2d2012-1-tutorial plaxis.pdf

PLAXIS 2D

Tutorial Manual

2012

Build 5848

TABLE OF CONTENTS

TABLE OF CONTENTS

1 Settlement of a circular footing on sand 71.1 Geometry 71.2 Case A: Rigid footing 81.3 Case B: Flexible footing 22

2 Submerged construction of an excavation 292.1 Input 302.2 Calculations 372.3 Results 41

3 Dry excavation using a tie back wall 453.1 Input 453.2 Calculations 493.3 Results 53

4 Construction of a road embankment 574.1 Input 574.2 Calculations 604.3 Results 624.4 Safety analysis 654.5 Using drains 674.6 Updated mesh + Updated water pressures analysis 69

5 Settlements due to tunnel construction 715.1 Input 725.2 Calculations 775.3 Results 79

6 Excavation of a NATM tunnel 836.1 Input 836.2 Calculations 856.3 Results 87

7 Stability of dam under rapid drawdown 897.1 Input 897.2 Case A: Classical mode 917.3 Case B: Advanced mode 96

8 Dry excavation using a tie back wall - ULS 998.1 Input 998.2 Calculations 1028.3 Results 103

9 Flow through an embankment 1059.1 Input 1059.2 Calculations 1069.3 Results 107

10 Flow around a sheet pile wall 111

PLAXIS 2D 2012 | Tutorial Manual 3

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10.1 Input 11110.2 Calculations 11210.3 Results 113

11 Potato field moisture content 11511.1 Input 11511.2 Calculation 11711.3 Results 119

12 Dynamic analysis of a generator on an elastic foundation 12112.1 Input 12112.2 Calculations 12412.3 Results 126

13 Pile driving 12913.1 Input 12913.2 Calculations 13213.3 Results 133

14 Free vibration and earthquake analysis of a building 13714.1 Input 13714.2 Calculations 14214.3 Results 144

Appendix A - Menu tree 147

Appendix B - Calculation scheme for initial stresses due to soil weight 153

4 Tutorial Manual | PLAXIS 2D 2012

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 2D. 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.


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SETTLEMENT OF A CIRCULAR FOOTING ON SAND

1 SETTLEMENT OF A CIRCULAR FOOTING ON SAND

In this chapter a first application is considered, namely the settlement of a circularfoundation footing on sand. This is the first step in becoming familiar with the practicaluse of PLAXIS 2D. The general procedures for the creation of a geometry model, thegeneration of a finite element mesh, the execution of a finite element calculation and theevaluation of the output results are described here in detail. The information provided inthis chapter will be utilised in the later tutorials. Therefore, it is important to complete thisfirst tutorial before attempting any further tutorial examples.

Objectives:

• Starting a new project.

• Creating soil stratigraphy using the Geometry line feature.

• Defining standard boundary fixities.

• Creating and assigning of material data sets for soil (Mohr-Coulomb model).

• Defining prescribed displacements.

• Creation of footing using the Plate feature.

• Creating and assigning material data sets for plates.

• Creating loads.

• Modifying the global mesh coarseness.

• Generating the mesh.

• Generating initial stresses using the K0 procedure.

• Defining a Plastic calculation.

• Activating and modifying the values of loads in calculation phases.

• Viewing the calculation results.

• Selecting points for curves.

• Creating a 'Load - displacement' curve.

1.1 GEOMETRY

A circular footing with a radius of 1.0 m is placed on a sand layer of 4.0 m thickness asshown in Figure 1.1. Under the sand layer there is a stiff rock layer that extends to a largedepth. The purpose of the exercise is to find the displacements and stresses in the soilcaused by the load applied to the footing. Calculations are performed for both rigid andflexible footings. The geometry of the finite element model for these two situations issimilar. The rock layer is not included in the model; instead, an appropriate boundarycondition is applied at the bottom of the sand layer. To enable any possible mechanism inthe sand and to avoid any influence of the outer boundary, the model is extended inhorizontal direction to a total radius of 5.0 m.


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2.0 m

4.0 m

load

footing

x

ysand

a

Figure 1.1 Geometry of a circular footing on a sand layer

1.2 CASE A: RIGID FOOTING

In the first calculation, the footing is considered to be very stiff and rough. In thiscalculation the settlement of the footing is simulated by means of a uniform indentation atthe top of the sand layer instead of modelling the footing itself. This approach leads to avery simple model and is therefore used as a first exercise, but it also has somedisadvantages. For example, it does not give any information about the structural forcesin the footing. The second part of this tutorial deals with an external load on a flexiblefooting, which is a more advanced modelling approach.

1.2.1 CREATING THE INPUT

Start PLAXIS 2D by double clicking the icon of the Input program. The Quick selectdialog box appears in which you can create a new project or select an existing one(Figure 1.2).

Figure 1.2 Quick select dialog box

• Click Start a new project. The Project properties window appears, consisting of twotabsheets, Project and Model (Figure 1.3 and Figure 1.4).



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 settings include the description ofthe problem, the type of model, the basic type of elements, the basic units and the size ofthe draw area.

Figure 1.3 Project tabsheet of the Project properties window

To enter the appropriate settings for the footing calculation follow these steps:

• In the Project tabsheet, enter "Tutorial 1" in the Title box and type "Settlements of acircular footing" in the Comments box.

• In the General options box the type of the model (Model) and the basic element type(Elements) are specified. Since this tutorial concerns a circular footing, selectAxisymmetry and 15-Node options from the Model and the Elements drop-downmenus respectively.

• The Acceleration box indicates a fixed gravity angle of -90◦, which is in the verticaldirection (downward). In addition to the Earth gravity, independent accelerationcomponents may be entered. These values should be kept zero for this exercise.

• Click the Next button below the tabsheets or click the Model tab.

• In the Model tabsheet, keep the default units in the Units box (Unit of Length = m;Unit of Force = kN; Unit of Time = day).

• In the Geometry dimensions box set the model dimensions to Xmin = 0.0, Xmax =5.0, Ymin = 0.0 and Ymax = 4.0.

• The Grid box contains values to set the grid spacing. The grid provides a matrix ofdots on the screen that can be used as reference points. It may also be used forsnapping to regular points during the creation of the geometry. The distancebetween the dots is determined by the Spacing value. The spacing of snappingpoints can be further divided into smaller intervals by the Number of snap intervalsvalue. Use the default values in this example.

• Click OK button to confirm the settings. Now the draw area appears in which thegeometry model can be drawn.


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Figure 1.4 Model tabsheet of the Project properties window

Hint: In the case of a mistake or for any other reason that the project propertiesneed to be changed, you can access the Project properties window byselecting the corresponding option from the File menu or by clicking on therulers when they are active.

Geometry contour

Once the general settings have been completed, the draw area appears with an indicationof the origin and direction of the system of axes. The x-axis is pointing to the right and they-axis is pointing upward. A geometry can be created anywhere within the draw area. Tocreate objects, you can either use the buttons from the toolbar or the options from theGeometry menu. For a new project, the Geometry line button is already active.Otherwise this option can be selected from the second toolbar or from the Geometrymenu. In order to construct the contour of the proposed geometry, follow these steps:

Select the Geometry line option (already selected).

• Position the cursor (now appearing as a pen) at the origin of the axes. Check thatthe units in the status bar read 0.0 x 0.0 and click the left mouse button once. Thefirst geometry point (number 0) has now been created.

Hint: The point and chain numbers are displayed in the model when thecorresponding options are selected in the View menu.

• Move along the x-axis to position (5.0; 0.0). Click the left mouse button to generatethe second point (number 1). At the same time the first geometry line is created frompoint 0 to point 1.

• Move upward to position (5.0; 4.0) and click again.

• Move to the left to position (0.0; 4.0) and click again.

• Finally, move back to the origin (0.0; 0.0) and click the left mouse button again.Since the latter point already exists, no new point is created, but only an additionalgeometry line is created from point 3 to point 0. The program will also detect acluster (area that is fully enclosed by geometry lines) and will give it a light colour.

• Click the right mouse button to stop drawing.



Hint: Mispositioned points and lines can be modified or deleted by first choosingthe Selection button from the toolbar. To move a point or line, select the pointor the line and drag it to the desired position. To delete a point or a line,select the point or the line and press the <Delete> key on the keyboard.Unwanted drawing operations can be removed by the Undo button in thetoolbar, by selecting the corresponding option from the Edit menu or bypressing <Ctrl-z> on the keyboard after terminating the drawing process.

» Lines can be drawn perfectly horizontal or vertical by holding down the<Shift> key on the keyboard while moving the cursor.

The proposed geometry does not include plates, hinges, geogrids, interfaces, anchors ortunnels. Hence, you can skip these buttons on the second toolbar.

Hint: The full geometry model has to be completed before a finite element meshcan be generated. This means that boundary conditions and modelparameters must be entered and applied to the geometry model first.

Boundary conditions

Boundary conditions can be found in the centre part of the second toolbar and in theLoads menu. For deformation problems two types of boundary conditions exist:Prescribed displacements and prescribed forces (loads).

In principle, all boundaries must have one boundary condition in each direction. That is tosay, when no explicit boundary condition is given to a certain boundary (a free boundary),the natural condition applies, which is a prescribed force equal to zero and a freedisplacement.

To avoid the situation where the displacements of the geometry are undetermined, somepoints of the geometry must have prescribed displacements. The simplest form of aprescribed displacement is a fixity (zero displacement), but non-zero prescribeddisplacements may also be given. In this problem the settlement of the rigid footing issimulated by means of non-zero prescribed displacements at the top of the sand layer.

To create the boundary conditions for this tutorial, follow these steps:

Click the Standard fixities button on the toolbar or choose the corresponding optionfrom the Loads menu to set the standard boundary conditions.

As a result the program will generate a full fixity at the base of the geometry and rollerconditions at the vertical sides (ux = 0; uy = free). A fixity in a certain direction appearson the screen as two parallel lines perpendicular to the fixed direction. Hence, rollersupports appear as two vertical parallel lines and full fixity appears as crosshatched lines.

Hint: The Standard fixities option is suitable for most geotechnical applications. Itis a fast and convenient way to input standard boundary conditions.


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Select the Prescribed displacements button from the toolbar or select thecorresponding option from the Loads menu.

• Move the cursor to point (0.0; 4.0) and click the left mouse button.

• Move along the upper geometry line to point (1.0; 4.0) and click the left mousebutton again.

• Click the right mouse button to stop drawing.

In addition to the new point (4), a prescribed downward displacement of 1 unit (1.0 m) ina vertical direction and a fixed horizontal displacement are created at the top of thegeometry. Prescribed displacements appear as a series of arrows starting from theoriginal position of the geometry and pointing in the direction of movement.

Figure 1.5 Geometry model in the Input window

Hint: The input value of a prescribed displacement may be changed by firstclicking the Selection button and then double clicking the line at which aprescribed displacement is applied. On selecting Prescribed displacementsfrom the Select dialog box, a new window will appear in which the changescan be made.

» The prescribed displacement is actually activated when defining thecalculation stages (Section 1.2.2). Initially it is not active.

Material data sets

In order to simulate the behaviour of the soil, a suitable soil model and appropriatematerial parameters must be assigned to the geometry. In PLAXIS 2D, 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 walls, plates, anchors, geogrids, etc.) the system is similar, but differenttypes of structures have different parameters and therefore different types of data sets.



PLAXIS 2D distinguishes between material data sets for Soil and interfaces, Plates,Geogrids, Embedded pile row and Anchors.

The creation of material data sets is generally done after the input of boundaryconditions. Before the mesh is generated, all material data sets should have been definedand all clusters and structures must have an appropriate data set assigned to them.

The input of material data sets can be selected by means of the Materials button on thetoolbar or from the options available in the Materials menu.

To create a material set for the sand layer, follow these steps:

Click the Materials button on the toolbar. The Material sets window pops up (Figure1.6).

Figure 1.6 Material sets window

• Click the New button at the lower side of the Material sets window. A new dialog boxwill appear with five tabsheets: General, Parameters, Flow parameters, Interfacesand Initial.

• In the Material set box of the General tabsheet, write "Sand" in the Identification box.

• The default material model (Mohr-Coulomb) and drainage type (Drained) are validfor this example.

• Enter the proper values in the General properties box (Figure 1.7) according to thematerial properties listed in Table 1.1.

• 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).

• Enter the model parameters of Table 1.1 in the corresponding edit boxes of theParameters tabsheet (Figure 1.8). A detailed description of different soil models andtheir corresponding parameters can be found in the Material Models Manual.


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Table 1.1 Material properties of the sand layer

Parameter Name Value Unit

General

Material model Model Mohr-Coulomb -

Type of material behaviour Type Drained -

Soil unit weight above phreatic level γunsat 17.0 kN/m3

Soil unit weight below phreatic level γsat 20.0 kN/m3

Parameters

Young's modulus (constant) E ' 1.3 · 104 kN/m2

Poisson's ratio ν ' 0.3 -

Cohesion (constant) c'ref 1.0 kN/m2

Friction angle ϕ' 30.0 ◦

Dilatancy angle ψ 0.0 ◦

Figure 1.7 General tabsheet of the Soil window of Soil and interfaces set type

Figure 1.8 Parameters tabsheet of the Soil window of Soil and interfaces set type

• Since the soil material is drained, the geometry model does not include interfacesand the default initial conditions are valid for this case, the remaining tabsheets canbe skipped. Click OK to confirm the input of the current material data set. Now thecreated data set will appear in the tree view of the Material sets window.

• Drag the data set "Sand" from the Material sets window (select it and hold down the



left mouse button while moving) to the soil cluster in the draw area and drop it(release the left mouse button). Notice that the cursor changes shape to indicatewhether or not it is possible to drop the data set. Correct assignment of a data set toa cluster is indicated by a change in colour of the cluster.

• Click OK in the Material sets window to close the database.

Hint: Existing data sets may be changed by opening the Material sets window,selecting the data set to be changed from the tree view and clicking the Editbutton. As an alternative, the Material sets window can be opened by doubleclicking a cluster and clicking the Change button behind the Material set boxin the properties window. A data set can now be assigned to thecorresponding cluster by selecting it from the project database tree view andclicking the OK button.

» The program performs a consistency check on the material parameters andwill give a warning message in the case of a detected inconsistency in thedata.

Mesh generation

When the geometry model is complete, the finite element model (or mesh) can begenerated. PLAXIS 2D allows for a fully automatic mesh generation procedure, in whichthe geometry is divided into elements of the basic element type and compatible structuralelements, if applicable.

The mesh generation takes full account of the position of points and lines in the geometrymodel, so that the exact position of layers, loads and structures is accounted for in thefinite element mesh. The generation process is based on a robust triangulation principlethat searches for optimised triangles and which results in an unstructured mesh.Unstructured meshes are not formed from regular patterns of elements. The numericalperformance of these meshes, however, is usually better than structured meshes withregular arrays of elements. In addition to the mesh generation itself, a transformation ofinput data (properties, boundary conditions, material sets, etc.) from the geometry model(points, lines and clusters) to the finite element mesh (elements, nodes and stress points)is made.

In order to generate the mesh, follow these steps:

• In the Mesh menu, select the Global coarseness option. The Mesh generation setupwindow pops up. The Medium option is by default selected in the Elementdistribution drop-down menu (Figure 1.9).

Figure 1.9 Mesh generation setup window


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• Click Generate. After the generation of the mesh a new window is opened (Outputwindow) in which the generated mesh is presented (Figure 1.10). Note that PLAXISautomatically refines the mesh near loads and structural objects.

• Click the Close button to return to the geometry input mode.

Figure 1.10 Axisymmetric finite element mesh of the geometry around the footing

Hint: Additional options are available in the Mesh menu to refine the mesh globallyor locally.

» At this stage of input it is still possible to modify parts of the geometry or toadd geometry objects. If modifications are made at this stage, then the finiteelement mesh has to be regenerated.

1.2.2 PERFORMING CALCULATIONS

After clicking the Calculations tab and saving the input data, the Input program is closedand the Calculations program is started. Note that the program gives by default theproject title defined in the Project properties as an option for project file name.

The Calculations program may be used to define and execute calculation phases.It can also be used to select calculated phases for which output results are to be

viewed.

• The Select calculation mode window is displayed (Figure 1.11). By default theClassical mode is selected. This calculation mode is considered in this tutorial.Press OK to proceed.

The Calculations window consists of a menu, a toolbar, a set of tabsheets and a list ofcalculation phases, as indicated in Figure 1.12.

The tabsheets General, Parameters and Multipliers are used to define a calculationphase. This can be a loading, construction or excavation phase, a consolidation period ora safety analysis. For each project multiple calculation phases can be defined. Alldefined calculation phases appear in the list at the lower part of the window. The Preview



Figure 1.11 Select calculation mode window

Figure 1.12 The General tabsheet of the Calculations window

tabsheet can be used to show the actual state of the geometry. A preview is onlyavailable after calculation of the selected phase.

Initial phase: Initial conditions

In general, the initial conditions comprise the initial groundwater conditions, the initialgeometry configuration and the initial effective stress state. The sand layer in the currentfooting project is dry, so there is no need to enter groundwater conditions. The analysisdoes, however, require the generation of initial effective stresses.

• The calculation type is by default K0 procedure. This procedure will be used in thisexample to generate initial stresses.

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

• In the Parameters tabsheet keep the default values.


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• In the Multipliers tabsheet, keep the total multiplier for soil weight, ΣMweight , equalto 1.0. This means that the full weight of the soil is applied for the generation ofinitial stresses.

Phase 1: Footing

In order to simulate the settlement of the footing in this analysis, a plastic calculation isrequired. PLAXIS 2D has a convenient procedure for automatic load stepping, which iscalled 'Load advancement'. This procedure can be used for most practical applications.Within the plastic calculation, the prescribed displacements are activated to simulate theindentation of the footing. In order to define the calculation phase, follow these steps:

• Click Next to add a new phase, following the initial phase.

Hint: Calculation phases may be added, inserted or deleted using the Next, Insertand Delete buttons.

• In the Phase ID box write (optionally) an appropriate name for the current calculationphase (for example "Indentation") and select the phase from which the current phaseshould start (in this case the calculation can only start from Phase 0 - Initial phase).

• In the General tabsheet, the Plastic option is by default selected in the Calculationtype drop-down menu. Click the Parameters tab or the Parameters button in theCalculation type box. The Parameters tabsheet contains the calculation controlparameters, as indicated in Figure 1.13.

• Keep the default value for the maximum number of Additional steps (250) and theStandard setting option in the Iterative procedure box. See the Reference Manualfor more information about the calculation control parameters.

Figure 1.13 Parameters tabsheet of the Calculations window

• Staged construction loading input is valid for this phase and it is automaticallyselected by the program. Click Define.



Hint: Soil clusters and structural elements can be easily activated and de-activatedby clicking them once. Double-clicking will activate or de-activate the featureas well as open the corresponding dialog box to define its properties. In casemore features are defined here, a selection window will pop up.

• In the Staged construction mode select the prescribed displacement by doubleclicking the correponding line. A dialog box pops up.

• In the Prescribed displacement (static) dialog box the magnitude and direction of theprescribed displacement can be specified, as indicated in Figure 1.14. In this caseenter a Y-value of −0.05 in both input fields, signifying a downward displacement of0.05 m. All X-values should remain zero. Click OK. An active prescribeddisplacement is indicated by a blue colour.

Figure 1.14 The Prescribed displacement (static) dialog box

• No changes are required in the Water conditions mode.

• Click the Update tab to return to the Parameters tabsheet of the Calculationprogram.

Hint: When a calculation phase is being defined, the Staged construction andWater conditions modes are activated by clicking the corresponding tabs inthe Input program.

The calculation definition is now complete.

Click the Calculate button. Ignore the warning that no nodes and stress points havebeen selected for curves.This will start the calculation process. All calculationphases that are selected for execution, as indicated by the blue arrow, will becalculated in the order controlled by the Start from phase parameter.

During the execution of a calculation a window appears which gives information about theprogress of the actual calculation phase (Figure 1.15). The information, which iscontinuously updated, comprises a load-displacement curve, the level of the loadsystems (in terms of total multipliers) and the progress of the iteration process (iterationnumber, global error, plastic points, etc.). See the Reference Manual for more information


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about the calculations info window.

Figure 1.15 The Active tasks window displaying information about the calculation process

When a calculation ends, the list of calculation phases is updated and a messageappears in the corresponding Log info memo box. The Log info memo box indicateswhether or not the calculation has finished successfully.

Hint: Check the list of calculation phases carefully after each execution of a (seriesof) calculation(s). A successful calculation is indicated in the list with a greencheck mark (

√) whereas an unsuccessful calculation is indicated with a

white cross (×) in a red or orange circle, depending on the type of the erroroccurred. Calculation phases that are selected for execution are indicated bya blue arrow (→).

• To check the applied load that results from the prescribed displacement of 0.05 m,click the Multipliers tab and select the Reached values radio button. In addition tothe reached values of the multipliers in the two existing columns, additionalinformation is presented at the left side of the window. For the current applicationthe value of Force-Y is important. This value represents the total reaction forcecorresponding to the applied prescribed vertical displacement, which corresponds tothe total force under 1.0 radian of the footing (note that the analysis isaxisymmetric). In order to obtain the total footing force, the value of Force-Y shouldbe multiplied by 2π (this gives a value of about 592 kN).

1.2.3 VIEWING RESULTS

Once the calculation has been completed, the results can be evaluated in the Outputprogram. In the Output window you can view the displacements and stresses in the fullgeometry as well as in cross sections and in structural elements, if applicable.



The computational results are also available in tabulated form. To view the results of thefooting analysis, follow these steps:

• Select the last calculation phase in the list in the Calculations program.

Click the View calculation results button. As a result, the Output program is started,showing the deformed mesh at the end of the selected calculation phase (Figure1.16). The deformed mesh is scaled to ensure that the deformations are visible.

Figure 1.16 Deformed mesh

• In the Deformations menu select the Total displacements→ |u| option. The plotshows colour shadings of the total displacements. The colour distribution isdisplayed in the legend at the right of the plot.

Hint: The legend can be toggled on and off by clicking the corresponding option inthe View menu.

The total displacement distribution can be displayed in contours by clicking thecorresponding button in the toolbar. The plot shows contour lines of the totaldisplacements, which are labelled. An index is presented with the displacementvalues corresponding to the labels.

Clicking the Arrows button, the plot shows the total displacements of all nodes asarrows, with an indication of their relative magnitude.

Hint: In addition to the total displacements, the Deformations menu allows for thepresentation of Incremental displacements. The incremental displacementsare the displacements that occurred within one calculation step (in this casethe final step). Incremental displacements may be helpful in visualising aneventual failure mechanism.

• In the Stresses menu point to the Principal effective stresses and select theEffective principal stresses option from the appearing menu. The plot shows theaverage effective principal stresses at the center of each soil element with anindication of their direction and their relative magnitude (Figure 1.17).


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Hint: The plots of stresses and displacements may be combined with geometricalfeatures, as available in the Geometry menu.

Figure 1.17 Effective principal stresses

Click the Table button on the toolbar. A new window is opened in which a table ispresented, showing the values of the principal stresses in each stress point of allelements.

1.3 CASE B: FLEXIBLE FOOTING

The project is now modified so that the footing is modelled as a flexible plate. Thisenables the calculation of structural forces in the footing. The geometry used in thisexercise is the same as the previous one, except that additional elements are used tomodel the footing. The calculation itself is based on the application of load rather thanprescribed displacement. It is not necessary to create a new model; you can start fromthe previous model, modify it and store it under a different name. To perform this, followthese steps:

Modifying the geometry

Click the Input button at the right hand side of the toolbar.

• Select the Save as option of the File menu. Enter a non-existing name for thecurrent project file and click the Save button.

Select the geometry line on which the prescribed displacement was applied andpress the <Delete> key on the keyboard.

• Select the Prescribed displacement from the Select items to delete window (Figure1.18) and click Delete. Note that the created line and its end points are not deleted.

Click the Plate button in the toolbar.

• Move to position (0.0; 4.0) and click the left mouse button.



Figure 1.18 Select items to delete window

Figure 1.19 The dialog box for distributed load

• Move to position (1.0; 4.0) and click the left mouse button, followed by the rightmouse button to finish the drawing. A plate from point 3 to point 4 is created whichsimulates the flexible footing.

Click the Distributed load - load system A button in the toolbar.

• Click point (0.0; 4.0) and then on point (1.0; 4.0).

• Press <Esc> key to finish the input of distributed loads. The Selection button willbecome active again.

• Double-click the created load. Select the Distributed load - load system A option inthe Select window and click OK. A dialog window where the load can be definedpops up (Figure 1.19).

• Accept the default input value of the distributed load (1.0 kN/m2 perpendicular to theboundary) and close the window by clicking OK. The input value will later bechanged to the real value when the load is activated.

Adding material properties for the footing

Click the Materials button.

• Select Plates from the Set type drop-down menu in the Material sets window.

• Click the New button. A new window appears where the properties of the footingcan be entered.

• Write "Footing" in the Identification box. The Elastic option is selected by default forthe material type. Keep this option for this example.

• Enter the properties as listed in Table 1.2.


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• Click OK. The new data set now appears in the tree view of the Material setswindow.

Hint: The equivalent thickness is automatically calculated by PLAXIS from thevalues of EA and EI. It cannot be defined manually.

Table 1.2 Material properties of the footing


Material type Type Elastic; Isotropic -

Normal stiffness EA 5 · 106 kN/m

Flexural rigidity EI 8.5 · 103 kNm2/m

Weight w 0.0 kN/m/m

Poisson's ratio ν 0.0 -

• Drag the set "Footing" to the draw area and drop it on the footing. Note that theshape of the cursor changes to indicate that it is valid to drop the material set.

Hint: If the Material sets window is displayed over the footing and hides it, click onits header and drag it to another position.

• Close the database by clicking the OK button.

Generating the mesh

Click the Generate mesh button to generate the finite element mesh. Note that themesh is automatically refined under the footing.

• After viewing the mesh, click the Close button.

Hint: Regeneration of the mesh results in a redistribution of nodes and stresspoints.

Calculations

After clicking the Calculations button and saving the input data, the Input program isclosed and the Calculations program is started.

• The initial phase is the same as in the previous case.

• Select the following phase (Phase_1) and enter an appropriate name for the phaseidentification. Keep Plastic as Calculation type.

• In the Parameters tabsheet, keep the Staged construction option as loading inputand click Define.

• In the Staged construction mode click the geometry line where the load and plateare present. A Select items dialog box will appear. Activate both the plate and theload by clicking on the check boxes.



• While the load is selected, click the Change button at the bottom of the dialog box.The Distributed load - static load system A dialog box will appear to set the loads.Enter a Y-value of −188.44 kN/m2 for both geometry points. Note that this gives atotal load that is approximately equal to the footing force that was obtained from thefirst part of this tutorial. (188.44kN/m2 · π · (1.0m)2 ≈ 596kN).

• Close the dialog boxes. No changes are required in the Water conditions tabsheet.

• Click Update.

The calculation definition is now complete. Before starting the calculation it is advisableto select nodes or stress points for a later generation of load-displacement curves orstress and strain diagrams. To do this, follow these steps:

Click the Select points for curves button on the toolbar. As a result, all the nodesand stress points are displayed in the model in the Output program. The points canbe selected either by directly clicking on them or by using the options available in theSelect points window.

• In the Select points window enter (0; 4) for the coordinates of the point of interestand click Search closest. The nodes and stress points located near that specificlocation are listed.

• Select the node at exactly (0; 4) by checking the box in front of it. The selected nodeis indicated by ’A’ in the model when the Selection labels option is selected in theMesh menu.

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 select the desired nodes by clicking on them, it may be convenient to usethe Zoom in option on the toolbar to zoom into the area of interest.

• Click the Update button to return to the Calculations program.

• Check if both calculation phases are marked for calculation by a blue arrow. If this isnot the case double click the calculation phase or right click and select Markcalculate from the pop-up menu.

Click the Calculate button to start the calculation.

Viewing the results

• After the calculation the results of the final calculation step can be viewed by clickingthe View calculation results button. Select the plots that are of interest. Thedisplacements and stresses should be similar to those obtained from the first part ofthe exercise.

Click the Select structures button in the side toolbar and double click the footing. Anew window opens in which either the displacements or the bending moments of thefooting may be plotted (depending on the type of plot in the first window).

• Note that the menu has changed. Select the various options from the Forces menu


TUTORIAL MANUAL

to view the forces in the footing.

Hint: Multiple (sub-)windows may be opened at the same time in the Outputprogram. All windows appear in the list of the Window menu. PLAXIS followsthe Windows standard for the presentation of sub-windows (Cascade, Tile,Minimize, Maximize, etc).

Generating a load-displacement curve

In addition to the results of the final calculation step it is often useful to view aload-displacement curve. In order to generate the load-displacement curve as given inFigure 1.21, follow these steps:

Click the Curves manager button in the toolbar. The Curves manager window popsup.

Figure 1.20 Curve generation window

• In the Charts tabsheet, click New. The Curve generation window pops up (Figure1.20).

• For the x−axis, select the point A (0.00 / 4.00) from the drop-down menu. Select the|u| option for the Total displacements option of the Deformations.

• For the y−axis, select the Project option from the drop-down menu. Select theΣMstage option of the Multipliers. Hence, the quantity to be plotted on the y-axis isthe amount of the specified changes that has been applied. Hence the value willrange from 0 to 1, which means that 100% of the prescribed load has been appliedand the prescribed ultimate state has been fully reached.



Hint: To re-enter the Settings window (in the case of a mistake, a desiredregeneration or modification) you can double click the chart in the legend atthe right of the chart. Alternatively, you may open the Settings window byselecting the corresponding option from the Format menu.

» The properties of the chart can be modified in the Chart tabsheet whereasthe properties curve can be modified in the corresponding tabsheet.

• Click OK to accept the input and generate the load-displacement curve. As a resultthe curve of Figure 1.21 is plotted.

Figure 1.21 Load-displacement curve for the footing


TUTORIAL MANUAL


SUBMERGED CONSTRUCTION OF AN EXCAVATION

2 SUBMERGED CONSTRUCTION OF AN EXCAVATION

This tutorial illustrates the use of PLAXIS for the analysis of submerged construction ofan excavation. Most of the program features that were used in Tutorial 1 will be utilisedhere again. In addition, some new features will be used, such as the use of interfacesand anchor elements, the generation of water pressures and the use of multiplecalculation phases. The new features will be described in full detail, whereas the featuresthat were treated in Tutorial 1 will be described in less detail. Therefore it is suggestedthat Tutorial 1 should be completed before attempting this exercise.

This tutorial concerns the construction of an excavation close to a river. The excavation iscarried out in order to construct a tunnel by the installation of prefabricated tunnelsegments. The excavation is 30 m wide and the final depth is 20 m. It extends inlongitudinal direction for a large distance, so that a plane strain model is applicable. Thesides of the excavation are supported by 30 m long diaphragm walls, which are braced byhorizontal struts at an interval of 5.0 m. Along the excavation a surface load is taken intoaccount. The load is applied from 2 meter from the diaphragm wall up to 7 meter from thewall and has a magnitude of 5 kN/m2/m (Figure 2.1).

The upper 20 m of the subsoil consists of soft soil layers, which are modelled as a singlehomogeneous clay layer. Underneath this clay layer there is a stiffer sand layer, whichextends to a large depth. 30 m of the sand layer are considered in the model.

x

y

43 m43 m 5 m5 m 2 m2 m 30 m

1 m

19 m

10 m

20 m

ClayClay

Sand

Diaphragm wall

to be excavated

Strut

5 kN/m2/m5 kN/m2/m

Figure 2.1 Geometry model of the situation of a submerged excavation

Since the geometry is symmetric, only one half (the left side) is considered in theanalysis. The excavation process is simulated in three separate excavation stages. Thediaphragm wall is modelled by means of a plate, such as used for the footing in theprevious tutorial. The interaction between the wall and the soil is modelled at both sidesby means of interfaces. The interfaces allow for the specification of a reduced wall frictioncompared to the friction in the soil. The strut is modelled as a spring element for whichthe normal stiffness is a required input parameter.


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Objectives:

• Modelling soil-structure interaction using the Interface feature.

• Advanced soil models (Soft Soil model and Hardening Soil model).

• Undrained (A) drainage type.

• Defining Fixed-end-anchor.

• Creating and assigning material data sets for anchors.

• Refining mesh around lines.

• Simulation of excavation (cluster de-activation).

2.1 INPUT

To create the geometry model, follow these steps:

General settings

• 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 titleand make sure that Model is set to Plane strain and that Elements is set to 15-Node.

• Keep the default units and set the model dimensions to Xmin = 0.0 m, Xmax = 65.0m, Ymin = -30.0 m and Ymax = 20.0 m. Keep the default values for the grid spacing(Spacing = 1 m; Number of intervals = 1).

Geometry contour, layers and structures

To define the geometry contour:

The Geometry line feature is selected by default for a new project. Move the cursorto (0.0; 20.0) and click the left mouse button. Move 50 m down (0.0; -30.0) and clickagain. Move 65 m to the right (65.0; -30.0) and click again. Move 50 m up (65.0;20.0) and click again. Finally, move back to (0.0; 20.0) and click again. A cluster isnow detected. Click the right mouse button to stop drawing.

To define the geometry of the soil layers:

• The Geometry line feature is still selected. Move the cursor to position (0.0; 0.0).Click the existing vertical line. A new point (4) now introduced. Move 65 m to theright (65.0; 0.0) and click the other existing vertical line. Another point (5) isintroduced and now two clusters are detected. Click the right mouse button to finishthe drawing.

To define the diaphragm wall:

Click the Plate button in the toolbar. Move the cursor to position (50.0; 20.0) at theupper horizontal line and click. Move 30 m down (50.0; -10.0) and click. In additionto the point at the toe of the wall, another point is introduced the intersection with themiddle horizontal line at (layer separation). Click the right mouse button to finish thedrawing.



To define the excavation levels:

• Select the Geometry line button again. Move the cursor to position (50.0; 18.0) atthe wall and click. Move the cursor 15 m to the right (65.0; 18.0) and click again.Click the right mouse button to finish drawing the first excavation stage. Now movethe cursor to position (50.0; 10.0) and click. Move to (65.0; 10.0) and click again.Click the right mouse button to finish drawing the second excavation stage.

Hint: Within the geometry input mode it is not strictly necessary to select thebuttons in the toolbar in the order that they appear from left to right. In thiscase, it is more convenient to create the wall first and then enter theseparation of the excavation stages by means of a Geometry line.

» When creating a point very close to a line, the point is usually snapped ontothe line, because the mesh generator cannot handle non-coincident pointsand lines at a very small distance. This procedure also simplifies the input ofpoints that are intended to lie exactly on an existing line.

» If the pointer is substantially mispositioned and instead of snapping onto anexisting point or line a new isolated point is created, this point may bedragged (and snapped) onto the existing point or line by using the Selectionbutton.

» In general, only one point can exist at a certain coordinate and only one linecan exist between two points. Coinciding points or lines will automatically bereduced to single points or lines. The procedure to drag points onto existingpoints may be used to eliminate redundant points (and lines).

To define interfaces:

Click the Interface button on the toolbar or select the Interface option from theGeometry menu. The shape of the cursor will change into a cross with an arrow ineach quadrant. The arrows indicate the side at which the interface will be generatedwhen the cursor is moved in a certain direction.

• Move the cursor (the centre of the cross defines the cursor position) to the top of thewall (50.0; 20.0) and click the left mouse button. Move to 1 m below the bottom ofthe wall (50.0; -11.0) and click again.

Hint: In general, it is a good habit to extend interfaces around corners of structuresto allow for sufficient freedom of deformation, to obtain a more accuratestress distribution and to avoid unrealistic bearing capacity. When doing so,make sure that the strength of the extended part of the interface is equal tothe soil strength and that the interface does not influence the flow field, ifapplicable. The latter can be achieved by switching off the extended part ofthe interface before performing a groundwater flow analysis.

• According to the position of the 'down' arrow at the cursor, an interface is generatedat the left hand side of the wall. Similarly, the 'up' arrow is positioned at the right sideof the cursor, so when moving up to the top of the wall and clicking again, an


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interface is generated at the right hand side of the wall. Move back to (50.0; 20.0)and click again. Click the right mouse button to finish drawing.

Hint: Interfaces are indicated as dotted lines along a geometry line. In order toidentify interfaces at either side of a geometry line, a positive sign (⊕) ornegative sign () is added. This sign has no physical relevance or influenceon the results.

To define the strut:

Click the Fixed-end anchor button in the toolbar or select the corresponding optionfrom the Geometry menu. Move the cursor to a position 1 metre below point 6 (50.0;19.0) and click the left mouse button. The Fixed-end anchor window pops up(Figure 2.2).

Figure 2.2 Fixed-end anchor window

• Enter an Equivalent length of 15 m (half the width of the excavation) and click OK(the orientation angle remains 0 ◦).

Hint: A fixed-end anchor is represented by a rotated T with a fixed size. This objectis actually a spring of which one end is connected to the mesh and the otherend is fixed. The orientation angle and the equivalent length of the anchormust be directly entered in the properties window. The equivalent length isthe distance between the connection point and the position in the direction ofthe anchor rod where the displacement is zero. By default, the equivalentlength is 1.0 unit and the angle is zero degrees (i.e. the anchor points in thepositive x-direction).

» Clicking the 'middle bar' of the corresponding T selects an existing fixed-endanchor.

To define the surface load:

Click the Distributed load - load system A button.

• Move the cursor to (43.0; 20.0) and click. Move the cursor 5 m to the right to (48.0;20.0) and click again. Right click to finish drawing.

• Click the Selection button and double click the distributed load.



• Select the Distributed load - load system A option from the list. Enter Y-values of –5kN/m2.

Boundary Conditions

To create the boundary conditions, click the Standard fixities button on the toolbar.As a result, the program will generate full fixities at the bottom and vertical rollers atthe vertical sides. These boundary conditions are in this case appropriate to modelthe conditions of symmetry at the right hand boundary (center line of theexcavation). The geometry model so far is shown in Figure 2.3.

Figure 2.3 Geometry model in the Input window

Material properties

After the input of boundary conditions, the material properties of the soil clusters andother geometry objects are entered in data sets. Interface properties are included in thedata sets for soil (Data sets for Soil and interfaces). Two data sets need to be created;one for the clay layer and one for the sand layer. In addition, a data set of the Plate typeis created for the diaphragm wall and a data set of the Anchor type is created for thestrut. To create the material data sets, follow these steps:

Click the Material sets button on the toolbar. Select Soil and interfaces as the Settype. Click the New button to create a new data set.

• For the clay layer, enter "Clay" for the Identification and select Soft soil as theMaterial model. Set the Drainage type to Undrained (A).

• Enter the properties of the clay layer, as listed Table 2.1.


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Table 2.1 Material properties of the sand and clay layer and the interfaces

Parameter Name Clay Sand Unit

General

Material model Model Soft soil Hardening soil -

Type of material behaviour Type Undrained (A) Drained -

Soil unit weight above phreatic level γunsat 16 17 kN/m3

Soil unit weight below phreatic level γsat 18 20 kN/m3

Initial void ratio einit 1.0 - -

Parameters

Modified compression index λ∗ 3.0· 10-2 - -

Modified swelling index κ∗ 8.5· 10-3 - -

Secant stiffness in standard drained triaxial test E ref50 - 4.0· 104 kN/m2

Tangent stiffness for primary oedometer loading E refoed - 4.0· 104 kN/m2

Unloading / reloading stiffness E refur - 1.2· 105 kN/m2

Power for stress-level dependency of stiffness m - 0.5 -

Initial void ratio einit ' 1.0 - kN/m2

Cohesion (constant) cref ' 1.0 0.0 kN/m2

Friction angle ϕ' 25 32 ◦

Dilatancy angle ψ 0.0 2.0 ◦

Poisson's ratio νur ' 0.15 0.2 -

Flow parameters

Permeability in horizontal direction kx 0.001 1.0 m/day

Permeability in vertical direction ky 0.001 1.0 m/day

Interfaces

Interface strength − Manual Manual -

Strength reduction factor inter. Rinter 0.5 0.67 -

Initial

K0 determination − Automatic Automatic -

Over-consolidation ratio OCR 1.0 1.0 -

Pre-overburden pressure POP 5.0 0.0 kN/m2

• Click the Interfaces tab. Select the Manual option in the Strength drop-down menu.Enter a value of 0.5 for the parameter Rinter . This parameter relates the strength ofthe soil to the strength in the interfaces, according to the equations:

tanϕinterface = Rinter tanϕsoil and cinter = Rinter csoil

where:

csoil = cref (see Table 2.1)

Hence, 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: A Virtual thickness factor can be defined for interfaces. This is a purelynumerical value, which can be used to optimise the numerical performanceof the interface. To define it, double click the structure and select the optioncorresponding to the interface from the appearing window. The Interfacewindow pops up where this value can be defined. Non-experienced usersare advised not to change the default value. For more information aboutinterface properties see the Reference Manual.

• For the sand layer, enter "Sand" for the Identification and select Hardening soil as



the Material model. The material type should be set to Drained.

• Enter the properties of the sand layer, as listed in Table 2.1, in the correspondingedit boxes of the General and Parameters tabsheet.

• Click the Interfaces tab. In the Strength box, select the Manual option. Enter a valueof 0.67 for the parameter Rinter . Close the data set.

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 thestiffness of the interface (Section 4.1.4 of the Reference Manual).

• In the Material sets window, click the Copy button while Sand is selected. A newmaterial set is created. Its properties are the same with 'Sand'. Identify it as "Bottominterface".

• Click the Interfaces tab. In the Strength box, select the Rigid option. The value ofthe parameter Rinter changes to 1. Close the data set.

Hint: Instead of accepting the default data sets of interfaces, data sets can directlybe assigned to interfaces in their properties window. This window appearsafter double clicking the corresponding geometry line and selecting theappropriate interface from the Select dialog box. On clicking the Changebutton behind the Material set parameter, the proper data set can beselected from the Material sets tree view.

• Drag the 'Sand' data set to the lower cluster of the geometry and drop it there.Assign the 'Clay' data set to the remaining four clusters (in the upper 20 m) andclose the Material sets window.

• By default, interfaces are automatically assigned the data set of the adjacent cluster.Double click to the bottom part of the interface (no wall) and assign 'Bottominterface' to both positive and negative interfaces.

• Set the Set type parameter in the Material sets window to Plates and click the Newbutton. Enter "Diaphragm wall" as an Identification of the data set and enter theproperties as given in Table 2.2. Click OK to close the data set.

• Drag the Diaphragm wall data set to the wall in the geometry and drop it as soon asthe cursor indicates that dropping is possible.

Table 2.2 Material properties of the diaphragm wall (Plate)


Type of behaviour Material type Elastic; Isotropic

Normal stiffness EA 7.5 · 106 kN/m


Unit weight w 10.0 kN/m/m


• Set the Set type parameter in the Material sets window to Anchors and click New.


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Enter "Strut" as an Identification of the data set and enter the properties as given inTable 2.3. Click the OK button to close the data set.

• Drag the Strut data set to the anchor in the geometry and drop it as soon as thecursor indicates that dropping is possible. Close the Material sets window.

Table 2.3 Material properties of the strut (anchor)


Type of behaviour Material type Elastic -

Normal stiffness EA 2·106 kN

Spacing out of plane Lspacing 5.0 m

Hint: PLAXIS 2D 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 data sets of all tutorials in this TutorialManual are stored in the global database during the installation of theprogram. To copy an existing data set, click the Show global button of theMaterial sets window. Drag the appropriate data set from the tree view of theglobal database to the project database and drop it. Now the global data setis available for the current project. Similarly, data sets created in the projectdatabase may be dragged and dropped in the global database.

Mesh Generation

The default global coarseness parameter (Medium) can be accepted in this case. Thegenerated mesh is displayed in the Output program (Figure 2.4).

Figure 2.4 Resulting mesh



Hint: The mesh settings are stored together with the rest of the input. Onre-entering an existing project and not changing the geometry configurationand mesh settings, the same mesh can be regenerated by just clicking theGenerate mesh button on the toolbar. However, any slight change of thegeometry will result in a different mesh.

2.2 CALCULATIONS

In practice, the construction of an excavation is a process that can consist of severalphases. First, the wall is installed to the desired depth. Then some excavation is carriedout to create space to install an anchor or a strut. Then the soil is gradually removed tothe final depth of the excavation. Special measures are usually taken to keep the waterout of the excavation. Props may also be provided to support the retaining wall.

In PLAXIS, these processes can be simulated with the Staged construction calculationoption. Staged construction enables the activation or deactivation of weight, stiffness andstrength of selected components of the finite element model. The current tutorial explainsthe use of this powerful calculation option for the simulation of excavations.

Click the Calculations tab. The calculation process for this example will be performed inthe Classical mode.

Phase 0: Initial phase

The initial conditions of the current project require the generation of water pressures, thedeactivation of structures and loads and the generation of initial stresses. Waterpressures (pore pressures and water pressures on external boundaries) can begenerated in two different ways: A direct generation based on the input of phreatic levelsand groundwater heads or an indirect generation based on the results of a groundwaterflow calculation. The current tutorial only deals with the direct generation procedure.Generation based on groundwater flow is presented in Section 3.2.

Within the direct generation option there are several ways to prescribe the waterconditions. The simplest way is to define a general phreatic level, under which the waterpressure distribution is hydrostatic, based on the input of a unit water weight. The generalphreatic level is automatically assigned to all clusters for the generation of porepressures. It is also used to generate external water pressures, if applicable. Instead ofthe general phreatic level, individual clusters may have a separate phreatic level or aninterpolated pore pressure distribution. The latter advanced options will be demonstratedin Section 3.2. Here only a general phreatic level is defined at 2.0 m below the groundsurface.

In order to define the water conditions of the initial phase, follow these steps:

• The K0 procedure is automatically selected as calculation type of the initial phase.

• In the Parameters tabsheet, click the Define button to enter the Staged constructionmode.

• In the Water conditions mode the General water level is generated at the bottom ofthe geometry.

Click the Phreatic level button. Move the cursor to position (0; 18.0) and click the left


TUTORIAL MANUAL

Hint: The water weight can be modified after selecting the Water option in theGeometry menu of the Input program opened for Staged construction.

mouse button. Move to the right (65; 18.0) and click again. Click the right mousebutton to finish drawing. The plot now indicates a new General phreatic level 2.0 mbelow the ground surface.

The Generate by phreatic level option is selected in the drop-down menu at the leftof the Water pressures button.

Click the Water pressures button to generate the water pressures. The pressuredistribution is displayed in the Output program (Figure 2.5).

• Click the Close button to go to the Input program.

Figure 2.5 Steady state pore pressures

Hint: An existing water level may be modified by using the Selection button. Ondeleting the General phreatic level (selecting it and pressing the <Delete>key on the keyboard), the default general phreatic level will be created againat the bottom of the geometry. The graphical input or modification of waterlevels does not affect the existing geometry.

» To create an accurate pore pressure distribution in the geometry, anadditional geometry line can be included corresponding with the level of thegroundwater head or the position of the phreatic level in a project.

• Make sure that the structural elements (structures, interfaces and loads) are notactive in the Staged construction mode. The program automatically deactivatesthem for the initial phase.

• Click the Update button to proceed with the definition of phases in the Calculationsprogram.

Phase 1: External load

• Click Next to add a new phase.



• In the General tabsheet, accept all defaults.

• In the Parameters tabsheet, accept all defaults. Click the Define button.

• In the Staged construction mode the full geometry is active except for the wall, strutand load. Click the wall to activate it. The wall becomes the color that is specified inthe material dataset.

• Click the load to activate it. The load has been defined in Input as −5kN/m2. Thevalue can be checked in the window that pops up when the load is double clicked.

Hint: You can also enter or change the values of the load at this time by doubleclicking the load and entering a value. If a load is applied on a structuralobject such as a plate, load values can be changed by clicking the load orthe object. As a result a window appears in which you can select the load.Then click the Change button to modify the load values.

• Make sure all the interfaces in the model are active. In the Water conditions modenote that the interfaces below the wall are not activated (not indicated by the orangecolour). This is correct because there is no impermeability below the wall.

Hint: The selection of an interface is done by selecting the correspondinggeometry line and subsequently selecting the corresponding interface(positive or negative) from the Select dialog box.

• Click the Update button to finish the definition of the construction phase. As a result,the Input program is closed and the Calculations program re-appears. The firstcalculation phase has now been defined and saved.

Phase 2: First excavation stage


• A new calculation phase appears in the list. Note that the program automaticallypresumes that the current phase should start from the previous one.

• In the General tabsheet, accept all defaults. Enter the Parameters tabsheet andclick Define.

• In the Staged construction mode all the structure elements except the fixed-endanchor are active. Click the top right cluster in order to deactivate it and simulate thefirst excavation step.

• Click the Update button to finish the definition of the first excavation phase.

Phase 3: Installation of strut


• In the Parameters tabsheet click Define.

• In the Staged construction mode activate the strut by clicking the horizontal line. The


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strut should turn black to indicate it is active.

• Click Update to return to the calculation program and define another calculationphase.

Phase 4: Second (submerged) excavation stage


• In the Parameters tabsheet keep all default settings and click Define. This phase willsimulate the excavation of the second part of the building pit. In the Stagedconstruction mode deactivate the second cluster from the top on the right side of themesh. It should be the topmost active cluster.

• Click Update to proceed with the definition of the final stage.

Hint: Note that in PLAXIS the pore pressures are not automatically deactivatedwhen deactivating a soil cluster. Hence, in this case, the water remains in theexcavated area and a submerged excavation is simulated.

Phase 5: Third excavation stage


• In the final calculation stage the excavation of the last clay layer inside the pit issimulated. Deactivate the third cluster from the top on the right hand side of themesh.

• Click Update to return to the Calculations program.

The calculation definition is now complete. Before starting the calculation it is suggestedthat you select nodes or stress points for a later generation of load-displacement curvesor stress and strain diagrams. To do this, follow the steps given below.

Click the Select points for curves button on the toolbar. The connectivity plot isdisplayed in the Output program and the Select points window is activated.

• Select some nodes on the wall at points where large deflections can be expected(e.g. 50.0; 10.0). The nodes located near that specific location are listed. Select theconvenient one by checking the box in front of it in the list. Close the Select pointswindow.

• Click the Update button to go back to the Calculations program.

Calculate the project.

During a Staged construction calculation, a multiplier called ΣMstage is increased from0.0 to 1.0. This parameter is displayed on the calculation info window. As soon asΣMstage has reached the value 1.0, the construction stage is completed and thecalculation phase is finished. If a Staged construction calculation finishes while ΣMstageis smaller than 1.0, the program will give a warning message. The most likely reason fornot finishing a construction stage is that a failure mechanism has occurred, but there canbe other causes as well. See the Reference Manual for more information about Stagedconstruction.



In this example, all calculation phases should successfully finish, which is indicated bythe green check marks in the list. In order to check the values of the ΣMstage multiplier,click the Multipliers tab and select the Reached values radio button. The ΣMstageparameter is displayed at the bottom of the Other box that pops up. Verify that this valueis equal to 1.0. You also might wish to do the same for the other calculation phases.

2.3 RESULTS

In addition to the displacements and the stresses in the soil, the Output program can beused to view the forces in structural objects. To examine the results of this project, followthese steps:

• Click the final calculation phase in the Calculations window.

Click the View calculation results button on the toolbar. As a result, the Outputprogram is started, showing the deformed mesh (scaled up) at the end of theselected calculation phase, with an indication of the maximum displacement (Figure2.6).

Figure 2.6 Deformed mesh after the third excavation stage

Hint: In the Output program, the display of the loads, fixities and prescribeddisplacements applied in the model can be toggled on/off by clicking thecorresponding options in the Geometry menu.

• Select |∆u| from the side menu displayed as the mouse pointer is located on theIncremental displacements option of the Deformations menu. The plot shows colourshadings of the displacement increments.

Click the Arrows button in the toolbar. The plot shows the displacement incrementsof all nodes as arrows. The length of the arrows indicates the relative magnitude.

• In the Stresses menu point to the Principal effective stresses and select theEffective principal stresses option from the appearing menu. The plot shows theaverage effective principal stresses at the center of each soil element with an


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indication of their direction and their relative magnitude. Note that the Centralprincipal stresses button is selected in the toolbar. The orientation of the principalstresses indicates a large passive zone under the bottom of the excavation and asmall passive zone behind the strut (Figure 2.7).

Figure 2.7 Principal stresses after excavation

To plot the shear forces and bending moments in the wall follow the steps given below.

• Double-click the wall. A new window is opened showing the axial force.

• Select the bending moment M from the Forces menu. The bending moment in thewall is displayed with an indication of the maximum moment (Figure 2.8).

Figure 2.8 Bending moments in the wall

• Select Shear forces Q from the Forces menu. The plot now shows the shear forcesin the wall.

Hint: The Window menu may be used to switch between the window with theforces in the wall and the stresses in the full geometry. This menu may alsobe used to Tile or Cascade the two windows, which is a common option in aWindows environment.



• Select the first window (showing the effective stresses in the full geometry) from theWindow menu. Double-click the strut. The strut force (in kN/m) is shown in thedisplayed table. This value must be multiplied by the out of plane spacing of thestruts to calculate the individual strut forces (in kN).

• Click the Curves manager button on the toolbar. As a result, the Curves managerwindow will pop up.

• Click New to create a new chart. The Curve generation window pops up.

• For the x-axis select the point A from the drop-down menu. In the tree selectDeformations - Total displacements - |u|.

• For the y-axis keep the Project option in the drop-down menu. In the tree selectMultiplier - ΣMstage.

• Click OK to accept the input and generate the load-displacement curve. As a resultthe curve of Figure 2.9 is plotted.

Figure 2.9 Load-displacement curve of deflection of wall

The curve shows the construction stages. For each stage, the parameter ΣMstagechanges from 0.0 to 1.0. The decreasing slope of the curve in the last stage indicatesthat the amount of plastic deformation is increasing. The results of the calculationindicate, however, that the excavation remains stable at the end of construction.


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DRY EXCAVATION USING A TIE BACK WALL

3 DRY EXCAVATION USING A TIE BACK WALL

This example involves the dry construction of an excavation. The excavation is supportedby concrete diaphragm walls. The walls are tied back by prestressed ground anchors.

10 m 2 m 20 m

5 m

Silt

Sand

Loam

ground anchor

Final excavation level

3 m

3 m

4 m

10 kN/m2

Figure 3.1 Excavation supported by tie back walls

PLAXIS allows for a detailed modelling of this type of problem. It is demonstrated in thisexample how ground anchors are modelled and how prestressing is applied to theanchors. Moreover, the dry excavation involves a groundwater flow calculation togenerate the new water pressure distribution. This aspect of the analysis is explained indetail.

Objectives:

• Modelling ground anchors.

• Generating pore pressures by groundwater flow.

• Displaying the contact stresses and resulting forces in the model (Forces view).

• Scaling the displayed results.

3.1 INPUT

The excavation is 20 m wide and 10 m deep. 16 m long concrete diaphragm walls of 0.35m thickness are used to retain the surrounding soil. Two rows of ground anchors areused at each wall to support the walls. The anchors have a total length of 14.5 m and aninclination of 33.7◦ (2:3). On the left side of the excavation a surface load of 10 kN/m2 istaken into account.

The relevant part of the soil consists of three distinct layers. From the ground surface to adepth of 3 m there is a fill of relatively loose fine sandy soil. Underneath the fill, down to aminimum depth of 15 m, there is a more or less homogeneous layer consisting of densewell-graded sand. This layer is particular suitable for the installation of the groundanchors. The underlying layer consists of loam and lies to a large depth. 15 m of thislayer is considered in the model. In the initial situation there is a horizontal phreatic levelat 3 m below the ground surface (i.e. at the base of the fill layer).


TUTORIAL MANUAL

General settings



• Keep the default units and set the model dimensions to Xmin = 0.0, Xmax = 100.0,Ymin = 0.0 and Ymax = 30.0. Keep the default values for the grid spacing (Spacing =1 m; Number of intervals = 1).

Geometry model

The proposed geometry model is given in Figure 3.2.

x

y

28 m 10 m 2 m

11

20 m 40 m

3

3

4

5

13

(0; 0)

(0; 15)

(0; 27)

(0; 30)

Embedded pile row

Node-to-node anchors

Figure 3.2 Geometry model of building pit

To define the geometry:

• Define the soil clusters as shown in Figure 3.2. The excavation is constructed inthree excavation stages. The separation between the stages is modelled using theGeometry line as well.

Model the diaphragm walls (16 m long) as plates.

The interfaces around the plates are used to model the soil-structure interactioneffects. Extend the interfaces 1 m under the wall.

Hint: The extended part of an interface is not used for soil-structure interaction andshould therefore have the same strength as the surrounding soil. This can beachieved with a strength reduction factor Rinter = 1.0, which is automaticallyadopted in the Rigid selection. If necessary, a separate material data setmust be created for the extended part of an interface. In addition, theextended part of an interface should not influence the flow field. This isachieved by deactivating the interface when generating the pore pressures.

A ground anchor can be modelled by a combination of a node-to-node anchor and anembedded pile. The embedded pile simulates the grout body whereas the node-to-nodeanchor simulates the anchor rod. In reality there is a complex three-dimensional state of



stress around the grout body.

Define the node-to-node anchors according to Table 3.1.

Table 3.1 Node to node anchor coordinatesAnchor location First point Second point

TopLeft (40; 27) (31; 21)

Right (60; 27) (69; 21)

BottomLeft (40; 23) (31; 17)

Right (60; 23) (69; 17)

Define the grout body using the Embedded pile row button according to Table 3.2.

Table 3.2 Grout coordinatesGrout location First point Second point

TopLeft (31; 21) (28; 19)

Right (69; 21) (72; 19)

BottomLeft (31; 17) (28; 15)

Right (69; 17) (72; 15)

• Double click the grout part of one of the ground anchors. In the appearing windowselect the Embedded pile row option and press OK.

• In the appearing window set the connection of the embedded piles to Free (Figure3.3). This is needed to set the top free from the underlying soil element. Theconnection with the anchor will be automatically established.

• Do the same for the remaining three ground anchors.

Figure 3.3 Geometry model of building pit

Although the precise stress state and interaction with the soil cannot be modelled withthis 2D model, it is possible in this way to estimate the stress distribution, thedeformations and the stability of the structure on a global level, assuming that the groutbody does not slip relative to the soil. With this model it is certainly not possible toevaluate the pullout force of the ground anchor.

Define a distributed load between (28; 30) and (38; 30).

The Standard fixities can be used to generate the proper boundary conditions.

Material properties

The properties of the concrete diaphragm wall are entered in a material set of the Platetype. The concrete has a Young's modulus of 35 GN/m2 and the wall is 0.35 m thick. Theproperties are listed in Table 3.3.


TUTORIAL MANUAL

Table 3.3 Properties of the diaphragm wall (plate)



End bearing − Yes -



Weight w 8.3 kN/m/m


For the properties of the ground anchors, two material data sets are needed: One of theAnchor type and one of the Embedded pile row type. The Anchor data set contains theproperties of the anchor rod and the Embedded pile row data set contains the propertiesof the grout body. The data are listed in Table 3.4 and 3.5.

Table 3.4 Properties of the anchor rod (node-to-node anchor)


Material type Type Elastic -

Normal stiffness EA 5.0· 105 kN

Spacing out of plane Ls 2.5 m

Table 3.5 Properties of the grout body (embedded pile row)


Stiffness E 2.5·106 -

Unit weight γ 0 kN/m3

Pile type Type Predefined -

Predefined pile type Type Massive circular pile -

Diameter D 0.3 m

Pile spacing Lspacing 2.5 m

Skin resistanceTtop,max 400 kN/m

Tbot ,max 400 kN/m

Base resistance Fmax 0 kN/m

Interface stiffness factor - Default values -

The soil consists of three distinct layers. Enter three data sets for soil and interfaces withthe parameters given in Table 3.6.

Mesh generation

The default global coarseness parameter (Medium) can be accepted in this case. Thegenerated mesh is displayed in the Output program (Figure 3.4).




Table 3.6 Soil and interface properties

Parameter Name Silt Sand Loam Unit

General

Material model Model Hardening soil Hardening soil Hardening soil -

Type of material behaviour Type Drained Drained Drained -

Soil unit weight above phreatic level γunsat 16 17 17 kN/m3

Soil unit weight below phreatic level γsat 20 20 19 kN/m3

Parameters

Secant stiffness in standard drainedtriaxial test

E ref50 2.0· 104 3.0· 104 1.2· 104 kN/m2

Tangent stiffness for primaryoedometer loading

E refoed 2.0· 104 3.0· 104 8.0· 103 kN/m2

Unloading / reloading stiffness E refur 6.0· 104 9.0· 104 3.6· 104 kN/m2

Power for stress-level dependency ofstiffness

m 0.5 0.5 0.8 -

Cohesion cref ' 1.0 0.0 5.0 kN/m2

Friction angle ϕ' 30 34 29 ◦

Dilatancy angle ψ 0.0 4.0 0.0 ◦

Poisson's ratio νur ' 0.2 0.2 0.2 -

Flow parameters

Data set - USDA USDA USDA -

Model - VanGenuchten

VanGenuchten

VanGenuchten

-

Soil type - Silt Sand Loam -

< 2µm - 6.0 4.0 20.0 %2µm − 50µm - 87.0 4.0 40.0 %50µm − 2mm - 7.0 92.0 40.0 %Set parameters to defaults - Yes Yes Yes -

Permeability in horizontal direction kx 0.5996 7.128 0.2497 m/day

Permeability in vertical direction ky 0.5996 7.128 0.2497 m/day

Interfaces

Interface strength − Manual Manual Rigid -

Strength reduction factor inter. Rinter 0.65 0.70 1.0 -

Consider gap closure − Yes Yes Yes -

Initial

K0 determination − Automatic Automatic Automatic -

Over-consolidation ratio OCR 1.0 1.0 1.0 -

Pre-overburden pressure POP 0.0 0.0 25.0 kN/m2

3.2 CALCULATIONS

The calculation of this project is performed in the Classical mode and it consists of sixphases. In the initial phase (Phase 0), the initial stresses are generated. In the Phase 1,the walls are constructed and the surface loads are activated. In the Phase 2, the first 3m of the pit is excavated without connection of anchors to the wall. At this depth theexcavation remains dry. In the Phase 3, the first anchor is installed and pre-stressed. ThePhase 4 involves further excavation to a depth of 7 m. At this depth the excavation stillremains dry. In the Phase 5, the second anchor is installed and pre-stressed. The Phase6 is a further excavation to the final depth of 10 m including the dewatering of theexcavation. This involves a groundwater flow analysis to calculate the new pore waterdistribution.

All calculation phases are defined as Plastic calculations using Staged construction asLoading input and standard settings for all other parameters. The instructions givenbelow are limited to a description of how the phases are defined within the Staged


TUTORIAL MANUAL

construction mode.

Initial phase:

The initial stress field is generated by means of the K0 procedure using the defaultK0-values in all clusters defined automatically by the program.

• Initially, all structural components are inactive. Hence, make sure that the plates, thenode-to-node anchors, the embedded pile rows and the surface loads aredeactivated in the Staged construction mode.

In the Water conditions mode of the Input program, click the Phreatic level buttonand draw the phreatic level through (0; 23) and (100; 23).

Hint: Note that when the pore pressures are generated by phreatic level, thegeometry of the defined phreatic level is important.

Phase 1:


• In the Staged construction mode activate the walls and the interfaces (all).

• Double click the load. Enter a Y-value = −10 kPa.

• Clicking an interface in the Water conditions mode activates or deactivates theinterface during groundwater calculations. An active interface is marked with anorange circle and is considered impermeable during groundwater calculations. Notethat all the interfaces except the ones below the walls are active in the Waterconditions mode. Those should remain inactive (permeable) during the groundwaterflow calculation.

Configuration of Phase 1 in the Staged construction mode

Phase 2:


• In the Staged construction mode de-activate the upper cluster of the excavation.




Phase 3:


• In the Staged construction mode activate the upper embedded pile rows.

• Double-click the upper node-to-node anchors. A node-to-node anchor propertieswindow appears with the anchor pre-stress options. Select the Adjust pre-stressforce box and enter a pre-stress force of 200 kN/m. Click OK to close the window.


Hint: A pre-stress force is exactly matched at the end of a finished stagedconstruction calculation and turned into an anchor force. In successivecalculation phases the force is considered to be just an anchor force and cantherefore further increase or decrease, depending on the development of thesurrounding stresses and forces.

Phase 4:


• Deactivate the second cluster of the excavation.

Phase 5


• In the Staged construction mode activate the lower embedded pile rows.


TUTORIAL MANUAL


• Double-click the lower node-to-node anchors. In the Node-to-node anchor window,select the Adjust pre-stress force box and enter a pre-stress force of 400 kN/m.

• Click OK to close the window.


Phase 6


• In the Staged construction mode, deactivate the third cluster of the excavation.

Now the boundary conditions for the groundwater flow calculation have to be entered. Atthe side boundaries, the groundwater head remains at a level of 23.0 m. The bottomboundary of the problem should be closed. The flow of groundwater is triggered by thefact that the pit is pumped dry. At the bottom of the excavation the water pressure is zero,which means that the groundwater head is equal to the vertical level (head = 20.0 m).This condition can be met drawing a new general phreatic level and performing agroundwater flow calculation. Activating the interfaces during the groundwater flowcalculation prevents flow through the wall.

In order to prescribe correctly these boundary conditions, follow these steps:

In the Water conditions mode click the Phreatic level button and draw a newphreatic level. Start at (0.0; 23.0) and draw the phreatic level through (40.0; 20.0),(60.0; 20.0) and end in (100.0; 23.0).

The Steady state groundwater flow option should be selected in the drop-downmenu in the toolbar.



Configuration of Phase 6 in the Water conditions mode

Hint: Note that for Groundwater flow (steady or transient) the points of intersectionof the water level and boundaries are important. The program calculates thewater level accordingly. The line drawn connecting these points has no effectin the calculation. It only helps as a visualisation tool.

After all calculation phases have been defined, some points for load-displacement curvesshould be selected (for example the connection points of the ground anchors on thediaphragm wall). Start the calculation by clicking the Calculate button.

3.3 RESULTS

Figures 3.11 to 3.15 show the deformed meshes at the end of calculation phases 2 to 6.

Figure 3.11 Deformed mesh (scaled up 50.0 times) - Phase 2



TUTORIAL MANUAL



Figure 3.15 Deformed mesh (scaled up 50.0 times) - Final phase

Figure 3.16 shows the effective principal stresses in the final situation. The passivestress state beneath the bottom of the excavation is clearly visible. It can also be seenthat there are stress concentrations around the grout anchors.

Figure 3.16 Principal stress directions (final stage)

Figure 3.17 shows the bending moments in the diaphragm walls in the final state. Thetwo dips in the line of moments are caused by the anchor forces.



Figure 3.17 Bending moments in the diaphragm walls in the final stage

Select the Forces view option in the Tools menu to display the contact stresses andforces in the final calculation phase. The Forces dialog window pops up where aselection of the resulting forces to be displayed can be made. Accept the defaultselection.

Click the Hide soil button and keep the <Shift> key pressed while clicking all the soilclusters. The resulting stresses in structures is displayed in Figure 3.18.

Figure 3.18 Contact stresses in structures

The anchor force can be viewed by double clicking the anchor. When doing this for theresults of the third and the fifth calculation phase, it can be checked that the anchor forceis indeed equal to the specified pre-stress force in the calculation phase they areactivated. In the following phases this value might change due to the changes in themodel.


TUTORIAL MANUAL


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 three new calculation options areintroduced, namely a consolidation analysis, an updated mesh analysis and thecalculation of a safety factor by means of a safety analysis (phi/c-reduction).

4 m

3 m

3 m

12 m12 m 16 m

road embankment

peat

clay

dense sand

Figure 4.1 Situation of a road embankment on soft soil

Objectives:

• Consolidation analysis

• Modelling drains

• Change of permeability during consolidation

• Updated mesh analysis (large deformations)

• Safety analysis (phi-c reduction)

4.1 INPUT

Figure 4.1 shows a cross section of a road embankment. The embankment is 16.0 mwide and 4.0 m high. The slopes have an inclination of 1:3. The problem is symmetric, soonly one half is modelled (in this case the right half is chosen). The embankment itself iscomposed of loose sandy soil. The subsoil consists of 6.0 m of soft soil. The upper 3.0 mof this soft soil layer is modelled as a peat layer and the lower 3.0 m as clay. The phreaticlevel is located 1 m below the original ground surface. Under the soft soil layers there is adense sand layer of which 4.0 m are considered in the model.

General settings




TUTORIAL MANUAL

• Keep the default units and set the model dimensions to Xmin = 0.0, Xmax = 60.0,Ymin = −10.0 and Ymax = 4.0. Keep the default values for the grid spacing (Spacing= 1 m; Number of intervals = 1).

Geometry model

The full geometry can be drawn using the Geometry line option. In this model, theground level before the construction of the embankment is the reference level in thevertical direction (y = 0) (Figure 4.2).

In this example the effect of the drains on the consolidation process will beinvestigated. Drains are defined in the soft layers (clay and peat; y = 0.0 to y = -6).The distance between two consecutive drains is 2 m. Considering the symmetry, thefirst drain is located at 1 m distance from the model boundary.

The Standard fixities can be used to define the boundary conditions. The geometrymodel is shown in Figure 4.2.

x

y

embankment

peat

sand

clay

4 m

(0; 4)

(0; 2)

(0; 0)

(0; -3)

(0; -6)

(0; -10)

8 m 12 m 40 m

1 m 2 m

2 m

2 m

3 m

3 m

Figure 4.2 Geometry model of road embankment project

Material sets and mesh generation

The properties of the different soil types are given in Table 4.1. The clay and the peatlayer are undrained. This type of behaviour leads to an increase of pore pressures duringthe construction of the embankment. Assign the data to the corresponding clusters in thegeometry model. After the input of material parameters, a simple finite element meshmay be generated. The default mesh settings will be used in this tutorial.

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 only recommended when usingadvanced models.




Table 4.1 Material properties of the road embankment and subsoil

Parameter Name Embankment Sand Peat Clay Unit

General

Material model Model Hardeningsoil

Hardeningsoil

Soft soil Soft soil -

Type of materialbehaviour

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

Soil unit weight abovephreatic level

γunsat 16 17 8 15 kN/m3

Soil unit weight belowphreatic level

γsat 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

λ∗ - - 0.15 0.05 -

Modified swelling index κ∗ - - 0.03 0.01 -

Cohesion cref ' 1.0 0.0 2.0 1.0 kN/m2

Friction angle ϕ' 30 33 23 25 ◦

Dilatancy angle ψ 0.0 3.0 0 0 ◦

Advanced: Set todefault

Yes Yes Yes Yes Yes Yes

Flow parameters

Data set - USDA USDA USDA USDA -


VanGenuchten

VanGenuchten

VanGenuchten

-

Soil type - Loamy sand Sand Clay Clay -

> 2µm - 6.0 4.0 70.0 70.0 %2µm − 50µm - 11.0 4.0 13.0 13.0 %50µm − 2mm - 83.0 92.0 17.0 17.0 %Set to default - Yes Yes No Yes -

Horizontal permeability kx 3.499 7.128 0.1 0.04752 m/day

Vertical permeability ky 3.499 7.128 0.02 0.04752 m/day

Change 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

4.2 CALCULATIONS

The embankment construction is divided into two phases. After the first constructionphase a consolidation period of 30 days is introduced to allow the excess pore pressuresto dissipate. After the second construction phase another consolidation period isintroduced from which the final settlements may be determined. Hence, a total of fourcalculation phases have to be defined besides the initial phase. The calculation processis defined and performed in the Classical mode.


In the initial situation the embankment is not present. In order to generate the initialstresses therefore, the embankment must be deactivated first in the Staged constructionmode.

• In the Staged construction mode click once in the two clusters that represent theembankment, just like in a staged construction calculation. When the embankmenthas been deactivated (the corresponding clusters should have the backgroundcolour), the remaining active geometry is horizontal with horizontal layers, so the K0procedure can be used to calculate the initial stresses.

The initial water pressures are fully hydrostatic and based on a general phreatic levelthrough the points (0.0; -1.0) and (60.0; -1.0). In addition to the phreatic level, attentionmust be paid to the boundary conditions for the consolidation analysis that will beperformed during the calculation process. Without giving any additional input, allboundaries are draining so that water can freely flow out of all boundaries and excesspore pressures can dissipate in all directions. In the current situation, however, the leftvertical boundary must be closed because this is a line of symmetry, so horizontal flowshould not occur. The right vertical boundary should also be closed because there is nofree outflow at that boundary. The bottom is open because the excess pore pressurescan freely flow into the deep and permeable sand layer. The upper boundary is obviouslyopen as well. In order to create the appropriate consolidation boundary conditions, followthese steps:

In the Water conditions mode click the Closed boundary button in the toolbar.

• Define closed boundaries between (0.0; 4.0) and (0.0; -10.0) and between (60.0;0.0) and (60.0; -10.0).

• Select the boundary at the bottom of the model and press <Delete>. In theappearing window select the Closed flow boundary option.

• Click the Update button to proceed with definition of the calculation phases.

Hint: Closed consolidation boundaries can only be defined by clicking existinggeometry points. The program will automatically find intermediate geometrypoints.



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:

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 for a given number of steps, using incremental multipliers to globallyincrease load systems in time or to apply rate loading (Incremental multiplier).

4. Consolidate until a specified degree of saturation is reached (Degree ofconsolidation).

The first two possibilities will be used in this exercise. To define the calculation phases,follow these steps:

Phase 1: The first calculation stage is a Consolidation analysis, Staged construction.

• In the General tabsheet select Consolidation option from the Calculation typedrop-down menu.

• Make sure that the Staged construction option is selected for the Loading input.Enter a Time interval of 2 days.

• Click the Define button. In the Staged construction mode activate the first part of theembankment

• In the Water conditions mode check that the left boundary of the first embankmentlayer is Closed.

• Click the Update button to go back to the Calculations window and click the Nextbutton to introduce the next calculation phase.

Phase 2: The second phase is also a Consolidation analysis, Staged construction. Inthis phase no changes to the geometry are made as only a consolidation analysis toultimate time is required.

• In the General tabsheet define the calculation type as Consolidation (EPP).

• In the Parameters window enter a time interval of 30 days and click the Next buttonto introduce the next calculation phase.

Phase 3: The third phase is once again a Consolidation analysis, Staged construction.

• In the General tabsheet define the calculation type as Consolidation.

• In the Parameters tabsheet enter a time interval of 1 days.

• Click the Define button and activate the second part of the embankment in theStaged construction mode.

• In the Water conditions mode check that the left boundary of the secondembankment layer is Closed.


TUTORIAL MANUAL

• Click the Update button to go back to the Calculations window and click the Nextbutton to introduce the next calculation phase.

Phase 4: The fourth phase is a Consolidation analysis to a minimum pore pressure.

• In the General tabsheet define the calculation type as Consolidation. In theParameters tabsheet, select Minimum pore pressure from the Loading input box andaccept the default value of 1 kN/m2 for the minimum pressure.

Before starting the calculation, click the Select points for curves button and selectthe following points: As Point A, select the toe of the embankment. The second

point (Point B) will be used to plot the development (and decay) of excess pore pressures.To this end, a point somewhere in the middle of the soft soil layers is needed, close to(but not actually on) the left boundary. After selecting these points, start the calculation.

During a consolidation analysis the development of time can be viewed in the upper partof the calculation info window (Figure 4.4). In addition to the multipliers, a parameterPmax occurs, which indicates the current maximum excess pore pressure. Thisparameter is of interest in the case of a Minimum pore pressure consolidation analysis,where all pore pressures are specified to reduce below a predefined value.

Figure 4.4 Calculation progress displayed in the Active tasks window

4.3 RESULTS

After the calculation has finished, select the third phase and click the Viewcalculation results button. The Output window now shows the deformed mesh after

the undrained construction of the final part of the embankment (Figure 4.5). Consideringthe results of the third phase, the deformed mesh shows the uplift of the embankment toeand hinterland due to the undrained behaviour.

• In the Deformations menu select the Incremental displacements→ |∆u|.



Figure 4.5 Deformed mesh after undrained construction of embankment (Phase 3)

Select the Arrows option in the View menu or click the corresponding button in thetoolbar to display the results arrows.

On evaluating the total displacement increments, it can be seen that a failure mechanismis developing (Figure 4.6).

Figure 4.6 Displacement increments after undrained construction of embankment

• Click <Ctrl> + <7> to display the developed excess pore pressures (see Appendix Cof Reference Manual for more shortcuts). They can be displayed by selecting thecorresponding option in the side menu displayed as the Pore pressures option isselected in the Stresses menu.

Click the Center principal directions. The principal directions of excess pressuresare displayed at the center of each soil element. The results are displayed in Figure4.7. It is clear that the highest excess pore pressure occurs under the embankmentcentre.

Figure 4.7 Excess pore pressures after undrained construction of embankment

• Select Phase 4 in the drop down menu.

Click the Contour lines button in the toolbar to display the results as contours.

Use the Draw scanline button or the corresponding option in the View menu todefine the position of the contour line labels.

It can be seen that the settlement of the original soil surface and the embankmentincreases considerably during the fourth phase. This is due to the dissipation of theexcess pore pressures (= consolidation), which causes further settlement of the soil.


TUTORIAL MANUAL

Figure 4.8 Excess pore pressure contours after consolidation to Pexcess < 1.0 kN/m2

Figure 4.8 shows the remaining excess pore pressure distribution after consolidation.Check that the maximum value is below 1.0 kN/m2.

The Curves manager can be used to view the development, with time, of the excess porepressure under the embankment. In order to create such a curve, follow these steps:

Click the Curves manager button in the toolbar. The corresponding window pops up.

• In the Charts tabsheet click New. The Curve generation window pops up

• For the x-axis, select the Project option from the drop-down menu and select Timein the tree.

• For the y -axis select the point in the middle of the soft soil layers (Point B) from thedrop-down menu. In the tree select Stresses→ Pore pressure→ pexcess.

• Select the Invert sign option for y-axis. After clicking the OK button, a curve similarto Figure 4.9 should appear.

Figure 4.9 Development of excess pore pressure under the embankment

Figure 4.9 clearly shows the four calculation phases. During the construction phases theexcess pore pressure increases with a small increase in time while during theconsolidation periods the excess pore pressure decreases with time. In fact,consolidation already occurs during construction of the embankment, as this involves a



small time interval. From the curve it can be seen that more than 80 days are needed toreach full consolidation.

• Save the chart before closing the Output program.

4.4 SAFETY ANALYSIS

In the design of an embankment it is important to consider not only the final stability, butalso the stability during the construction. It is clear from the output results that a failuremechanism starts to develop after the second construction phase.

It is interesting to evaluate a global safety factor at this stage of the problem, and also forother stages of construction.

In structural engineering, the safety factor is usually defined as the ratio of the collapseload to the working load. For soil structures, however, this definition is not always useful.For embankments, for example, most of the loading is caused by soil weight and anincrease in soil weight would not necessarily lead to collapse. Indeed, a slope of purelyfrictional soil will not fail in a test in which the self weight of the soil is increased (like in acentrifuge test). A more appropriate definition of the factor of safety is therefore:

Safety factor = Smaximum available

Sneeded for equilibrium(4.1)

Where S represents the shear strength. The ratio of the true strength to the computedminimum strength required for equilibrium is the safety factor that is conventionally usedin soil mechanics. By introducing the standard Coulomb condition, the safety factor isobtained:

Safety factor =c − σn tanϕ

cr −σn tanϕr(4.2)

Where c and ϕ are the input strength parameters and σn is the actual normal stresscomponent. The parameters cr and ϕr are reduced strength parameters that are justlarge enough to maintain equilibrium. The principle described above is the basis of themethod of Safety that can be used in PLAXIS to calculate a global safety factor. In thisapproach the cohesion and the tangent of the friction angle are reduced in the sameproportion:

ccr

=tanϕtanϕr

= ΣMsf (4.3)

The reduction of strength parameters is controlled by the total multiplier ΣMsf . Thisparameter is increased in a step-by-step procedure until failure occurs. The safety factoris then defined as the value of ΣMsf at failure, provided that at failure a more or lessconstant value is obtained for a number of successive load steps.

The Safety calculation option is available in the Calculation type drop-down menu in theGeneral tabsheet. If the Safety option is selected the Loading input on the Parameterstabsheet is automatically set to Incremental multipliers.

To calculate the global safety factor for the road embankment at different stages ofconstruction, follow these steps:

• We first want to calculate the safety factor after the first construction stage. In theCalculations program introduce a new calculation phase and select Phase 1 in theStart from phase drop-down menu.


TUTORIAL MANUAL

• In the General tabsheet, select Safety as calculation type.

• In the Parameters tabsheet set the number of Additional steps to 30. In order toexclude existing deformations from the resulting failure mechanism, select the Resetdisplacements to zero option. The Incremental multipliers option is already selectedin the Loading input box. The first increment of the multiplier that controls thestrength reduction process, Msf, is set to 0.1. The first safety calculation has nowbeen defined.

• Follow the same steps to create new calculation phases that analyse the stability atthe end of each consolidation phase.

Hint: The default value of Additional steps in a Safety calculation is 100. Incontrast to an Staged construction calculation, the number of additional stepsis always fully executed. In most Safety calculations, 100 steps are sufficientto arrive at a state of failure. If not, the number of additional steps can beincreased to a maximum of 1000.

» For most Safety analyses Msf = 0.1 is an adequate first step to start up theprocess. During the calculation process, the development of the totalmultiplier for the strength reduction, ΣMsf , is automatically controlled by theload advancement procedure.

Before starting the calculations, make sure that only the new calculation phases areselected for execution (→); the others should be indicated with the

√-sign.

Evaluation of results

Additional displacements are generated during a Safety calculation. The totaldisplacements do not have a physical meaning, but the incremental displacements in thefinal step (at failure) give an indication of the likely failure mechanism.

In order to view the mechanisms in the three different stages of the embankmentconstruction:

Select one of these phases and click the View calculation results button.

• From the Deformations menu select Incremental displacements→ |∆u|.Change the presentation from Arrows to Shadings. The resulting plots give a goodimpression of the failure mechanisms (Figure 4.10). The magnitude of thedisplacement increments is not relevant.

Figure 4.10 Shadings of the total displacement increments indicating the most applicable failuremechanism of the embankment in the final stage



The safety factor can be obtained from the Calculation info option of the Project menu.The Multipliers tabsheet of the Calculation information window represents the actualvalues of the load multipliers. The value of ΣMsf represents the safety factor, providedthat this value is indeed more or less constant during the previous few steps.

The best way to evaluate the safety factor, however, is to plot a curve in which theparameter ΣMsf is plotted against the displacements of a certain node. Although thedisplacements are not relevant, they indicate whether or not a failure mechanism hasdeveloped.

In order to evaluate the safety factors for the three situations in this way, follow thesesteps:

• Click the Curves manager button in the toolbar.

• Click New in the Charts tabsheet.

• In the Curve generation window, select the embankment toe (Point A) for the x-axis.Select Deformations→ Total displacements→ |u|.

• For the y -axis, select Project and then select Multipliers→ ΣMsf . The Safetyphases are considered in the chart. As a result, the curve of Figure 4.11 appears.

The maximum displacements plotted are not relevant. It can be seen that for all curves amore or less constant value of ΣMsf is obtained. Hovering the mouse cursor over a pointon the curves, a box showing the exact value of ΣMsf can be obtained.

Figure 4.11 Evaluation of safety factor

4.5 USING DRAINS

In this section the effect of the drains in the project will be investigated. Four new phaseswill be introduced having the same properties as the first four consolidation phases. Thedifferences in the new phases are:


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• The drains should be active in all the new phases. Activate them in the Waterconditions mode.

• The Time interval in the first three of the consolidation phases (1 to 3) is 1 day. Thelast phase is set to Minimum pore pressure and a value of 1.0 kN/m2 is assigned tothe minimum pressure (|P-stop|).

After the calculation is finished, select the last phase and click the View calculationresults button. The Output window now shows the deformed mesh after the drained

construction of the final part of the embankment. In order to compare the effect of thedrains, the excess pore pressure dissipation in node B can be used.

Open the Curves manager.

• In the Chart tabsheet double click Chart 1 (pexcess of node B versus time). The chartis displayed. Close the Curves manager.

• Double click the curve in the legend at the right of the chart. The Settings windowpops up.

• Click the Add curve button and select the Add from current project option in theappearing menu. The Curve generation window pops up.

• Select the Invert sign option for y-axis and click OK to accept the selected options.

• In the chart a new curve is added and a new tabsheet corresponding to it is openedin the Settings window. Click the Phases button. From the displayed window selectthe Initial phase and the last four phases (drains) and click OK.

• In the Settings window click Apply to preview the generated cure. Click OK to closethe Settings window. The chart (Figure 4.12) gives a clear view of the effect ofdrains in the time required for the excess pore pressures to dissipate.

Figure 4.12 Effect of drains



Hint: Instead of adding a new curve, the existing curve can be regenerated usingthe corresponding button in the Curves settings window.

4.6 UPDATED MESH + UPDATED WATER PRESSURES ANALYSIS

As can be seen from the output of the Deformed mesh at the end of consolidation (stage4), the embankment settles about one metre since the start of construction. Part of thesand fill that was originally above the phreatic level will settle below the phreatic level.

As a result of buoyancy forces the effective weight of the soil that settles below the waterlevel will change, which leads to a reduction of the effective overburden in time. Thiseffect can be simulated in PLAXIS using the Updated mesh and Updated water pressuresoptions. For the road embankment the effect of using these options will be investigated.

• In the Calculation program click Next to add a new phase.

• In the General tabsheet select the Initial phase as starting phase.

• Define the new phase in the same way as Phase 1. In the Advanced generalsettings window check the Updated mesh and Updated water pressures options

• Define in the same way the other 3 phases.

• Start the calculation.

When the calculation has finished, compare the settlements for the two differentcalculation methods.

• In the Curve generation window select time for the x-axis and select the verticaldisplacement (uy ) of the point in the middle of the soft soil layers (Point B) for they -axis. Invert the sign of the y-axis.

• In this curve the results for Initial phase and phases from 1 to 4 will be considered.

• Add a new curve to the chart.

• In this curve the results for Initial phase and phases from 13 to 16 will beconsidered. The resulting chart is shown in Figure 4.13.

In Figure 4.13 it can be seen that the settlements are less when the Updated mesh andUpdated water pressures options are used (red curve). This is partly because theUpdated mesh procedure includes second order deformation effects by which changes ofthe geometry are taken into account, and partly because the Updated water pressuresprocedure results in smaller effective weights of the embankment. This last effect iscaused by the buoyancy of the soil settling below the (constant) phreatic level. The use ofthese procedures allows for a realistic analysis of settlements, taking into account thepositive effects of large deformations.


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Figure 4.13 Effect of Updated mesh and water pressures analysis on resulting settlements


SETTLEMENTS DUE TO TUNNEL CONSTRUCTION

5 SETTLEMENTS DUE TO TUNNEL CONSTRUCTION

PLAXIS 2D has special facilities for the generation of circular and non-circular tunnelsand the simulation of a tunnel construction process. In this chapter the construction of ashield tunnel in medium soft soil and the influence on a pile foundation is considered. Ashield tunnel is constructed by excavating soil at the front of a tunnel boring machine(TBM) and installing a tunnel lining behind it. In this procedure the soil is generallyover-excavated, which means that the cross sectional area occupied by the final tunnellining is always less than the excavated soil area. Although measures are taken to fill upthis gap, one cannot avoid stress re-distributions and deformations in the soil as a resultof the tunnel construction process. To avoid damage to existing buildings or foundationson the soil above, it is necessary to predict these effects and to take proper measures.Such an analysis can be performed by means of the finite element method. This tutorialshows an example of such an analysis.

x

y

+3 m

0 m

-10 m

-12 m

-17 m

-30 m

5 m 10 m 20 m

clay

piles

sand

deep clay

deep sand

Figure 5.1 Geometry of the tunnel project with an indication of the soil layers

The tunnel considered in this tutorial has a diameter of 5.0 m and is located at an averagedepth of 20 m. The soil profile indicates four distinct layers: The upper 13 m consists ofsoft clay type soil with stiffness that increases approximately linearly with depth. Underthe clay layer there is a 2.0 m thick fine sand layer. This layer is used as a foundationlayer for old wooden piles on which traditional brickwork houses were built. The pilefoundation of such a building is modelled next to the tunnel. Displacements of these pilesmay cause damage to the building, which is highly undesirable. Below the sand layerthere is a 5.0 m thick deep loamy clay layer.

This is one of the layers in which the tunnel is constructed. The other part of the tunnel is


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constructed in the deep sand layer, which consists of dense sand and some gravel. Thislayer is very stiff. The pore pressure distribution is hydrostatic. The phreatic level islocated 3 m below the ground surface (at a level of y = 0 m). Since the situation is moreor less symmetric, only one half (the right half) is taken into account in the plane strainmodel. From the centre of the tunnel the model extends for 35 m in horizontal direction.This is a Plane strain model and the 15-node element is adopted.

Objectives:

• Modelling of the tunnel boring process

• Modelling of piles

• Modelling undrained behaviour using the Undrained (B) option

5.1 INPUT

The basic geometry including the four soil layers, as shown in Figure 5.1 (excluding thetunnel and the foundation elements), can be created using the Geometry line option.Since the ground surface is located at 3.0 m above the reference level, the ymaxparameter is defined as +3.0 m and the ymin as -30.0 m in the Project properties window.For the generation of the tunnel we will use the tunnel designer, which is a special toolwithin PLAXIS that enables the use of circle segments (arcs) and lines to model thegeometry of a tunnel. The tunnel considered here is the right half of a circular tunnel andwill be composed of four sections. After generating the basic geometry, follow thesesteps to design the circular tunnel:

Click the Tunnel button in the toolbar. The Tunnel designer window appears, with anumber of options in its toolbar for creating tunnel shapes.

Click the Half tunnel - Right half button in the toolbar. The tunnel designer will showa default (half) tunnel shape composed of three sections of which the lower one(Section 1) is selected.

Hint: In the tunnel as considered here the sections do not have a specific meaningas the tunnel lining is homogeneous and the tunnel will be constructed atonce. In general, the meaning of sections becomes significant when:• It is desired to excavate or construct the tunnel (lining) in different

stages.• Different tunnel sections have different lining properties.• One would consider hinge connections in the lining (hinges can be

added after the design of the tunnel in the general draw area).• The tunnel shape is composed of arcs with different radii (for example

NATM tunnels).

• Note that the Circular tunnel option is automatically selected for bored tunnels.

• Keep the Type of tunnel on the default value of a Bored tunnel. Make sure that thelower tunnel section is selected (if not, select it by clicking with the mouse in thelower section).



• For a circular (bored) tunnel the radius can be entered here. Enter a radius of 2.5 m.The result of this action is directly visible in the drawing.

• The value below the radius represents the angle over which the section extends.Enter an angle of 90 degrees (which is the maximum angle of one section).

• The local x- and y-coordinates of the first arc centre point is always located at thelocal origin (x = 0; y = 0) for a bored tunnel.

• Make sure that the options Shell and Outside interface are selected for this section.

Hint: A tunnel lining consists of curved plates. The lining properties can bespecified in the material database for plates. Similarly, a tunnel interface isnothing more than a curved interface.

• Proceed to the next section (2) by clicking the right arrow at the bottom of thewindow. Alternatively, you may click the second tunnel section in the designerwindow.

• The angle is automatically defined as 90 degrees. This is valid for this example. It isnot necessary, nor possible, to enter the radius of the second tunnel segment. Thisvalue is automatically adopted from the first tunnel segment in case of a circulartunnel.

• Make sure that the Shell and Outside interface options are selected for section 2.The tunnel has now been completely defined (Figure 5.2).

Hint: A shell and interface can be assigned directly to all tunnel sections byclicking the corresponding buttons at the top of the tunnel window.

Figure 5.2 Tunnel designer with current tunnel model

• Click the OK button to close the tunnel designer.

• Back in the draw area, the tunnel must be included in the geometry model. This is


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done by entering the global position of the origin of the local tunnel axes. Click theexisting point at position (0.0; -17.0) (13.0 m above the bottom of the geometrymodel). The tunnel will be drawn with its centre at this location.

The building itself will be represented by a stiff plate founded on piles.

Draw a plate from (5.0; 3.0) to (15.0; 3.0), representing the building.

Draw two piles from (5.0; 3.0) to (5.0; -11.0) and from (15.0; 3.0) to (15.0; -11.0).

Boundary conditions

Click the Standard fixities button to apply the appropriate boundary conditions. Inaddition to the standard displacement fixities, fixed rotations are introduced to theupper and lower point of the tunnel lining.

Hint: In the Standard fixities option, a plate that extends to a geometry boundarythat is fixed in at least one direction obtains fixed rotations, whereas a platethat extends to a free boundary obtains a free rotation.

Material properties

The material properties for the four different soil layers are listed in Table 5.1.

For the upper clay layer we use the advanced option to let the stiffness and shearstrength increase with depth. Therefore values for E 'inc and su,inc are entered in theAdvanced parameters box. The values of E 'ref and su,ref become the reference values atthe reference level yref . Below yref , the actual values of E ' and su, increase with depthaccording to:

E '(y ) = E 'ref + E 'inc(yref − y )su(y ) = su,ref + su,inc(yref − y )

The data sets of the two lower soil layers include appropriate parameters for the tunnelinterfaces. In the other data sets the interface properties just remain at their defaultvalues. Enter four data sets with the properties as listed in Table 5.1 and assign them tothe corresponding clusters in the geometry model. The advanced parameters for the Claydata set are defined in the Advanced dialog box in the Parameters tabsheet.

Hint: The soil data sets should be assigned to the clusters inside the tunnel as wellas to the ones outside the tunnel.



Table 5.1 Material properties of soil in the tunnel project

Parameter Name Clay Sand Deep Clay Deep sand Unit

General

Material model Model Mohr-Coulomb

Hardeningsoil

Mohr-Coulomb

HS small -

Drainage type Type Undrained(B)

Drained Undrained(B)

Drained -

Soil unit weight above p.l. γunsat 15 16.5 16 17 kN/m3

Soil unit weight below p.l. γsat 18 20 18.5 21 kN/m3

Parameters

Young's modulus at referencelevel

E ' 3.4·103 - 9.0· 103 - kN/m2

Secant stiffness in standarddrained triaxial test

E ref50 - 2.5· 104 - 4.2· 104 kN/m2


E refoed - 2.5· 104 - 4.2· 104 kN/m2

Unloading / reloading stiffness E refur - 7.5· 104 - 1.26· 105 kN/m2


m - 0.5 - 0.5 -

Cohesion c'ref - 0 - 0 kN/m2

Undrained shear strength atreference level

su,ref 5 - 40 - kN/m2

Friction angle ϕ' - 31 - 35 ◦

Dilatancy angle ψ - 1.0 - 5 ◦

Shear strain at which Gs =0.722G0

γ0.7 - - - 1.3·10-4 -

Shear modulus at very smallstrains

Gref0 - - - 1.1· 105 kN/m2

Poisson's ratio ν ' 0.33 0.3 0.33 0.3 -

Young's modulus inc. E 'inc 400 - 600 - kN/m3

Reference level yref 3.0 - -12 - m

Undrained shear strength inc. su,inc 2 - 3 - kN/m2

Reference level yref 3.0 - -12 - m

Flow parameters

Horizontal permeability kx 1·10-4 1.0 1·10-2 0.5 m/day

Vertical permeability ky 1·10-4 1.0 1·10-2 0.5 m/day

Interfaces

Interface strength type Type Rigid Rigid Manual Manual -

Interface strength Rinter 1.0 1.0 0.7 0.7 -

Initial

K0 determination − Manual Automatic Manual Automatic -

Lateral earth pressurecoefficient

K0,x 0.60 0.485 0.60 0.4264 -

In addition to the four data sets for the soil and interfaces, material datasets will becreated for the plate representing the building and the tunnel lining and for the pilefoundation. The properties for the plates and piles are listed in Table 5.2 and 5.3respectively.

Table 5.2 Material properties of the plates

Parameter Name Lining Building Unit

Material type Type Elastic;Isotropic

Elastic;Isotropic

-

Normal stiffness EA 1.4·107 1·1010 kN/m

Flexural rigidity EI 1.43·105 1·1010 kNm2/m

Weight w 8.4 25 kN/m/m

Poisson's ratio ν 0.15 0.0 -


TUTORIAL MANUAL

Table 5.3 Material properties of the piles

Parameter Name Foundationpiles

Unit

Stiffness E 1.0·107 kN/m2

Unit weight γ 24.0 kN/m3

Diameter D 0.25 m

Pile spacing Lspacing 3.0 m

Skin resistanceTtop,max 1.0 kN/m

Tbot ,max 100.0 kN/m

Base resistance Fmax 100.0 kN

Interface stiffness factors - Default kN

Assign the Lining data set to the tunnel lining and the building data set to the foundationplate representing the building. The weight of this beam also represents the load of theentire building. Assign the corresponding material set to the foundation piles.

Mesh generation

The default global coarseness parameter (Medium) can be accepted in this case. Notethat the structural elements (plate and embedded piles) are internally automaticallyrefined by a factor of 0.25. This will cause a very fine mesh in the cluster surrounded bythese elements. In order to obtain a smoother transition of mesh of the soil layersbetween the embedded piles,the line between the soil layers ((5; -10) to (15; -10)) iscoarsened by a factor of 4 (Figure 5.3). The generated mesh is displayed in the Outputprogram (Figure 5.4).

Figure 5.3 Local coarsening of the mesh

Figure 5.4 The generated mesh



5.2 CALCULATIONS

To simulate the construction of the tunnel it is clear that a staged construction calculationis needed after defining the initial conditions. The calculation process is modelled andexecuted in the Classical mode.


The K0 procedure can be used to generate the initial effective stresses. The waterpressures can be generated on the basis of a general phreatic level at a level of y = 0.0m. Make sure that the building, piles, pile toes and tunnel lining are deactivated.

Phase 1: Building

The first calculation phase is used to activate the building.

• Click the Next button to introduce a next calculation phase. The option Plastic isautomatically selected for the calculation type.

• In the Parameters tabsheet select the Ignore undrained behaviour option.

• In the Staged construction mode activate the piles and the foundation plate.

• Click the Update button to return to the calculation window.

Simulation of the construction of the tunnel

A staged construction calculation is needed in which the tunnel lining is activated and thesoil clusters inside the tunnel are deactivated. Deactivating the soil inside the tunnel onlyaffects the soil stiffness and strength and the effective stresses. Without additional inputthe water pressures remain. To remove the water pressure inside the tunnel the two soilclusters in the tunnels must be set to dry in the Water conditions mode and the waterpressures should be regenerated. The calculation phases are Plastic analyses, Stagedconstruction. To create the input, follow these steps.

Phase 2: Tunnel

• Click the Next button to introduce a next calculation phase.

• In the Parameters tabsheet, the Reset displacements to zero option should bechecked.

• In the Staged construction mode deactivate the two soil clusters inside the tunnel.

• Activate the tunnel lining.

• In the Water conditions mode select both soil clusters inside the tunnelsimultaneously (using the <Shift> key). Double-click one of the clusters whileholding the <Shift> key. The Cluster pore pressure distribution window pops up.

• Select the Cluster dry option and press OK.


In addition to the installation of the tunnel lining, the excavation of the soil and thedewatering of the tunnel, the volume loss is simulated by applying a contraction to thetunnel lining. This contraction will be defined in a staged construction calculation phase:


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Figure 5.5 Cluster pore pressure distribution window

Phase 3: Contraction

• Click the Next button to introduce the next calculation phase.

• In the Staged construction mode double click the centre of the tunnel to open theTunnel contraction window. Enter a contraction of 0.5% (Figure 5.6) and click OK.


Hint: For a more realistic model, different properties should be defined for thelining in this phase and in the final one.

Figure 5.6 Tunnel contraction window

Hint: The contraction of the tunnel lining by itself does not introduce forces in thetunnel lining. Eventual changes in lining forces as a result of the contractionprocedure are due to stress redistributions in the surrounding soil or tochanging external forces.

Phase 4: Grouting

At the tail of the tunnel boring machine (TBM), grout is injected to fill up the gap betweenthe TBM and the final tunnel lining. The grouting process is simulated by applying apressure on the surrounding soil.


• In the Parameters tabsheet, do not select the Reset displacements to zero option.



• In the Staged construction mode deactivate the tunnel lining.

• In the Water conditions mode multi select the the clusters inside the tunnel.Double-click one of the clusters while holding the <Shift> key. The Cluster porepressure distribution window pops up.

• Select the User-defined pore pressure distribution option and assign a value of−230kN/m2 to pref . Note the minus sign (Figure 5.7). The pressure distribution inthe tunnel is constant.

Figure 5.7 Assigning User-defined pore pressure distribution

Phase 5: Final lining


• In the Parameters tabsheet, do not select the Reset displacements to zero option.

• In the Water conditions mode set the clusters inside the tunnel to Dry.

• In the Staged construction mode activate the tunnel lining.

• Select some characteristic points for load-displacement curves (for example thecorner point at the ground surface above the tunnel and the corner points of thebuilding).

• Start the calculations.

5.3 RESULTS

After the calculation, select the last calculation phase and click the View calculationresults button. The Output program is started, showing the deformed meshes at the endof the calculation phases (Figure 5.8).

As a result of the second calculation phase (removing soil and water out of the tunnel)there is some settlement of the soil surface and the tunnel lining shows somedeformation. In this phase the axial force in the lining is the maximum axial force that willbe reached. The lining forces can be viewed by double clicking the lining and selectingforce related options from the Force menu. The plots of the axial forces and bendingmoment are scaled by factors of 1·10-3 and 0.2 respectively (Figure 5.9).


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Figure 5.8 Deformed mesh after construction of the tunnel (Phase 5; scaled up 20.0 times)

Figure 5.9 Axial forces and Bending moments in the lining after the second phase

The plot of effective stresses, Figure 5.10, shows that arching occurs around the tunnel.This arching reduces the stresses acting on the tunnel lining. As a result, the axial forcein the final phase is lower than that after the second calculation phase.

To display the tilt of the structure:

Click the Distance measurement in the side toolbar.

• Click the node located at the left corner of the structure (5.0; 3.0).

• Click the node located at the right corner of the structure (15.0; 3.0). The Distancemeasurement information window is displayed where the resulting tilt of the structureis given (Figure 5.11).



Figure 5.10 Principal stress directions after the construction of the tunnel

Figure 5.11 Distance measurement information window


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EXCAVATION OF A NATM TUNNEL

6 EXCAVATION OF A NATM TUNNEL

This tutorial illustrates the use of PLAXIS for the analysis of the construction of a NATMtunnel. The NATM is a technique in which ground exposed by excavation is stabilizedwith shotcrete to form a temporary lining. Rapid and consistent support of freshlyexcavated ground, easier construction of complex intersections and lower capital cost ofmajor equipment are some of the advantages of NATM. Some of the limitations of thismethod are that it is slow compared to shield tunnelling in uniform soils, dealing withwater ingress can be difficult, and it demands skilled man power.

x

y

28 m 8 m 7 m 7 m 50 m

5 m

6 m

13 m

11 m

Top layer

Clay - Siltstone

Clay - Limestone

(-50; 0)

(-50; 11)

(-50; 24)(-22; 24)

(-14; 30)

(-7; 35)

Figure 6.1 Geometry of the project

Objectives:

• Modelling the construction of an NATM tunnel (β-method).

• Using Gravity loading to generate initial stresses.

This is a Plane-strain model and the 15-Node elements are used. The project liesbetween Xmin = -50 and Xmax = 50 in the horizontal direction and between Ymin = 0 andYmax = 35 in the vertical direction.

6.1 INPUT

The basic geometry including the three soil layers, as shown in Figure 6.1 (excluding thetunnel), can be created using the geometry line option. In the model 11 m of theClay-limestone layer is considered. The bottom of this layer is considered as reference iny direction (ymin = 0). After generating the basic geometry, follow these steps to designthe tunnel:

Click the Tunnel button in the toolbar. The Tunnel designer window appears, with anumber of options in its toolbar for creating tunnel shapes. By default the Wholetunnel button is active. This is valid in this project.

• The Symmetric option is selected for the shape of the tunnel by default. This optionis valid in this example.

• Select NATM tunnel as tunnel type in the corresponding drop-down menu.

• Define the sections of the tunnel according to the Table 6.1.

• Assign both shell and interface to each section.


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Table 6.1 Section properties of the tunnel

Section Type Radius Angle Centre (y)

1 Arc 10.40 22.0 7.0

2 Arc 2.40 47.0 n/a

3 Arc 5.60 25.0 n/a

4 Arc 5.89 43.0 n/a

5 Arc 5.48 43.0 n/a

• Create the tunnel at (0; 16) in the model.

To create the temporary plate in the middle of the tunnel:

• In the View menu, de-activate the Snap to grid option.

Define a plate passing through (-5.596; 17.120), (-3; 16.3), (0; 16), (3; 16.3) and(5.596; 17.120). This can be best done by entering the coordinates in the commandline, with a space between the x- and y-coordinate.

Boundary conditions

Click the Standard fixities button to apply the appropriate boundary conditions.


A single material data set will be defined for the lining of the tunnel and the temporaryplate. Create the material dataset according to Table 6.2.

Table 6.2 Material properties of the plates

Parameter Name Lining Unit

Material type Type Elastic; Isotropic kN/m

Normal stiffness EA 6.0·106 kN/m

Flexural rigidity EI 2.0·104 kNm2/m

Weight w 5.0 kN/m/m


The properties of the different soil types are given in Table 6.3. The soil materials aredrained. As a result definition of flow parameters is not necessary. The initial parametersin the Initial tabsheet are not used, since the initial stresses will be generated by meansof Gravity loading. Assign the data to the corresponding clusters in the geometry modeland the clusters inside the tunnel.

Mesh generation

The default global coarseness parameter (Medium) can be accepted in this case. Thegenerated mesh is displayed in the Output program Figure 6.2.




Table 6.3 Material properties of the soil layers

Parameter Name Top layer Clay-siltstone Clay-limestone Unit

General

Material model Model Hardening soil Hoek-Brown Hoek-Brown -

Type of material behaviour Type Drained Drained Drained -

Soil unit weight above phreaticlevel

γunsat 20 25 24 kN/m3

Soil unit weight below phreaticlevel

γsat 22 25 24 kN/m3

Initial void ratio einit 0.5 0.5 0.5 -

Parameters


E ref50 4.0·104 - - kN/m2


E refoed 4.0·104 - - kN/m2

Unloading / reloading stiffness E refur 1.2·105 - - kN/m2


m 0.5 - - -

Young's modulus E ' - 1.0·106 2.5·106 kN/m2

Poisson's ratio ν 'ur 0.2 0.25 0.25 -

Uniaxial compressive strength σci - 2.5·104 5.0·104 kN/m2

Material constant for the intactrock

mi - 4.0 10.0 -

Geological Strength Index GSI - 40.0 55.0 -

Disturbance factor D - 0.2 0.0 -

Cohesion c'ref 10.0 - - kN/m2

Friction angle ϕ' 30 - - ◦

Dilatancy parameter ψmax - 30.0 35.0 ◦

Dilatancy parameter σψ - 400 1000 kN/m2

Interfaces

Interface strength − Rigid Manual Rigid -

Strength reduction factor Rinter 1.0 0.5 1.0 -

6.2 CALCULATIONS

To simulate the construction of the tunnel it is clear that a staged construction calculationis needed after defining the initial conditions. The calculation process is modelled andexecuted in the Classical mode.


Note that the soil layers are not horizontal. As a result, the K0 procedure can not be usedto generate the initial effective stresses in this example. Instead Gravity loading shouldbe used. This option is available in the General tabsheet of the Calculations program forthe Initial phase. Water will not be considered in this example. The general phreatic levelshould remain at the model base. Make sure that the tunnel is inactive.

Simulation of the construction of the tunnel

A staged construction calculation is needed in which the tunnel lining is activated and thesoil clusters inside the tunnel are deactivated. Deactivating the soil inside the tunnel onlyaffects the soil stiffness and strength and the effective stresses. The calculation phasesare Plastic analyses, Staged construction. The three-dimensional arching effect isemulated by using the so-called β-method. The idea is that the initial stresses pk actingaround the location where the tunnel is to be constructed are divided into a part (1− β)


TUTORIAL MANUAL

pk that is applied to the unsupported tunnel and a part βpk that is applied to thesupported tunnel. To apply this in PLAXIS one can use the staged construction optionwith a reduced ultimate level of ΣMstage.

To define the calculation process follow these steps:

Phase 1


• In the Loading input box available in the Parameters tabsheet click Advanced. TheAdvanced parameters window pops up.

• Define a value of 0.6 for ΣMstage. This corresponds to a β-value of 1-ΣMstage =0.4.

• In the Staged construction mode deactivate the upper cluster in the tunnel. Do NOTactivate the tunnel lining.

Phase 2


• In the Staged construction mode activate the lining and interfaces of the part of thetunnel excavated in the previous phase (top heading).

• Note that the value of ΣMstage is automatically reset to 1.0.

Phase 3


• In the Loading input box available in the Parameters tabsheet click Advanced. TheAdvanced parameters window pops up.

• Define a value of 0.6 for ΣMstage (β = 0.4).

• In the Staged construction mode deactivate the lower cluster (invert) and thetemporary lining in the middle of the tunnel.

Phase 4


• In the Staged construction mode activate the remaining lining and interfaces. All theplates and interfaces around full tunnel are active.

• Note that the value of ΣMstage is automatically reset to 1.0.

• Select node at slope crest point and the tunnel crest. These points might be ofinterest to evaluate the deformation during the construction phases.




6.3 RESULTS

After the calculation, select the last calculation phase and click the View calculationresults button. The Output program is started, showing the deformed mesh at the end ofthe calculation phases (Figure 6.3).

Figure 6.3 The deformed mesh at the end of the the final calculation phase

To display the bending moments resulting in the tunnel:

To select the lining of all the tunnel sections, click the corresponding button in theside toolbar and drag the mouse to define a rectangle where all the tunnel sectionsare included. Select the Plate option in the appearing window (Figure 6.4) andpress View. Note that the tunnel lining is displayed in the Structures view.

Figure 6.4 Select structures window

• From the Forces menu select the Bending moment M option. The result, scaled by afactor or 0.5 is displayed in Figure 6.5.

Figure 6.5 Resulting bending moments in the NATM tunnel


TUTORIAL MANUAL


STABILITY OF DAM UNDER RAPID DRAWDOWN

7 STABILITY OF DAM UNDER RAPID DRAWDOWN

This example concerns the stability of a reservoir dam under conditions of drawdown.Fast reduction of the reservoir level may lead to instability of the dam due to high porewater pressures that remain inside the dam. To analyse such a situation using the finiteelement method, a transient groundwater flow calculation is required. Pore pressuresresulting from the groundwater flow analysis are transferred to the deformation analysisprogram and used in a stability analysis. This example demonstrates how deformationanalysis, transient groundwater flow and stability analysis can interactively be performedin PLAXIS 2D.

The dam to be considered is 30 m high and the width is 172.5 m at the base and 5 m atthe top. The dam consists of a clay core with a well graded fill at both sides. Thegeometry of the dam is depicted in Figure 7.1. The normal water level behind the dam is25 m high. A situation is considered where the water level drops 20 m. The normalphreatic level at the right hand side of the dam is 10 m below ground surface. Thesub-soil consists of overconsolidated silty sand. The data of the dam materials and thesub-soil are given in Table 1.

x

y

50 m 77.5 m

5 m

5 m

25 m

20 m 120 m120 m

37.5 m

30 m

30 m

90 m

Core

FillFill

Subsoil

Figure 7.1 Geometry of the dam

Objectives:

• Using transient flow and coupled analysis

• Defining time-dependent hydraulic conditions

• Using unsaturated flow parameters

• Using Advanced calculation mode

7.1 INPUT

The dam shown in Figure 7.1 can be analyzed with a Plain strain model. The situationcan be modelled with a geometry model in which the sub-soil is modelled to a depth of 30m. The left hand boundary can be taken 50 m left of the dam toe and the right handboundary can be taken 37.5 m right of the other dam toe. The Standard fixities can beused to define boundary conditions.

Material sets

The material data sets of the clay core, the fill material and the sub-soil are shown inTable 7.1. The Interfaces and Initial tabsheets are not relevant (no interfaces or K0


TUTORIAL MANUAL

procedure used).

Table 7.1 Material properties of the dam and sub-soil

Parameter Name Core Fill Sub-soil Unit

General

Material model Model Mohr Coulomb MohrCoulomb

MohrCoulomb

-

Drainage type Type Undrained B Drained Drained -

Soil unit weight above p.l. γunsat 16.0 16.0 17.0 kN/m3

Soil unit weight below p.l. γsat 18.0 20.0 21.0 kN/m3

Parameters

Young's modulus E ' 1.5·103 2.0·104 5.0·104 kN/m2

Poisson's ratio ν ' 0.35 0.33 0.3 -

Cohesion c'ref - 5.0 1.0 kN/m2

Undrained shear strength su,ref 5.0 - - kN/m2

Friction angle ϕ' - 31 35.0 ◦

Dilatancy angle ψ - 1.0 5.0 ◦

Young's modulus inc. E 'inc 300 - - kN/m2

Reference level yref 30 - - m

Undrained shear strength inc. su,inc 3.0 - - kN/m2


Flow

Flow data set Model Hypres Hypres Hypres -


VanGenuchten

VanGenuchten

-

Soil - Subsoil Subsoil Subsoil -

Soil coarseness - Very fine Coarse Coarse -

Horizontal permeability kx 1.0·10-4 0.25 0.01 m/day

Vertical permeability ky 1.0·10-4 0.25 0.01 m/day

Mesh generation

For the generation of the mesh it is advisable to set the Global coarseness parameter toFine. To modify the global coarseness:

• Click the Mesh option in the menu bar. The Mesh menu is displayed.

• Select the Global coarseness option form the appearing menu. The Meshgeneration setup window is displayed.

• Select the Fine option from the Element distribution drop-down menu.

• Click the OK to close the Mesh generation setup window.

Figure 7.2 Modification of the Global coarseness

The line connecting the right toe of the embankment, (92.5; 0) and the right modelboundary, (130; 0) is refined by a factor of 0.5. Note that refinement is usually needed incases of material with low permeability (refinement of clay clusters) and in cases of high



variation of relative permeability refinement of sand clusters)∗. The finite element mesh isshown in Figure 7.3.

Figure 7.3 Finite element mesh

7.2 CASE A: CLASSICAL MODE

In this case the calculations will be performed in the Classical calculation mode.

7.2.1 CALCULATIONS

In addition to the Initial phase, the calculation consists of eight phases. In the initialphase, initial stresses and initial pore water pressures of the dam under normal workingconditions are calculated using Gravity loading. For this situation the water pressuredistribution is calculated using a steady-state groundwater flow calculation. This phase isfollowed by a so-called 'nil step' to increase the accuracy of the stress field, beforeconsidering drawdown situations. The third and fourth phase both start from thisstandard situation (i.e. a dam with a reservoir level at 25 m) and the water level islowered to 5 m. A distinction is made in the time interval at which this is done (i.e.different speeds of water level reduction; rapid drawdown and slow drawdown). In bothcases the water pressure distribution is calculated using a transient groundwater flowcalculation. The fifth calculation phase also starts from the second phase and considersthe long-term behaviour of the dam at the low reservoir level of 5 m, which involves asteady-state groundwater flow calculation to calculate the water pressure distribution.Finally, for all four water pressure situations the safety factor of the dam is calculated bymeans of phi-c reduction. This leads to the following cases being considered:

• long term situation with water level at 25m.

• water level drops quickly from 25 to 5m.

• water level drops slowly from 25 to 5m.

• long term situation with water level at 5m.

Initial phase: Gravity loading

• In the General tabsheet select the Gravity loading as calculation type. In theParameters tabsheet the Staged construction option should be selected.

In the Water conditions mode a closed boundary is automatically created at thebottom of the model. This is relevant for this example.

∗ Galavi V.(2010). Groundwater flow, fully coupled flow deformation and undrained analysis in PLAXIS 2D and3D. Plaxis BV


TUTORIAL MANUAL

Define a new general water level consisting of four points; starting at the very leftside at a level of 25 m above the ground surface; the second point is just inside thedam at a level of 25 m; the third point is near the dam toe (93, -10) and the forthpoint just outside the right boundary at a level of 10 m below the ground surface(Figure 7.4).

The pore pressures should be generated from steady state groundwater flowcalculations. Select that option in the drop down menu at the left of the Waterpressures button.

Figure 7.4 General water level in the initial phase

Phase 1: Nil step

In order to solve large out-of-balance forces and to restore equilibrium a nil step phase isintroduced. Such a situation can occur after a calculation phase in which large loadingswere activated (for example Gravity loading). A plastic nil-step is a Plastic analysis phasein which no additional loading is applied. No changes should be made to the geometryconfiguration or to the water conditions. In this case the undrained behaviour is neglectedby selecting the corresponding option in the Parameters tabsheet of the Calculationwindow. No further settings are required.

Phase 2: Rapid drawdown

In this phase rapid drawdown of the reservoir level is considered.

• In the General tabsheet, select the Consolidation as calculation type.

• In the Parameters tabsheet, select Reset displacements to zero and set the Loadinginput to Staged construction.

• Enter a value of 5 days for the Time interval.

In the Water conditions mode, select Transient groundwater flow from thedrop-down menu to generate pore water pressures based on a transientgroundwater flow calculation.

• Double click on the first part of the water level (left from the dam, at the reservoirside). The Time dependent head window pops up in which time-dependent settingsof the groundwater head can be generated on the basis of the water level.

• Activate the Use time dependent data option. The Linear option, which is selectedby default is valid for this example.

• Enter a value of -20 m for the ∆y parameter. As a result, this part of the water levelwill drop 20 m in the specified time interval (4 m per day).

• In the Water conditions mode the water conditions that are affected by the



time-dependent water level are indicated by h(t) (Figure 7.5).

• Press Update to return to the calculation mode.

Figure 7.5 Boundary conditions for transient groundwater flow calculation

Hint: Note that as PLAXIS 2D simultaneously performs the groundwater flow andplastic calculations simultaneously, it is not possible to view the resultsrelated to water conditions at this point.

Phase 3: Slow drawdown

In this phase the drawdown of the reservoir level is performed at a lower rate.

• In the General tabsheet, set the Start from phase parameter to Phase 1 (nil step)and select the Consolidation as calculation type.

• In the Parameters tabsheet, select Reset displacements to zero. The Loading inputshould be Staged construction.

• Enter a value of 50 days for the Time interval.

• In this case, a reduction of the reservoir level at a rate of 0.4 m per day is considered(see phase 2 for definition of the groundwater flow boundary conditions.


Phase 4: Low level

This phase considers the steady-state situation of a low reservoir level.

• In the General tabsheet, set the Start from phase parameter to Phase 1.

• Select the Plastic as calculation type.

• In the Parameters tab, set the Loading input to Staged construction and selectReset displacements to zero and Ignore undrained behaviour.

• In the Water conditions mode, select Steady state groundwater flow from thedrop-down menu to generate pore water pressures based on a steady stategroundwater flow calculation.

• Make sure that the bottom of the model is still closed. Generate groundwater headconditions at the other model boundaries by creating a new general water levelconsisting of four points; starting at the very left side at a level of 5 m above theground the surface; the second point is inside the dam at a level of 5 m; third pointat (93; -10) and the fourth point just outside the right boundary at a level of 10 m


TUTORIAL MANUAL

below the ground surface (Figure 7.6).


Figure 7.6 Boundary conditions for steady state groundwater flow calculation (phase 4)

Phase 5 to 8:

In Phases 5 to 8 stability calculations are defined for the phases 1 to 4 respectively.Therefore, select the corresponding phase in the Start from phase parameter and set theCalculation type to Safety. In the Parameter tabsheet set the number of additional stepsto 30 for Phase 5 and to 50 for phases 6 to 8 and select Reset displacement to zero.

Before calculating the project select nodes located at the crest (-2.5; 30) and at the toe ofthe dam (-80; 0).

7.2.2 RESULTS

After the calculation is finished, select Phase 8 and click the Output button. The Outputwindow now shows the deformed mesh for each phase. The results of the fourgroundwater flow calculations in terms of pore pressure distribution are shown in Figures7.7 to 7.10. Four different situations were considered:

• The steady-state situation with a high (standard) reservoir level (Figure 7.7).

Figure 7.7 Steady-state pore pressure distribution for high reservoir level (phase 1)

• The transient situation after rapid drawdown of the reservoir level (Figure 7.8).

Figure 7.8 Pore pressure distribution after rapid drawdown (phase 2)

• The transient situation after slow drawdown of the reservoir level (Figure 7.9).



Figure 7.9 Pore pressure distribution after slower drawdown (phase 3)

• The steady-state situation with a low reservoir level (Figure 7.10).

Figure 7.10 Steady-state pore pressure distribution for low reservoir level (phase 4)

When the change of pore pressure is taken into account in a deformation analysis, someadditional deformation of the dam will occur. These deformations and the effective stressdistribution can be viewed on the basis of the results of phases 1 to 4. Here, attention isfocused on the variation of the safety factor of the dam for the different situations.Therefore, the development of ΣMsf is plotted for the phases 5 to 8 as a function of thedisplacement of the dam crest point (see Figure 7.11).

Figure 7.11 Safety factors for different situations in Classical mode

Rapid drawdown of a reservoir level can reduce the stability of a dam significantly.Transient groundwater flow calculations in combination with deformation and stabilityanalysis can be performed with PLAXIS 2D to effectively analyze such situations


TUTORIAL MANUAL

7.3 CASE B: ADVANCED MODE

In this case the calculations will be performed in the Advanced calculation mode.

7.3.1 CALCULATIONS

Save the project under a different name. Redefine the calculation mode as Advanced.The Select calculation mode window is displayed when the Calculation mode option isselected in the Tools menu.

In the phase list:

• Make sure that the phases are defined as described in Case A.

• Recalculate the project. A warning will pop up as suction is taken into account (Porepressure tension cut-off is inactive) and thus a higher value of the safety factor willbe obtained (see also Section 5.5.5 of the Reference Manual). As this safety factorwill be more realistic, ignore this warning by clicking the Yes button.

7.3.2 RESULTS

For a comparison of results obtained from these two different calculation modes in thecurve generated displaying the factors of safety for the Classical mode include the resultsobtained in the Advanced mode (Figure 7.12).

Figure 7.12 Safety factors for different situations in Advanced mode



Hint: Safety factor is influenced by suction. This is particularly the case for phase8 (low reservoir level), because of the high suction in the part of the fill whenthe failure mechanism occurs. Consideration of suction in the safety analysisusually produces higher safety factor. Suction can be ignored in the safetyanalysis by means of a nil-step phase, in which suction is set to zero (or verysmall value), followed by a safety analysis.


TUTORIAL MANUAL


DRY EXCAVATION USING A TIE BACK WALL - ULS

8 DRY EXCAVATION USING A TIE BACK WALL - ULS

In this tutorial a Ultimate Limit State (ULS) calculation will be defined and performed forthe submerged construction of an excavation. The geometry model of Chapter 3 will beused. The Design approaches feature is introduced in this example. This feature allowsfor the use of partial factors for loads and model parameters after a serviceabilitycalculation has already been performed.

Objectives:

• Using Design approaches

8.1 INPUT

In order to define a design approach:

• Open the project created in Chapter 3 and save it under a different name.

• Click the Load menu and select the Design approaches option in the appearingmenu. The corresponding window is displayed.

• Click the Add button. The New design approach window is displayed.

• In this example the design approach 3 of the Eurocode 7 will be used. This designapproach involves partial factors for loads and partial factors for materials (strength).Specify a representative name (ex: 'EC7 - Design approach 3').

• In the lower part of the window the partial factors can be defined for loads andmaterials. By default the Partial factors for loads tabsheet is displayed.

• The default value of the partial factors ( = 1.0) is valid except for the Variableunfavorable. To change the value click the corresponding cell and type 1.3.

Figure 8.1 Partial factors for loads tabsheet in the Design approaches window


TUTORIAL MANUAL

• Click the Partial factors for materials tab. In the Material cases table a case namedEffective strength is added (Figure 8.2).

Figure 8.2 Partial factors for materials tabsheet in the Design approaches window

• The Hardening Soil model is used to model the soil behaviour in this project. Clickthe cell next to the Hardening soil. The General tabsheet of the Materials window isdisplayed. However, in this case it shows the partial factors for the materialparameters rather than the parameters itself. The idea is to define here partialfactors for some parameters of material data sets in which the Hardening Soil modelis used as soil model.

• Proceed to the Parameters tabsheet. Assign a value of 1.25 to c'ref and φ' (Figure8.3).

Figure 8.3 Assignment of partial factors to the material parameters



Hint: Note that a partial factor for φ and ψ apply to the tangent of φ and ψrespectively.

• Press <OK> to go back to the Partial factors for materials and note that the Materialcase option for the Hardening soil materials in the Materials in the current projectgroup has changed from none available to none.

• Click the cell where the none option is displayed. Note that it will change to a dropdown menu. Select the Effective strength option in the menu. In this way the definedset of partial factors will be assigned to the material. Note that more than onematerial case can be defined for a specific design approach.

• Do the same for the remaining two soil materials. A view of the Partial factors formaterials tabsheet of the Design approaches window is given in Figure 8.4.

Hint: In order to review a predefined set of partial factors for materials, click on themagnifying glass that appears in the cell next to the corresponding materialmodel after moving the mouse over this cell.

Figure 8.4 Assignment of material cases

The definition of the partial factors is complete. The values of the parameters after theapplication of the factors are displayed in the material dataset.

Open the Materials sets window and display the material corresponding to Loam.Note that information regarding the design approach and the partial parameters isprovided as well as the resulting values of the material parameters after theapplication of the factors (Figure 8.5).

• Do the same for the remaining material sets.


TUTORIAL MANUAL

• Click the Calculations tab to proceed to the Calculations program.

Figure 8.5 Parameters tabsheet after the assignment of the design approach

8.2 CALCULATIONS

There are two main schemes to perform design calculations in relation to serviceabilitycalculations (Section 3.6 of the Reference Manual). The first approach is used in thistutorial.

• In the Calculations program introduce a new calculation phase at the end of the listof existing phases.

• Assign Phase_1 as its starting phase.

• In the Parameters tabsheet click the Define button.

• In the Staged construction window change the drop-down list in the upper left cornerfrom Reference values to EC7 - Design approach 3 to consider the defined materialpartial factors in the calculation of the phase.

• Double click the line load. In the appearing Load window note that the selecteddesign approach is indicated.

• Select the Variable unfavourable option from the Label drop down menu. Note thatthe value of the factor is indicated as well as the value of the load when the factor isapplied. Click OK to close the Load window.

• In the Staged construction window make sure that the load is active. Note that thelabel and the value of the partial function is indicated (Figure 8.6).

• Follow the same steps to define ULS phases for all the remaining SLS phases.



Figure 8.6 Indication of the design approach in the Input program

Make sure that the Phase 7 starts from Phase 1, Phase 8 from Phase 2, Phase 9from Phase 3 and so on.

Calculate the project.

8.3 RESULTS

The results obtained for the design approach phases can be evaluated in Output. Figure8.7 displays the ΣMstage - |u| plot.

Figure 8.7 Σ−Mstage - |u| plot for the ULS phases


TUTORIAL MANUAL

If the ULS calculations have successfully finished, the model complies with thecorresponding design approach. If there are doubts about this due to excessivedeformations, an additional Safety calculation may be considered using the same designapproach, which should then result in a stable ΣMsf value larger than 1.0. Note that ifpartial factors have been used it is not necessary that ΣMsf also includes a safety margin.Hence, in this case ΣMsf just larger that 1.0 is enough. Figure 8.8 displays the ΣMsf -|u| plot for the Safety calculations of the Phase 6 and the corresponding ULS phase(Phase 12). It can be concluded that the situation complies with the design requirements.

Figure 8.8 ΣMsf - |u| plot for the last calculation phase and the corresponding ULS phase


FLOW THROUGH AN EMBANKMENT

9 FLOW THROUGH AN EMBANKMENT

In this chapter the flow through an embankment will be considered in the Flow mode.The crest of the embankment has a width of 2.0 m. Initially the water in river is 1.5 mdeep. The difference in water level between the river and the polder is 3.5 m.

Figure 9.1 shows the layout of the embankment problem where free surface groundwaterflow occurs. Flow takes place from the left side (river) to the right side (polder). As aresult seepage will take place at the right side of the embankment. The position of thephreatic level depends on the river water level, which varies in time.

x

y

1 m

2 m2 m

3 m

3 m

3 m10 m

5 m

6 m

Figure 9.1 Geometry of the embankment

Objectives:

• Using Flow mode

• Defining harmonic variation of water level

• Using cross section curves

9.1 INPUT

In the horizontal direction the model lies between Xmin = 0 m to Xmax = 23 m. In thevertical direction the model lies between Ymin = 0 m to Ymax = 6 m. In the Model tabsheetof the Project properties window define the Number of snap intervals as 2.

Geometry model

The geometry can be completed using the Geometry line tool and clicking at (0, 0), (23,0), (23, 1), (20, 1), (10, 6), (8, 6), (2, 3), (0, 3) and (0, 0). The standard boundaryconditions can be used in this example. Note that these fixities will not be used in the flowanalysis. The boundary conditions for flow analysis will be defined in the Waterconditions mode for each phase.


Define the soil material according to the Table 9.1 and assign the material dataset to thecluster. Skip the Interfaces and initial tabsheets as these parameters are not relevant.

After assigning the material to the soil cluster, set the Global coarseness to Very fine andgenerate the mesh. Save the project and proceed to the calculation process.


TUTORIAL MANUAL

Table 9.1 Properties of the embankment material (sand)

Parameter Name Sand Unit

General

Material model Model Linear elastic -



γunsat 20 kN/m3

Soil unit weight below phreaticlevel

γsat 20 kN/m3

Parameters

Stiffness E ' 1.0· 104 kN/m2


Flow parameters

Data set - Standard -

Soil type - Medium fine -

Set permeability to default - Yes -

Horizontal permeability kx 0.02272 m/day

Vertical permeability ky 0.02272 m/day

9.2 CALCULATIONS

The calculation of this project is performed in the Flow mode and it consists of threephases. In the initial phase, the groundwater flow in steady state is calculated for anaverage river level. In Phase 1, the transient groundwater flow is calculated for aharmonic variation of the water level. In Phase 2, the calculation is similar as in Phase 1,but the period is longer.

Initial phase:

• Select the Steady state groundwater flow option in the General tabsheet of theCalculation program.

• The default parameters defined in the Parameters tabsheet are valid for this phase.Click Define.

In the Water conditions mode define a phreatic level passing through points (-0.5,4.5), (8, 4.5), (20, 1) and (23.5, 1).

• Check that the bottom boundary is closed.

Phase 1:

• Select the Transient groundwater flow option in the General tabsheet of theCalculation program.

• Set the Time interval to 0.5 days and the Max number of steps stored to 100.

• The default values for the remaining parameters defined in the Parameters tabsheetare valid for this phase. Click Define.

• In the Water conditions mode double click general water level. The Time dependenthead window pops up.

• Select Harmonic and assign a value of 2 m to H and 0.5 days to T (Figure 9.2).



Hint: Only the saved calculation steps are used in animations. The default value ofMax number of steps stored is 1 and as a result only the final calculation stepis saved. Increasing the value of Max saved step numbers provides a moredetailed animation. However an optimum number of steps should be savedin order to avoid excessive usage of memory.

Figure 9.2 Defined time dependent boundary condition for Phase 1

Phase 2:

• Select the Transient groundwater flow option in the General tabsheet of theCalculation program. This phase starts from the Initial phase as well.

• Set the Time interval to 5 days and the Max number of steps stored to 100. Thedefault values for the remaining parameters defined in the Parameters tabsheet arevalid for this phase. Click Define.

• In the Water conditions mode double click general water level. The Time dependenthead window pops up.

• Select Harmonic and assign a value of 2 m to H and 5 days to T.

Definition of the calculation process is completed. Save the project and calculate. Nopoints will be selected for curves.

9.3 RESULTS

In the Output program the Create animation tool can be used to animate the resultsdisplayed in the Output program. To create the animation follow these steps:

• In the Stresses menu select the Pore pressures→ Groundwater head.

• Select the Create animation option in the File menu. The corresponding windowpops up (Figure 9.3).


TUTORIAL MANUAL

• Define the name of the animation file and the location where it will be stored. Bydefault the program names it according to the project and stores it in the projectfolder. In the same way animations can be created to compare the development ofpore pressures or flow field.

Figure 9.3 Create animation window

To view the results in a cross section:

Click the Cross section button in the side toolbar. The Cross section points windowpops up and the start and the end points of the cross section can be defined. Drawa cross section through the points (2; 3) and (20; 1). The results in the cross sectionare displayed in a new window.

• In the Cross section view select Pore pressures→ pactive in the Stresses menu.

• Select the Cross section curves option in the Tools menu. The Select steps forcurves window pops up.

• Select the Phase 1. The variation of the results in the cross section is displayed in anew window.

• Do the same for the Phase 2.

• The variation of the results due to different time intervals in harmonic variation at aspecific cross section can be compared (Figure 9.4 and Figure 9.5).

It can be seen that the slower variation of the external water level has a more significantinfluence on the pore pressures in the embankment and over a larger distance.



Figure 9.4 Active pore pressure variation in the cross section in Phase 1

Figure 9.5 Active pore pressure variation in the cross section in Phase 2


TUTORIAL MANUAL


FLOW AROUND A SHEET PILE WALL

10 FLOW AROUND A SHEET PILE WALL

In this tutorial the flow around a sheetpile wall will be analyzed. The geometry model ofChapter 3 will be used. The Well feature is introduced in this example.

Objectives:

• Using wells

10.1 INPUT

To create the geometry:

• Open the project defined in Chapter 3.

• Save the project under a different name (ex. 'Flow around a sheet pile wall'). Thematerial parameters remain unchanged. The used flow parameters are shown inTable 10.1.

Table 10.1 Flow parameters

Parameter Name Silt Sand Loam Unit

Flow parameters

Data set - USDA USDA USDA -

Model - Van Genuchten Van Genuchten Van Genuchten -

Soil type - Silt Sand Loam -

> 2µm - 6.0 4.0 20.0 %2µm − 50µm - 87.0 4.0 40.0 %50µm − 2mm - 7.0 92.0 40.0 %Set parameters to defaults - Yes Yes Yes -

Permeability in horizontal direction kx 0.5996 7.128 0.2497 m/day

Permeability in vertical direction ky 0.5996 7.128 0.2497 m/day

Click the Well button in the toolbar. Insert wells at (42, 17) and (58, 17).

Generate the mesh using the default settings (Figure 10.1).

• Save the project and proceed to the Calculations program.



TUTORIAL MANUAL

10.2 CALCULATIONS

The project will be calculated in the Flow only mode. Delete all the previously definedphases.

Initial phase

In this phase the initial steady-state pore pressure distribution is considered. To definethe initial phase:

• In the General tabsheet the calculation type is defined as Steady state groundwaterflow.

• The standard settings in the Parameters tabsheet are valid for this phase.

• In the Water conditions mode keep the general water level at y = 23 m.

• Check whether the bottom boundary is closed

Phase 1

In this phase the lowering of the phreatic level in the excavation down to y = 20 m. Thiscorresponds to the final excavation level in the project in Chapter 3.

• In the General tabsheet the calculation type is defined as Steady state groundwaterflow.

• The standard settings in the Parameters tabsheet are valid for this phase.

• In the Water conditions mode activate the interface elements along the wall (not theextra one's below the wall).

• Double click in the middle of the small line representing a well. The Well windowpops up.

• Select the Extraction option. Set the discharge value to 0.7 m3/day/m. Set the Ψminto Equal to well location (Figure 10.2), which corresponds to an elevation height of y= 17 m in this case. This means that water will be extracted as long as thegroundwater head at the wall location is at least 17 m.

• Do the same for the other well.

Figure 10.2 Well properties

The definition of the calculation process is complete. Calculate the project.


FLOW AROUND A SHEET PILE WALL

Hint: Total discharge in Phase 1 is similar to the total outflow at the final excavationlevel as obtained from Chapter 3.

10.3 RESULTS

To display the flow field:

• Select the Phase 1 in the drop down menu.

• From the Stresses menu select Groundwater flow → |q|. A scaled representation ofthe results (scale factor = 5.0 ) is shown in Figure 10.3.

Figure 10.3 The resulting flow field at the end of Phase 1

From the Stresses menu select Pore pressures→ pactive. Compare the results with theones of the Phase 4 of the project defined in Chapter 3.

In Figure 10.4 the resulting active pore pressures when the water level in the excavationis at y = 20 m is displayed for both projects.

a. Active pore pressures (Phase 5 in Chapter 3)

b. Active pore pressures (Phase 2 in the current project)

Figure 10.4 Comparison of the resulting active pore pressures.


TUTORIAL MANUAL


POTATO FIELD MOISTURE CONTENT

11 POTATO FIELD MOISTURE CONTENT

This tutorial demonstrates the applicability of PLAXIS to agricultural problems. Thepotato field tutorial involves a loam layer on top of a sandy base. Regional conditionsprescribe a water level at the position of the material interface. The water level in theditches remains unchanged. The precipitation and evaporation may vary on a daily basisdue to weather conditions. The calculation aims to predict the variation of the watercontent in the loam layer in time as a result of time-dependent boundary conditions.

precipitation precipitation

sand

loam

15 m15 m0.75 m

0.75 m

0.75 m

0.50 m

1.25 m

Figure 11.1 Potato field geometry

Due to the symmetry of the problem, it is sufficient to simulate a strip with a width of15.0 m, as indicated in Figure 11.1. The thickness of the loam layer is 2.0 m and the sandlayer is 3.0 m deep. The problem is modelled as Plane strain model and the 15-Nodeelements are used. The limits of the model geometry are Xmin = 0, Xmax = 15; Ymin = 0and Ymax = 5. Set the Spacing options for grid to 0.25 m.

11.1 INPUT

To create the geometric model, follow these steps:

Create the geometry contour using the following points: (0.0; 0.0), (15.0; 0.0),(15.0; 5.0), (2.0; 5.0), (1.25; 4.25), (0.75; 3.75), (0.0; 3.75).

• Separate the sand and the loam layer by creating a geometry line through the two(points 0.0; 3.0) and (15.0; 3.0). The geometry will now look like Figure 11.2.

Figure 11.2 Potato field geometry model

The standard fixities are used in this model.


TUTORIAL MANUAL

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.

Material data

Create the material data sets according to Table 11.1. Assign the material data set to thecorresponding clusters in the model.

Table 11.1 Material properties for potato field

Parameter Name Loam Sand Unit

General

Material model - Linear elastic Linear elastic -

Type of material behaviour Type Drained Drained -

Parameters

Young's modulus E ' 1.0·103 1.0·103 kN/m2

Poisson's ratio ν ' 0.3 0.3 -

Flow parameters

Data set Type Staring Staring -

Model - Van Genuchten Van Genuchten -

Subsoil/Topsoil - Topsoil Subsoil -

Type - Clayey loam Loamy sand -

Set parameters to default - Yes Yes -

Horizontal permeability kx 0.01538 0.1270 m/day

Vertical permeability ky 0.01538 0.1270 m/day

Finite element mesh

The default global coarseness option (Medium) will be used. To refine the upperboundary of the model:

• Multiple select the line segments composing the upper boundary of the model ((0;3.75) to (15; 5)) by holding the <Shift> key down while clicking on them.

• In the Mesh menu select the Refine line option. Note that the program will apply afactor of 0.5 to the Local element size factor. The program will automaticallygenerate the mesh. Figure 11.3 shows the generated mesh.

Figure 11.3 Potato field mesh



11.2 CALCULATION

The project will be calculated in the Flow mode.

Initial phase

• The default parameters defined in the General and Parameters tabsheets are valid.

In the Water conditions mode define a horizontal water level through the points(-1.0; 4.25)(16.0; 4.25).

• Double click the boundary line at the bottom of the geometry model. Change theclosed flow boundary to a constant prescribed groundwater head (Head(user-defined)). Assign a head of 3 m to both points (Figure 11.4).

Figure 11.4 Boundary conditions at the bottom of the geometry model

Close the boundaries for all the vertical lines as the vertical lines are lines ofsymmetry. The initial conditions are shown in Figure 11.5.

Figure 11.5 Initial conditions

Transient phase

In the transient phase the time-dependent variation of precipitation is defined.

• Add a new calculation phase. In the General tabsheet set the calculation type toTransient groundwater flow.


TUTORIAL MANUAL

• In the Parameters tabsheet set the Time interval to 15 days and the Max saved stepnumber to 250. The Standard settings and the default number of additional stepsare valid.

• Click Define.

In the Water conditions tabsheet click the Precipitation button in the toolbar. This willactivate the Precipitation window.

• The default values for discharge (q) and condition parameters (Ψmax = 0.1 m andΨmin = -1.0 m) are valid. Click Time-dependent. The Time-dependent precipitationwindow pops up.

• Select the Table option for the data.

• In the table displayed at the right side of the window enter the values as shown inTable 11.2.

Table 11.2 Precipitation data

ID Time [day] ∆q [m/day]

1 0 0

2 1 1·10-2

3 2 3·10-2

4 3 0

5 4 -2·10-2

6 5 0

7 6 1·10-2

8 7 1·10-2

9 8 0

10 9 -2·10-2

11 10 -2·10-2

12 11 -2·10-2

13 12 -1·10-2

14 13 -1·10-2

15 14 0

16 15 0

• Click the Graph tab to display the specified time-dependent precipitation conditiongraphically (Figure 11.6).

Figure 11.6 Variation of precipitation in time



• Close the windows by clicking OK.

• Click Update.


11.3 RESULTS

The calculation was focused on the time-dependent saturation of the potato field. To viewthe results:

• From the Stresses menu select Groundwater flow → Saturationeff .

• Double click the legend. The Legend settings window pops up. Define the settingsas shown in Figure 11.7.

Figure 11.7 Value for settings

• Figure 11.8 shows the spatial distribution of the saturation for the last time step.

Figure 11.8 Saturation field at day 15

• Create an animation of the the transient phase for a better visualisation of theresults.

• It is also interesting to create a vertical cross section at x = 4 m and draw crosssection curves for pore pressure and saturation.


TUTORIAL MANUAL


DYNAMIC ANALYSIS OF A GENERATOR ON AN ELASTIC FOUNDATION

12 DYNAMIC ANALYSIS OF A GENERATOR ON AN ELASTIC FOUNDATION

Using PLAXIS, it is possible to simulate soil-structure interaction. Here the influence of avibrating source on its surrounding soil is studied.

Due to the three dimensional nature of the problem, an axisymmetric model is used. Thephysical damping due to the viscous effects is taken into consideration via the Rayleighdamping. Also, due to axisymmetry 'geometric damping' can be significant in attenuatingthe vibration.

The modelling of the boundaries is one of the key points. In order to avoid spurious wavereflections at the model boundaries (which do not exist in reality), special conditions haveto be applied in order to absorb waves reaching the boundaries.

12.1 INPUT

The vibrating source is a generator founded on a 0.2 m thick concrete footing of 1 m indiameter, see Figure 12.1. Oscillations caused by the generator are transmitted throughthe footing into the subsoil. These oscillations are simulated as a uniform harmonicloading, with a frequency of 10 Hz and amplitude of 10 kN/m2. In addition to the weight ofthe footing, the weight of the generator is assumed 8 kN/m2, modelled as a uniformlydistributed load.

sandy clay

1m

generator

Figure 12.1 Generator founded on elastic subsoil

12.1.1 GEOMETRY MODEL

The problem is simulated using an axisymmetric model with 15-noded elements. Thegeometry model is shown in Figure 12.2. Use [s] (seconds) as the unit of time, sincedynamic effects are usually in the order of seconds rather than days.

The model boundaries should be sufficiently far from the region of interest, to avoiddisturbances due to possible reflections. Although special measures are adopted in orderto avoid spurious reflections (absorbent boundaries), there is always a small influenceand it is still a good habit to put boundaries far away. In a dynamic analysis, modelboundaries are generally taken further away than in a static analysis.


TUTORIAL MANUAL

To set up the problem geometry, the following steps are necessary:

• Enter the geometry model as shown in Figure 12.2.

• Use plate elements to model the footing.

• Use Standard fixities.

• Apply a distributed load (system A) on the footing to model the weight of thegenerator.

• Apply a distributed load (system B) on the footing to model the dynamic load.

• In the Loads menu, set the Dynamic load system to load system B.

12.1.2 ABSORBENT BOUNDARIES

Special boundary conditions have to be defined to account for the fact that in reality thesoil is a semi-infinite medium. Without these special boundary conditions the waveswould be reflected on the model boundaries, causing perturbations. To avoid thesespurious reflections, absorbent boundaries are specified at the bottom and right handside boundary.

To add the absorbent boundaries you can use the Standard absorbent boundaries optionin the Loads menu. If necessary, the absorbent boundaries can be generated manuallyas:

• Select the menu option Absorbent boundaries in the Loads menu.

• Click on the lower left point of the geometry.

• Proceed to the lower right point and click again.

• Proceed to the upper right point and click again.

Only the right and bottom boundaries are absorbent boundaries. The left boundary is anaxis of symmetry and the upper boundary is a free surface.

x

y

x = 0.5

A B

standard fixities

absorbentboundaries

0 20

10

Figure 12.2 Generator model with absorbent boundaries



12.1.3 MATERIAL PROPERTIES

The properties of the subsoil are given in Table 12.1. It consists of sandy clay, which isassumed to be elastic. The Young's modulus in Table 12.1 seems relatively high. This isbecause the dynamic stiffness of the ground is generally considerably larger than thestatic stiffness, since dynamic loadings are usually fast and cause very small strains. Theunit weight suggests that the soil is saturated; however the presence of the groundwateris neglected. The footing has a weight of 5 kN/m2 and is also assumed to be elastic. Theproperties are listed in Table 12.2.

Table 12.1 Material properties of the subsoil


General

Material model Model Linearelastic

-


Soil unit weight above phreatic level γunsat 20 kN/m3

Soil unit weight below phreatic level γsat 20 kN/m3

Parameters

Young's modulus (constant) E ' 5.0 · 104 kN/m2


Initial

K0 determination − Manual -

Lateral earth pressure coefficient K0,x 0.50 -

Table 12.2 Material properties of the footing





Weight w 5.0 kN/m/m


Hint: When using Mohr-Coulomb or linear elastic models the wave velocities Vpand Vs are calculated from the elastic parameters and the soil weight. Vpand Vs can also be entered as input; the elastic parameters are thencalculated automatically. See also Elastic parameters and the Wave Velocityrelationships in Section 4.1.2 of the Reference Manual.

12.1.4 MESH GENERATION

The mesh is generated with the default global coarseness option (Medium). The result isplotted in Figure 12.3.


TUTORIAL MANUAL

Figure 12.3 Geometry and mesh

12.2 CALCULATIONS

In the initial situation, the footing and the static load do not exist and therefore they aredeactivated in the Initial phase. The dynamic load seems active but the correspondingmultiplier is automatically set to zero.

In the Phase 1, the footing is built and the static load (weight of the generator) is applied.In the Phase 2 the situation when the generator is running is considered. In the Phase 3the generator is turned off and the soil is let to vibrate freely. The last two phases involvedynamic calculations. The calculations are performed in the Classical mode.

Initial phase

• The K0 procedure is selected by default as calculation type in the General tabsheetof the Calculations window. The default parameters are valid in this example.

• Ensure that the plate and the loads are not active in the Staged construction mode.The dynamic load seems active but the corresponding multiplier is automatically setto zero.

Phase 1

• Click Next to define a new phase.

• Select Plastic in the General tabsheet.

• The Staged construction option is automatically selected in the Parameter tabsheet.Click Define.

• In the Staged construction mode click on the plate element and select all objectsfrom the Select items window. By using the Change option, set the y-value of thestatic load (system A) to -8 kN/m2.

Phase 2

In this phase, a vertical harmonic load, with a frequency of 10 Hz and amplitude of 10kN/m2, is applied to simulate the vibrations transmitted by the generator. Five cycles with



a time interval of 0.5 sec are considered.


• Select Dynamic in the General tabsheet.

• The Additional steps is set by default to 100. Reset displacement to zero and setTime interval to 0.5 s.

• Change the Save max time steps parameter to 10000.

• In the Loading input box the Total multipliers option is selected. Click Define.

Click the button next to Σ MloadB in the Multipliers tabsheet to proceed with thedefinition of the dynamic load in the Dynamic loading - Load system B window.

• The option Harmonic load multiplier is selected by default. Set the Amplitudemultiplier to 10, frequency to 10 Hz and Initial phase angle to 0 (See Figure 12.4).

Figure 12.4 Harmonic load

Phase 3

In this phase, the generator is turned off. The soil is vibrating freely after the initialexcitation.


• Select the Dynamic option in the General tabsheet.

• In the Parameters tabsheet the number of Additional steps is 100. Set Time intervalto 0.5 s. The estimated end time is 1 sec.

• In the Loading input box the Total multipliers option is selected. Click Define.

Click the button next to Σ MloadB in the Multipliers tabsheet to proceed with thedefinition of the dynamic load in the Dynamic loading - Load system B window.

• The option Harmonic load multiplier is selected by default. Set all parameters tozero in the Dynamic loading window.

Before running the calculation, select points at the surface at about 1.4m, 1.9m and3.6m. They will be used to visualise the deformation as a function of time. You can

now start the calculation.


TUTORIAL MANUAL

12.2.1 ADDITIONAL CALCULATION WITH DAMPING

In a second calculation, material damping is introduced by means of Rayleigh damping.Rayleigh damping can be entered in the material data set. The following steps arenecessary:

• Start the Input program and select the generator project.

• Save the project under another name.

• Open the material data set of the soil. In the General tabsheet change the Rayleighdamping parameters α and β to 0.001 and 0.01 respectively in the Advanced box(Figure 12.5).

Figure 12.5 Input of Rayleigh damping

• Close the data base, proceed to the Calculations program, check whether thephases are still properly defined (according to the information given before) and startthe calculation.

12.3 RESULTS

The Curve generator feature is particularly useful for dynamic analysis. You can easilydisplay the actual loading versus time (input) and also displacements, velocities andaccelerations of the pre-selected points versus time. The evolution of the definedmultipliers with time can be plotted by assigning Dynamic time to x-axis and ΣMloadB,available under Multipliers, to the y-axis.

Figure 12.7 shows the response of the pre-selected points at the surface of the structure.It can be seen that even with no damping, the waves are dissipated which can beattributed to the geometric damping.



Figure 12.6 Multipliers – time curve

Figure 12.7 Vertical displ.- time on the surface at different distances to the vibrating source. Withoutdamping (Rayleigh α = 0; β = 0)

The presence of damping is clear in Figure 12.8. It can be seen that the vibration istotally seized when some time is elapsed after the removal of the force (at t = 0.5 s).Also, the displacement amplitudes are lower. Compare Figure 12.7 (without damping)with Figure 12.8 (with damping).

It is possible in the Output program to display displacements, velocities and accelerationsat a particular time, by choosing the appropriate option in the Deformations menu. Figure12.9 shows the total accelerations in the soil at the end of phase 2 (t = 0.5 s).


TUTORIAL MANUAL

Figure 12.8 Vertical displ.- time. With damping (Rayleigh α = 0.001 ; β = 0.01)

Figure 12.9 Total accelerations in the soil at the end of phase 2 (with damping)


PILE DRIVING

13 PILE DRIVING

This example involves driving a concrete pile through an 11 m thick clay layer into a sandlayer, see Figure 13.1. The pile has a diameter of 0.4 m. Pile driving is a dynamicprocess that causes vibrations in the surrounding soil. Moreover, excess pore pressuresare generated due to the quick stress increase around the pile.

In this example focus is placed on the irreversible deformations below the pile. In order tosimulate this process most realistically, the behaviour of the sand layer is modelled bymeans of the HS small model.

clay

sand

pile Ø 0.4 m 11 m

7 m

Figure 13.1 Pile driving situation

13.1 INPUT


The geometry is simulated by means of an axisymmetric model in which the pile ispositioned along the axis of symmetry (Figure 13.2). In the general settings, the standardgravity acceleration is used (9.8 m/s2). The unit of time should be set to seconds [s].

Both the soil and the pile are modelled with 15-noded elements. The subsoil is dividedinto an 11 m thick clay layer and a 7 m thick sand layer. The pile is defined as a column of0.2 m width. The Interface elements are placed around the pile to model the interactionbetween the pile and the soil. The interface should be extended to about half a meter intothe sand layer (see Figure 13.3). Note that the interface should be defined only at theside of the soil. A proper modelling of the pile-soil interaction is important to include thematerial damping caused by the sliding of the soil along the pile during penetration and toallow for sufficient flexibility around the pile tip. Use the zoom option to create the pileand the interface.

The boundaries of the model are taken sufficiently far away to avoid direct influence ofthe boundary conditions. Standard absorbent boundaries are used at the bottom and atthe right hand boundary to avoid spurious reflections.


TUTORIAL MANUAL

x

y

x = 0.2A

standard fixities

absorbentboundaries

0

18

30

y = 7y = 6.6

interface

Figure 13.2 Geometry model of pile driving problem

Hint: When boundary conditions are applied using the Standard fixities button,horizontal fixities are also applied to the pile top. The standard fixities optionassigns fixities to all lines that lie within certain limits from the boundaries ofthe geometry and as, due to its dimensions, the pile top falls within theselimits, boundary conditions are applied. Since this is not desired make sureto remove the horizontal fixities at the pile top.

In order to model the driving force, a distributed unit load (system A) is created on top ofthe pile. From the Loads menu set Load system A as a dynamic load system.

Pile

Interface

Clay

Extended interface

Sand

(0.0, 7.0)(0.2, 7.0)

(0.2, 6.6)

Figure 13.3 Extended interface


The clay layer is modelled with the Mohr-Coulomb model. The behaviour is considered tobe Undrained (B). An interface strength reduction factor is used to simulate the reducedfriction along the pile shaft.

In order to model the non-linear deformations below the tip of the pile in a right way, thesand layer is modelled by means of the HS small model. Because of the fast loadingprocess, the sand layer is also considered to behave undrained. The short interface inthe sand layer does not represent soil-structure interaction. As a result, the interface


PILE DRIVING

strength reduction factor should be taken equal to unity (rigid).

The pile is made of concrete, which is modelled by means of the linear elastic modelconsidering non-porous behaviour. In the beginning, the pile is not present, so initially theclay properties are also assigned to the pile cluster. The parameters of the two layers andthe concrete pile are listed in Table 13.1.

Table 13.1 Material properties of the subsoil and pile

Parameter Symbol Clay Sand Pile Unit

General

Material model Model Mohr-Coulomb HS small Linear elastic -

Type of behaviour Type Undrained (B) Undrained (A) Non-porous -

Unit weight above phreatic line γunsat 16 17 24 kN/m3

Unit weight below phreatic line γsat 18 20 - kN/m3

Parameters

Young's modulus (constant) E ' 5.0· 103 - 3·107 kN/m2


E ref50 - 5.0· 104 - kN/m2


E refoed - 5.0· 104 - kN/m2

Unloading / reloading stiffness E refur - 1.5· 105 - kN/m2

Power for stress-level dependencyof stiffness

m - 0.5 - -

Poisson's ratio ν 'ur 0.3 0.2 0.1 -

Cohesion c'ref - 0 - kN/m2

Undrained shear strength su,ref 5.0 - - kN/m2

Friction angle ϕ' 0 31.0 - ◦

Dilatancy parameter ψ 0 0 - ◦


γ0.7 - 1.0·10-4 - -


Gref0 - 1.2·105 - kN/m2

Young's modulus inc. E 'inc 1.0·103 - - kN/m2


Undrained shear strength inc. su,inc 3 - - kN/m2


Interface

Interface strength type Type Manual Rigid Rigid -

Interface strength Rinter 0.5 1.0 1.0 -

Initial

K0 determination − Manual Automatic Automatic -

Lateral earth pressure coefficient K0,x 0.5000 0.4850 1.0 -

It should be noted that there is a remarkable difference in wave velocities between theclay layer and the concrete pile due to the large stiffness difference. This may lead tosmall time increments (many sub steps) in the automatic time stepping procedure. Thiscauses the calculation process to be very time consuming. Many sub steps may also becaused by a very small (local) element size. In such situations it is not always vital tofollow the automatic time stepping criterion. You can reduce the number of sub steps inthe Manual setting of the Iterative procedure.

When the HS small model is used wave velocities are not shown because they vary dueto the stress-dependent stiffness.


TUTORIAL MANUAL


The mesh is generated using the default global coarseness (Medium). The result of themesh generation is plotted in Figure 13.4.

Figure 13.4 Finite element mesh for pile driving problem

13.2 CALCULATIONS

In the Initial phase, the initial stress conditions are generated. In the Phase 1 the pile iscreated. In the Phase 2 the pile is subjected to a single stroke, which is simulated byactivating half a harmonic cycle of load system A. In the Phase 3 the load is kept zeroand the dynamic response of the pile and soil is analysed in time. The last two phasesinvolve dynamic calculations.

The phreatic level is assumed to be at the ground surface. Hydrostatic pore pressuresare generated in the whole geometry according to this phreatic line.

Initial phase

Initial effective stresses are generated by the K0 procedure, using the default values.Note that in the initial situation the pile does not exist and that the clay properties shouldbe assigned to the corresponding cluster. The phreatic level is assumed to be at theground surface. Hydrostatic pore pressures are generated in the whole geometryaccording to this phreatic line.

Phase 1


• Select Plastic option in the General tabsheet.

• The Staged construction option is by default selected in the Parameter tabsheet.Click Define.


PILE DRIVING

• Assign the pile properties to the pile cluster.

• Activate the interface and the dynamic load at the top of the pile. Note that thedynamic load will be considered in the Dynamic calculation in the next phase.

Phase 2



• Use standard Additional steps (100).

• Reset displacements to zero.

• Enter 0.01 s for the Time interval.

• In the Multipliers tabsheet click the Dynamics button next to Load system A to definethe dynamic loading. Enter the values as indicated in Figure 13.5.

Figure 13.5 Dynamic loading parameters

The result of this phase is half a harmonic cycle of the external load in system A. At theend of this phase, the load is back to zero.

Phase 3


• Use standard Additional steps (100).

• Enter a Time interval of 0.19 s.

• In the Multiplier tabsheet, all multipliers remain at their default values.

Click the button next to Load system A and set all parameters in the Dynamicloading window to zero.

• Select a node at the top of the pile for load displacement curves.

13.3 RESULTS

Figure 13.6 shows the settlement of the pile (top point) versus time. From this figure thefollowing observations can be made:

• The maximum vertical settlement of the pile top due to this single stroke is about 13


TUTORIAL MANUAL

mm. However, the final settlement is almost 10 mm.

• Most of the settlement occurs in phase 3 after the stroke has ended. This is due tothe fact that the compression wave is still propagating downwards in the pile,causing additional settlements.

• Despite the absence of Rayleigh damping, the vibration of the pile is damped due tosoil plasticity and the fact that wave energy is absorbed at the model boundaries.

Figure 13.6 Pile settlement vs. time

When looking at the output of the second calculation phase (t = 0.01 s, i.e. just after thestroke), it can be seen that large excess pore pressures occur very locally around the piletip. This reduces the shear strength of the soil and contributes to the penetration of thepile into the sand layer. The excess pore pressures remain also in the third phase sinceconsolidation is not considered.

Figure 13.7 shows the shear stresses in the interface elements at t = 0.01 s. The plotshows that the maximum shear stress is reached all along the pile, which indicates thatthe soil is sliding along the pile.

When looking at the deformed mesh of the last calculation phase (t = 0.2 s), it can alsobe seen that the final settlement of the pile is about 10 mm. In order to see the wholedynamic process it is suggested to use the option Create Animation to view a 'movie' ofthe deformed mesh in time. You may notice that the first part of the animation is slowerthan the second part.


PILE DRIVING

Figure 13.7 Maximum shear stresses in the interface at t = 0.01 s.


TUTORIAL MANUAL


FREE VIBRATION AND EARTHQUAKE ANALYSIS OF A BUILDING

14 FREE VIBRATION AND EARTHQUAKE ANALYSIS OF A BUILDING

This example demonstrates the natural frequency of a five-storey building whensubjected to free vibration and earthquake loading.

The building consists of 5 floors and a basement. It is 10 m wide and 17 m high includingbasement. The total height from the ground level is 5 x 3 m = 15 m and the basement is2 m deep. A value of 5 kN/m2 is taken as the weight of the floors and the walls. Thebuilding is constructed on a clay layer of 15 m depth underlayed by a deep sand layer. Inthe model, 25 m of the sand layer will be considered.

14.1 INPUT

General settings



• Keep the default units and set the model dimensions to Xmin = −80, Xmax = 80, Ymin= −40 and Ymax = 15. Keep the default values for the grid spacing (Spacing = 1 m;Number of intervals = 1).

x

y15 m

15 m

25 m

75 m75 m 10 m

2 m

Figure 14.1 Geometry of the project


Use the Geometry line feature to define the soil clusters.

Click the Plate button in the toolbar and define the vertical walls of the buildingpassing through (-5; 0) to (-5; 15) and through (5; 0) to (5; 15).

• Use the same feature to define the vertical walls of the basement passing through(-5; -2) to (-5; 0) and through (5; -2) to (5; 0).

• Define the floors and the basement of the building, passing through (-5; -2) to (5; -2),(-5; 0) to (5; 0), (-5; 3) to (5; 3), (-5; 6) to (5; 6), (-5; 9) to (5; 9), (-5; 12) to (5; 12) and(-5; 15) to (5; 15).


TUTORIAL MANUAL

Click the Node-to-node anchor button to define the column at the centre of thebuilding connecting consecutive floors, (0; -2) to (0; 0), (0; 0) to (0; 3), (0; 3) to (0; 6),(0; 6) to (0; 9), (0; 9) to (0; 12) and (0; 12) to (0; 15).

Define an interface to model the interaction between soil and building around thebasement floor.

Define a static lateral force of 1 kN/m at the top left corner of the building by clickingthe Point load - Load system A button in the toolbar and by clicking on the location ofthe load.

Define a prescribed displacement at the bottom of the model, through (-80; -40) and(80; -40).

• Assign the values for the components of the prescribed displacement as (0.01; 0).

• In the Loads menu set point to Set dynamic load system and select the Prescribeddisplacement option from the appearing menu.

The option of Standard fixities is used to assign full restraints on the movements inhorizontal direction on the vertical boundaries on two sides and full restraints in boththe horizontal and vertical directions along the lowermost horizontal geometry line.

• Select the Standard earthquake boundaries option in the Loads menu. The modellayout is displayed in Figure 14.2.

Figure 14.2 Geometry of the model


The properties of the subsoil are given in Table 14.1 and the plate properties are providedin Table 14.3. The upper layer consists of mostly clayey soil and the lower one is sandy.Both have HS small model properties. The plates, representing the walls and the floors inthe building, are considered to be linear elastic. The presence of the groundwater isneglected. The clusters of the building are filled with soil material when generating themesh, but these clusters are deactivated in the initial situation. The physical damping inthe building is simulated by means of Rayleigh damping. The soil layers with HS smallmodel properties have inherent hysteretic damping.



Table 14.1 Material properties of the subsoil layers

Parameter Name Upper clayeylayer

Lower sandylayer

Unit

General

Material model Model HS small HS small -

Type of material behaviour Type Drained Drained -


γunsat 16 20 kN/m3


γsat 20 20 kN/m3

Parameters


E ref50 2.0·104 3.0·104 kN/m2


E refoed 2.561·104 3.601·104 kN/m2

Unloading / reloading stiffness E refur 9.484·104 1.108·105 kN/m2

Power for stress-level dependencyof stiffness

m 0.5 0.5 -

Cohesion c'ref 10 5 kN/m2

Friction angle ϕ' 18 28 ◦

Dilatancy angle ψ 0 0 ◦


γ0.7 1.2·10-4 1.5·10-4 -


Gref0 2.7·105 1.0·105 kN/m2

Poisson's ratio ν 'ur 0.2 0.2 -

When subjected to cyclic shear loading, the HS small model will show typical hystereticbehaviour. Starting from the small-strain shear stiffness, Gref

0 , the actual stiffness willdecrease with increasing shear. Figures 14.3 and 14.4 display the Modulus reductioncurves, i.e. the decay of the shear modulus with strain. The upper curve shows thesecant shear modulus and the lower curve shows the tangent shear modulus.

0

100000

50000

150000

200000

250000

She

arm

odul

us

Shear strain0.00001 0.0001 0.001 0.01

Gt Gsγ0.7

0.722G0

G used

Figure 14.3 Modulus reduction curves for the upper clayey layer


TUTORIAL MANUAL

20000

40000

60000

80000

100000

She

arm

odul

us

Shear strain0.00001 0.0001 0.001 0.01

GtGs

γ0.7

0.722G0

G used

Figure 14.4 Modulus reduction curve for the lower sandy layer

In the HS small model, the tangent shear modulus is bounded by a lower limit, Gur .

Gur =Eur

2(1 + νur )

The values of Grefur for the Upper clayey layer and Lower sandy layer and the ratio to Gref

0are shown in Table 14.2. This ratio determines the maximum damping ratio that can beobtained.

Table 14.2 Gur values and ratio to Gref0

Parameter Unit Upper clayeylayer

Lower sandylayer

Gur kN/m2 39517 41167

Gref0 /Gur - 6.75 2.5

Figures 14.5 and 14.6 show the damping ratio as a function of the shear strain for thematerial used in the model. For a more detailed description and elaboration from themodulus reduction curve to the damping curve can be found in the literature†.

0

0.2

0.15

0.1

0.05Dam

ping

ratio

Cyclic shear strain0.00001 0.0001 0.001 0.01

Figure 14.5 Damping curve for the upper clayey layer

† Brinkgreve, R.B.J., Kappert, M.H., Bonnier, P.G. (2007). Hysteretic damping in small-strain stiffness model. InProc. 10th Int. Conf. on Comp. Methods and Advances in Geomechanics. Rhodes, Greece, 737− 742



0

0.2

0.15

0.1

0.05D

ampi

ngra

tio

Cyclic shear strain0.00001 0.0001 0.001 0.01

Figure 14.6 Damping curve for the lower sandy layer

Define the material dataset for the plates representing the structure according to Table14.3. Note that two different material datasets are used. Assign the Basement materialdataset to the vertical plates (2) and the lowest horizontal plate (all under the groundlevel) in the model. A description of Rayleigh damping parameters is given in Section4.1.1 or the Reference Manual.

Table 14.3 Material properties of the building (plate properties)

Parameter Name Rest of building Basement Unit

Material type Type Elastic; Isotropic Elastic -

Normal stiffness EA 9.0·106 1.2·107 kN/m

Flexural rigidity EI 6.75·104 1.6·105 kNm2/m

Weight w 10 20 kN/m/m

Poisson's ratio ν 0.0 0.0 -

Rayleigh dampingα 0.2320 0.2320 -

β 8.0·10-3 8.0·10-3 -

Define the properties of the anchor according to Table 14.4.

Table 14.4 Material properties of the node-to-node anchor

Parameter Name Column Unit

Normal stiffness EA 2.5· 106 kN

Material type Type Elastic -

Spacing out of plane Lspacing 3.0 m


The mesh is generated using the default global coarseness (Medium). The result of themesh generation is plotted in (Figure 14.7).


TUTORIAL MANUAL

Figure 14.7 Mesh of the soil-building system

14.2 CALCULATIONS

The calculation process consists of the initial conditions phase, simulation of theconstruction of the building, loading, free vibration analysis and earthquake analysis.

Initial phase

• In the General tabsheet the K0 procedure option is automatically selected ascalculation type.

• In the Parameters window accept the default values and click Define.

• In the Staged construction mode check that the building and load are inactive.

• In the Water conditions mode define a phreatic level at y = -15.

• Click Update to proceed to the Calculations program.

Phase 1


• In the General tabsheet the Plastic option is automatically selected as calculationtype.

• In the Parameters window accept the default values and click Define.

• In the Staged construction mode construct the building (activate all the plates andthe anchor) and deactivate the basement volume.


Figure 14.8 Construction of the building



Phase 2


• In the General tabsheet the Plastic option is automatically selected as calculationtype.

• In the Parameters window select the Reset displacement to zero, accept the defaultvalues and click Define.

• In the Staged construction mode activate the load and assign a value of 10 kN/m toit.


Phase 3


• In the General tabsheet select the Free vibration option as calculation type.

• In the Parameters tabsheet, set the Time interval to 5 sec. Note that the Releaseload system A option is selected for the Loading input releasing the static loadapplied in the parent phase.

• The Additional steps parameter is automatically set to 100. Select the Manualsettings option in the Iterative procedure box and click Define.

• In the Manual settings window set the Dynamic sub steps to 10 and click OK.

Hint: Note that a warning appears when the Dynamic sub steps is set to 10. Thiswarning is deliberately ignored to reduce the calculation time. However, thewarning should generally be considered in order to obtain accurate results.

Phase 4


• In the General tabsheet set the Start from phase option to Phase 1 (construction ofbuilding).

• Select the Dynamic option as calculation type.

• In the Parameters tabsheet, set the Time interval to 20 sec.

• Set the Additional steps parameter to 200. Reset the displacements to zero.

• Set the Dynamic substeps to 20 and click OK.

In the Multipliers tabsheet click the button next to Σ−MdispX .

• In the Dynamic loading window select the Load multiplier from data file option. Thefile containing the earthquake data is available in the PLAXIS knowledge base(http://kb.plaxis.nl/sites/kb.plaxis.nl/files/kb-downloads/225a.smc).

Select interesting points for curves (e.g. top of the bulding, basement) and calculatethe project.


TUTORIAL MANUAL

14.3 RESULTS

Figure 14.9 shows the deformed structure at the end of the Phase 2 (application ofhorizontal load).

Figure 14.9 Deformed mesh of the system

Figure 14.10 shows the time history of displacements of the selected points A (0; 15) forthe free vibration phase. It may be seen from the figure that the vibration slowly decayswith time due to damping in the soil and in the building.

Figure 14.10 Time history of displacements at selected points

In the Chart tabsheet of the Settings window select the Use frequency representation(spectrum) and Use standard frequency (Hz) options in the Dynamics box. The plot isshown in Figure 14.11. From this figure it can be evaluated that the dominant buildingfrequency is around 1 Hz.

Figure 14.12 shows the time history of the lateral acceleration of the selected points A (0;



Figure 14.11 Frequency representation (spectrum)

15) for the earthquake phase (dynamic analysis). For a better visualisation of the resultsanimations of the free vibration and earthquake can be created.

Figure 14.12 Variation of acceleration in dynamic time


TUTORIAL MANUAL


APPENDIX A - MENU TREE


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TUTORIAL MANUAL

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TUTORIAL MANUAL

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TUTORIAL MANUAL

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APPENDIX B - CALCULATION SCHEME FOR INITIAL STRESSES DUE TO SOIL WEIGHT

APPENDIX B - CALCULATION SCHEME FOR INITIAL STRESSES DUE TO SOILWEIGHT

Start

Yes NoHorizontalsurface

Initial stressesGravity loading

Gravity loading

Ready

K0-Procedure

∑-Mweight = 1

∑-Mweight = 1

Loading input:Total multipliers

calculation

Examples of non-horizontal surfaces, and non-horizontal weight stratifications are:


TUTORIAL MANUAL


2d2012-1-tutorial plaxis.pdf

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