated near (37.5 19 -1.5)


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LOADING OF A SUCTION PILE

3 LOADING OF A SUCTION PILE

In this tutorial a suction pile in an off-shore foundation will be considered. A suction pile isa hollow steel pile with a large diameter and a closed top, which is installed in the seabedby pumping water from the inside. The resulting pressure difference between the outsideand the inside is the driving force behind this installation.

In this exercise, the length of the suction pile is 10 m and the diameter is 4.5 m. Ananchor line is attached on the side of the pile, 7 m from the top. To avoid local failure ofthe pile, the thickness of the tube where the anchor line acts on the pile is increased. Thesoil consists of silty sand. To model undrained behaviour, an undrained stress analysiswith undrained strength parameters will be performed (Section 6.2 of the ReferenceManual). This exercise will investigate the displacement of the suction pile under workingload. Four different angles of the working load will be considered. The installationprocess itself will not be modelled. The geometry for the problem is sketched in Figure3.1.

Objectives:

Importing volumes

Undrained effective stress analysis with undrained strength parameters

Soil cohesion increases with depth

Copying material data sets

Changing settings in Output

Selecting a node after calculation to generate a curve with structural forces

z = -6.5 mz = -7.0 m

z = -7.5 m

z = -10 m

z

x

4.5 m

Figure 3.1 Geometry of the suction pile

3.1 GEOMETRY

An area of 60 m wide and 60 m long surrounding the suction pile will be modelled. Withthese dimensions the model is sufficiently large to avoid any influence from the modelboundaries.


TUTORIAL MANUAL

Project properties

To define the geometry for this exercise, follow these steps:

Start the Input program and select New project from the Create/Open project dialogbox.

Enter an appropriate title for the exercise.

Keep the standard units and set the model dimensions to xmin = 30 m, xmax = 30m, ymin = 30 m, ymax = 30 m.

Click OK.


In the current example only one horizontal soil layer is present. A single borehole issufficient to define it.

Add a borehole to the geometry.

In the Modify soil layers window add a soil layer with top boundary at z = 0 m andbottom boundary at z = 30 m.

The Head value is 50.0 m, which means 50 m depth above the soil.

Open the Material sets window and create the data sets given in Table 3.1. In theParameters tabsheet deselect the Tension cut-off option in the advancedparameters for strength. In this exercise, the permeability of the soil will notinfluence the results. Instead of using effective strength properties, the cohesionparameter will be used in this example to model undrained shear strength.Advanced parameters can be entered after expanding the Advanced data tree in theParameters tabsheet.

Hint: The Interface data set can be quickly created by copying the 'Sand' data setand changing the Rinter value.

Assign the 'Sand' material data set to the soil layer and close the Material setswindow.


The suction pile is modelled in the Structures mode using predefined volumes. To modela suction pile:

Import the standard cylinder. The standard cylinder is saved in the file in the Importables folder of theinstallation directory of PLAXIS 3D. The imported volume is edited in the Importstructure volumes window. Import solid is a PLAXIS VIP feature.

Modify the scale such that the diameter is 4.5 m and the height is 10 m.



Table 3.1 Material properties of the sand layer and its interface

Parameter Name Sand Interface Unit

General

Material model Model Mohr-Coulomb Mohr-Coulomb Drainage type Type Undrained B Undrained B Soil weight unsat , sat 20 20 kN/m3

Parameters

Young's modulus E ' 1000 1000 kN/m2

Poisson's ratio ' 0.35 0.35 Shear strength su,ref 1.0 1.0 kN/m2

Friction angle u 0.0 0.0

Dilatancy angle 0.0 0.0

Increase in stiffness E 'inc 1000 1000 kN/m2/mReference level zref 0.0 0.0 mIncrease in cohesion su,inc 4.0 4.0 kN/m2/mReference level zref 0.0 0.0 m

Interfaces

Interface strength Manual Rigid Interface strength reduction Rinter 0.7 1.0 Initial

K0 determination Manual Manual Lateral earth pressure coeff. K0,x , K0,y 0.5 0.5

Define the coordinates of the insertion point such that the top of the anchor is at thesea bottom level (z = 0) and the bottom of the anchor is at z = 10 (Figure 3.2).

Figure 3.2 Import structure volumes window

Decompose the imported volume into surfaces by right-clicking it and selecting theDecompose into surfaces option from the appearing menu.


TUTORIAL MANUAL

Hint: As an alternative for the import of a cylinder, the corresponding cylindercommand can be used to create the suction pile. Information about thecommands available in the program is displayed when the Commandreference option is selected in the Help menu.

Make the cylinder mantle into a plate, positive interface and negative interface byright-clicking on it and selecting the corresponding options from the appearing menu.

Open the material data base. Select Plates as set type. Create three data setsaccording to the information in Table 3.2.

Table 3.2 Material properties for the suction pile

Parameter Name Thin wall Thick wall Top Unit

Thickness d 0.05 0.15 0.05 mWeight 58.5 58.5 68.5 kN/m3

Type ofbehaviour

Type Linear, isotropic Linear, isotropic Linear, isotropic

Young'smodulus

E 2.1 108 2.1 108 2.1 108 kN/m2

Poisson'sratio

0.1 0.1 0.1

Shearmodulus

G 9.545 107 9.545 107 9.545 107 kN/m2

Assign Thin wall to the anchor tube and close the Material data set window.

Hide the anchor tube and the original volume object using the Hide option in theright mouse button menu. Note that the top and the bottom surfaces are visible.

Select the top surface and click on the Create array button in the side tool bar.Select the 1D, in z direction option for Shape. Keep the number of columns as 2 anddefine z as 6.5 for the Distance between columns.

Repeat the previous step to create surfaces at z = 7.0 and z = 7.5. Make the top surface into a plate. Assign Top material data set to it.

Assign a positive interface to the bottom surface (z= -10 m). Assign the 'Interface'data set to the bottom interface.

Right-click on the surface located at z = 7.0 m and select the Decompose intooutlines option from the appearing menu.

Right-click on the point near (2.25 0.0 -7.0) and select the Create point load optionfrom the appearing menu. The actual load values will be assigned when thecalculation phases are defined.

The geometry of the project is defined.

3.2 MESH GENERATION

In order to generate the mesh:

The mesh is automatically refined near the plates and load. Select the point load byclicking on it in the model. In the Selection explorer note that the Fineness factor



value is 0.5 and it is displayed in a lighter shade of green in the model.

Generate the mesh. Set the element distribution to Coarse.

Proceed to the Staged construction mode.


The calculation for this exercise will consist of 6 phases. These are the determination ofinitial conditions, the installation of the suction pile and four different load conditions. Theeffect of the change of the load direction while keeping the magnitude unchanged will beanalysed.

Click on the Staged construction tab to proceed with the definition of the calculationphases. Keep the calculation type of the Initial phase to K0 procedure. Ensure thatall the structures and interfaces are switched off.

Add a new calculation phase and rename it as 'Install pile'.

Activate all the plates and interfaces in the project. Assign the Thick wall material tothe plate sections just above and just below the point load. It may be necessary tohide (NOT deactivate) the positive interface around the anchor. Load is not active.

Add a new phase and rename it as 'Load pile 30 degrees'. Open the Phaseswindow and check the Reset displacements to zero checkbox in the Deformationcontrol parameters subtree.

Activate the point load and set Fx = 3897 kN, Fz = 2250 kN.

Define the remaining phases according to the information in Table 3.3. For eachphase the Reset displacements to zero option is to be selected.

Calculate and save the project.

Table 3.3 Load informationPhase Reference phase Fx FzLoad pile 30 degrees [Phase_2] Phase_1 3897 kN 2250 kNLoad pile 40 degrees [Phase_3] Phase_1 3447 kN 2893 kNLoad pile 50 degrees [Phase_4] Phase_1 2893 kN 3447 kNLoad pile 60 degrees [Phase_5] Phase_1 2250 kN 3897 kN

The order of the phases is indicated in the Phases explorer (Figure 3.3). Calculation ofPhase_1 starts after the calculation of Initial phase is completed. The calculation of theremaining phases starts after the calculation of the pile installation phase is completed.

Figure 3.3 Phases explorer


TUTORIAL MANUAL

3.4 VIEWING THE RESULTS

To view the results:

View the results of the last calculation phase. The deformed mes of the wholegeometry will be shown. In particular, the displacements of the suction pile itself areof interest.

To make the suction pile visible deselect the Soil and the Interfaces option in Modelexplorer.

Click on the Select structures button and select the pile wall. This will select only apart of the wall. Press to select all the wall elements of the suction pile.

Keeping the key pressed, double click the pile walls. The results for the wallof the suction pile are displayed in a new window.

Select the shadings representation and rotate the model such that the xaxis isperpendicular to the screen.

If the axes are not visible, select this option from the View menu. It is quite clear thatthe point force acting on the pile does not disturb the displacement field locallyindicating that the pile is sufficiently thick here.

In the same manner, the total displacements of the suction pile under a differentdirection of the load can be inspected by selecting the appropriate phase from thedrop-down menu. In particular, is of interest, as in this phase thehorizontal part of the load will have the largest value (Figure 3.4).

Figure 3.4 Total displacement of the suction pile at the end of Phase_2


CONSTRUCTION OF A ROAD EMBANKMENT

4 CONSTRUCTION OF A ROAD EMBANKMENT

The construction of an embankment on soft soil with a high groundwater level leads to anincrease in pore pressure. As a result of this undrained behaviour, the effective stressremains low and intermediate consolidation periods have to be adopted in order toconstruct the embankment safely. During consolidation the excess pore pressuresdissipate so that the soil can obtain the necessary shear strength to continue theconstruction process.

This tutorial concerns the construction of a road embankment in which the mechanismdescribed above is analysed in detail. In the analysis two new calculation options areintroduced, namely a consolidation analysis and the calculation of a safety factor bymeans of a safety analysis (phi/c-reduction). It also involves the modelling of drains tospeed up the consolidation process.

12 m12 m 16 m

4 m

3 m

3 m

road embankment

peat

clay

dense sand

Figure 4.1 Situation of a road embankment on soft soil

Objectives:

Modelling drains

Consolidation analysis

Change of permeability during consolidation

Safety analysis (phi-c reduction)

4.1 GEOMETRY

Figure 4.1 shows a cross section of a road embankment. The embankment is 16 m wide.The slopes have an inclination of 1: 3. The problem is symmetric, so only one half ismodelled (in this case the right half is chosen). A representative section of 2 m isconsidered in the project. The embankment itself is composed of loose sandy soil. Thesubsoil consists of 6 m of soft soil. The upper 3 m of this soft soil layer is modelled as apeat layer and the lower 3 m as clay. The phreatic level is located 1 m below the originalground surface. Under the soft soil layers there is a dense sand layer of which 4 m areconsidered in the model.

Start the Input program and select Start a new project from the Quick select dialogbox.

In the Project tabsheet of the Project properties window, enter an appropriate title.

Keep the default units and set the model dimensions to xmin = 0, xmax = 60, ymin = 0and ymax = 2.


TUTORIAL MANUAL


The soil layers comprising the embankment foundation are defined using a borehole. Theembankment layers are defined in the Structures mode.

Create a borehole at (0 0). The Modify soil layers window pops up.

Define three soil layers as shown in Figure 4.2.

The water level is located at z = -1 m. In the borehole column specify a value of -1 toHead.

Open the Material sets window.

Create soil material data sets according to Table 4.1 and assign them to thecorresponding layers in the borehole (Figure 4.2).

Close the Modify soil layers window and proceed to the Structures mode to definethe structural elements.

Figure 4.2 Soil layer distribution

Hint: The initial void ratio (einit ) and the change in permeability (ck ) should bedefined to enable the modelling of a change in the permeability due tocompression of the soil. This option is recommended when using advancedmodels.



Table 4.1 Material properties of the road embankment and subsoil

Parameter Name Embankment Sand Peat Clay Unit

General

Material model Model Hardening soil Hardening soil Soft soil Soft soil -

Drainage type Type Drained Drained Undr. (A) Undr. (A) -

Soil unit weight abovephreatic level

unsat 16 17 8 15 kN/m3

Soil unit weight belowphreatic level

sat 19 20 12 18 kN/m3

Initial void ratio einit 0.5 0.5 2.0 1.0 -

Parameters

Secant stiffness instandard drainedtriaxial test

E ref50 2.5 104 3.5 104 - - kN/m2

Tangent stiffness forprimary oedometerloading

E refoed 2.5 104 3.5 104 - - kN/m2

Unloading / reloadingstiffness

E refur 7.5 104 1.05 105 - - kN/m2

Power for stress-leveldependency of stiffness

m 0.5 0.5 - - -

Modified compressionindex

- - 0.15 0.05 -

Modified swelling index - - 0.03 0.01 -Cohesion cref ' 1.0 0.0 2.0 1.0 kN/m2

Friction angle ' 30.0 33.0 23.0 25.0

Dilatancy angle 0.0 3.0 0.0 0.0

Advanced: Set todefault

- Yes Yes Yes Yes -

Flow parameters

Data set - USDA USDA USDA USDA -

Model - VanGenuchten

VanGenuchten

VanGenuchten

VanGenuchten

-

Soil type - Loamy sand Sand Clay Clay -

< 2m - 6.0 4.0 70.0 70.0 %2m 50m - 11.0 4.0 13.0 13.0 %50m 2mm - 83.0 92.0 17.0 17.0 %Set to default - Yes Yes No Yes -

Horizontal permeability(x-direction)

kx 3.499 7.128 0.1 0.04752 m/day

Horizontal permeability(y-direction)

ky 3.499 7.128 0.1 0.04752 m/day

Vertical permeability kz 3.499 7.128 0.02 0.04752 m/dayChange in permeability ck 1 1015 1 1015 1.0 0.2 -Interfaces

Interface strength Rigid Rigid Rigid Rigid -Strength reductionfactor

Rinter 1.0 1.0 1.0 1.0 -

Initial

K0 determination Automatic Automatic Automatic Automatic -Over-consolidation ratio OCR 1.0 1.0 1.0 1.0 -Pre-overburdenpressure

POP 0.0 0.0 5.0 0.0 kN/m2


TUTORIAL MANUAL

4.1.2 DEFINITION OF EMBANKMENT AND DRAINS

The embankment and the drains are defined in the Structures mode. To define theembankment layers:

Reorientate the model such that the front view is displayed by clicking thecorresponding button in the toolbar.

Create a surface by defining points at (0 0 0), (0 0 4), (8 0 4) and (20 0 0).

Create a line passing through (0 0 2) and (14 0 2) to define the embankment layers.

Select both the created line and surface by keeping the key pressed whileclicking them in the model.

Click the Extrude object button.

Assign a value of 2 to the y-component of the extrusion vector as shown in Figure4.3 and click Apply.

Figure 4.3 Extrusion window

Delete the surface and the line created before the extrusion.

Right-click the volume created by extrusion and point to the Soil_4 option in theappearing menu.

A new menu is displayed. Point to the Set material option and select Embankment.

In this project the effect of the drains on the consolidation time will be investigated bycomparing the results with a case without drains. Drains will only be active for thecalculation phases in the case with drains.

Drains are arranged in a square pattern, having a distance of 2 m between twoconsecutive drains in a row (or column). Only one row of drains will be considered in thistutorial. To create the drain pattern:

Click the Create hydraulic conditions button in the side toolbar.

Click the Create line drain button in the appearing menu. Define a line drain in themodel between points (1 1 0) and (1 1 -6).

Click the Create array button to define the drain pattern.

In the Create array window select the 1D, in x direction in the Shape drop-downmenu and specify the pattern as shown in Figure 4.4.



Figure 4.4 Settings of the drain pattern

The model geometry is shown in Figure 4.5.

Figure 4.5 Model geometry

4.2 MESH GENERATION

Proceed to the Mesh mode.

Click the Generate mesh button. Set the element distribution to Coarse.

View the generated mesh. The resulting mesh is shown in Figure 4.6.


TUTORIAL MANUAL

Figure 4.6 The generated mesh


The embankment construction process will be considered twice. In the first calculationthe drains will not be considered.

Initial phase

In the initial situation the embankment is not present. Therefore, the corresponding soilvolumes are deactivated in the initial phase. The K0 procedure can be used to calculatethe initial stresses. The initial water pressures are fully hydrostatic and based on ageneral phreatic level defined by the Head value assigned to the boreholes. For the Initialphase, the Phreatic option is selected for the pore pressure calculation type and theGlobal water level is set to BoreholeWaterlevel_1 corresponding to the water leveldefined by the heads specified for the boreholes.

The boundary conditions for flow can be specified in the Model conditions subtree in theModel explorer. In the current situation the left vertical boundary (Xmin) must be closedbecause of symmetry, so horizontal flow should not occur. The bottom is open becausethe excess pore pressures can freely flow into the deep and permeable sand layer. Theupper boundary is obviously open as well. The view of the GroundwaterFlow subtreeafter the definition is given in Figure 4.7.

Figure 4.7 Boundary conditions for groundwater flow



4.3.1 CONSOLIDATION ANALYSIS

A consolidation analysis introduces the dimension of time in the calculations. In order tocorrectly perform a consolidation analysis a proper time step must be selected. The useof time steps that are smaller than a critical minimum value can result in stressoscillations. The consolidation option in PLAXIS allows for a fully automatic time steppingprocedure that takes this critical time step into account. Within this procedure there arethree main possibilities for the Loading type parameter:

1. Consolidate for a predefined period, including the effects of changes to the activegeometry (Staged construction).

2. Consolidate until all excess pore pressures in the geometry have reduced to apredefined minimum value (Minimum pore pressure).

3. Consolidate until the soil has reached a specified degree of consolidation (Degree ofconsolidation).

Consolidation process - No drains

The embankment construction is divided into two phases. After the first constructio

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