Tutorial Plaxis2D

PLAXIS 2D

Tutorial Manual

2011

Build 5167

TABLE OF CONTENTS

TABLE OF CONTENTS

1 Introduction 5

2 Settlement of a circular footing on sand 72.1 Geometry 72.2 Case A: Rigid footing 82.3 Case B: Flexible footing 22

3 Submerged construction of an excavation 293.1 Input 303.2 Calculations 373.3 Results 41

4 Dry excavation using a tie back wall 454.1 Input 454.2 Calculations 494.3 Results 52

5 Construction of a road embankment 555.1 Input 555.2 Calculations 585.3 Results 615.4 Safety analysis 635.5 Using drains 665.6 Updated mesh + Updated water pressures analysis 67

6 Settlements due to tunnel construction 696.1 Input 706.2 Calculations 746.3 Results 77

7 Excavation of a NATM tunnel 797.1 Input 797.2 Calculations 817.3 Results 83

8 Stability of dam under rapid drawdown 858.1 Input 858.2 Case A: Classical mode 878.3 Case B: Advanced mode 91

9 Flow through an embankment 939.1 Input 939.2 Calculations 949.3 Results 95

10 Flow around a sheet pile wall 9910.1 Input 9910.2 Calculations 9910.3 Results 101

PLAXIS 2D 2011 | Tutorial Manual 3

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11 Potato field moisture content 10311.1 Input 10311.2 Calculation 10411.3 Results 106

12 Dynamic analysis of a generator on an elastic foundation 10912.1 Input 10912.2 Calculations 11212.3 Results 114

13 Pile driving 11713.1 Input 11713.2 Calculations 12013.3 Results 121

14 Free vibration and earthquake analysis of a building 12514.1 Input 12514.2 Calculations 13014.3 Results 132

Appendix A - Menu tree 135

Appendix B - Calculation scheme for initial stresses due to soil weight 141

4 Tutorial Manual | PLAXIS 2D 2011

INTRODUCTION

1 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 lessons deal with a wide range of interesting practical applications,this Tutorial Manual is intended to help new users become familiar with PLAXIS 2D. Thelessons 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 lessons arefollowed in the order that they appear in the manual. The tutorial lessons are alsoavailable in the examples folder of the PLAXIS program directory and can be used tocheck your results.

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


TUTORIAL MANUAL


SETTLEMENT OF A CIRCULAR FOOTING ON SAND

2 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 lessons. Therefore, it is important to complete thisfirst lesson 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.

2.1 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 2.1. 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.


TUTORIAL MANUAL

2.0 m

4.0 m

load

footing

x

ysand

a

Figure 2.1 Geometry of a circular footing on a sand layer

2.2 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 lesson deals with an external load on a flexiblefooting, which is a more advanced modelling approach.

2.2.1 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 2.2).

Figure 2.2 Quick select dialog box

Click Start a new project. The Project properties window appears, consisting of twotabsheets, Project and Model (Figure 2.3 and Figure 2.4).



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 2.3 Project tabsheet of the Project properties window

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

In the Project tabsheet, enter "Lesson 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 lesson 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.


TUTORIAL MANUAL

Figure 2.4 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 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 on the keyboard after terminating the drawing process.

Lines can be drawn perfectly horizontal or vertical by holding down the 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 lesson, 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 2.5 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 2.2.2). 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,Anchors and Geogrids.



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 (Figure2.6).

Figure 2.6 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 2.7) according to thematerial properties listed in Table 2.1.

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 2.1 in the corresponding edit boxes of theParameters tabsheet (Figure 2.8). A detailed description of different soil models andtheir corresponding parameters can be found in the Material Models Manual.


TUTORIAL MANUAL

Table 2.1 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 unsat 17.0 kN/m3

Soil unit weight below phreatic level sat 20.0 kN/m3

Parameters

Young's modulus (constant) E ' 1.3 104 kN/m2Poisson's ratio ' 0.3 -

Cohesion (constant) c'ref 1.0 kN/m2

Friction angle ' 30.0

Dilatancy angle 0.0

Figure 2.7 General tabsheet of the Soil window of Soil and interfaces set type

Figure 2.8 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 theleft 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 indicate



whether 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.

Select the Coarse option from the Element distribution drop-down menu.

Click Generate. After the generation of the mesh a new window is opened (Outputwindow) in which the generated mesh is presented (Figure 2.9).

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

2.2.2 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.


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Figure 2.9 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.

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 2.10). By default theClassical mode is selected. This calculation mode is considered in this lesson.Press OK to proceed.

Figure 2.10 Select calculation mode window

The Calculations window consists of a menu, a toolbar, a set of tabsheets and a list ofcalculation phases, as indicated in Figure 2.11.



Figure 2.11 The General tabsheet of the Calculations window

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 Previewtabsheet 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.

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


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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 2.12.

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 2.12 Parameters tabsheet of the Calculations window

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

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 the



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.

prescribed displacement can be specified, as indicated in Figure 2.13. 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 2.13 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. 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 2.14). 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 informationabout the calculations info window.

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.


TUTORIAL MANUAL

Figure 2.14 The Active tasks window displaying information about the calculation process

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 2pi (this gives a value of about 648 kN).

2.2.3 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 (Figure2.15). The deformed mesh is scaled to ensure that the deformations are visible.



Figure 2.15 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 2.16).


TUTORIAL MANUAL

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

Figure 2.16 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.

2.3 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 key on the keyboard.

Select the Prescribed displacement from the Select items to delete window (Figure2.17) 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.

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 which



Figure 2.17 Select items to delete window

simulates 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 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 2.18).

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.

Figure 2.18 The dialog box for distributed load

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 2.2.


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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 2.2 Material properties of the footing


Material type Type Elastic; Isotropic -Normal stiffness EA 5 106 kN/mFlexural rigidity EI 8.5 103 kNm2/mWeight w 0.0 kN/m/mPoisson's ratio 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 206 kN/m2 for both geometry points. Note that this gives a totalload that is approximately equal to the footing force that was obtained from the firstpart of this lesson. (206 kN/m2 x pi x (1.0 m)2 648 kN).

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 2.20, follow these steps:

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

Figure 2.19 Curve generation window

In the Charts tabsheet, click New. The Curve generation window pops up (Figure2.19).

For the xaxis, 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 yaxis, select the Project option from the drop-down menu. Select theMstage 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.

Click OK to accept the input and generate the load-displacement curve. As a resultthe curve of Figure 2.20 is plotted.



Hint: The Curve generation window may also be used to modify the attributes orpresentation of a curve.

Figure 2.20 Load-displacement curve for the footing

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.

Comparison between Case A and Case B

When comparing the calculation results obtained from Case A and Case B, it can benoticed that the footing in Case B, for the same maximum load of 648 kN, exhibited moredeformation than that for Case A. This can be attributed to the fact that in Case B a finermesh was generated due to the presence of a plate element (PLAXIS generates smallersoil elements at the contact region with a plate element by default). In general,geometries with coarse meshes may not exhibit sufficient flexibility, and hence mayexperience less deformation. The influence of mesh coarseness on the computationalresults is pronounced more in axisymmetric models. If, however, the same mesh wasused, the two results would match quite well.

Hint: Difference with previous model (Case A) is due to finer mesh around thefooting.


TUTORIAL MANUAL


SUBMERGED CONSTRUCTION OF AN EXCAVATION

3 SUBMERGED CONSTRUCTION OF AN EXCAVATION

This lesson illustrates the use of PLAXIS for the analysis of submerged construction of anexcavation. Most of the program features that were used in Lesson 1 will be utilised hereagain. In addition, some new features will be used, such as the use of interfaces andanchor elements, the generation of water pressures and the use of multiple calculationphases. The new features will be described in full detail, whereas the features that weretreated in Lesson 1 will be described in less detail. Therefore it is suggested that Lesson1 should be completed before attempting this exercise.

This lesson 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 3.1).

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 3.1 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 lesson. 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.

Objectives:

Modelling soil-structure interaction using the Interface feature.


TUTORIAL MANUAL

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).

3.1 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) at



the 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, aninterface 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.


TUTORIAL MANUAL

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 3.2).

Figure 3.2 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 3.3.

Figure 3.3 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 3.1.

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:

taninterface = Rinter tansoil and cinter = Rintercsoil

where:

csoil = cref (see Table 3.1)

Hence, using the entered Rinter -value gives a reduced interface friction and interfacecohesion (adhesion) compared to the friction angle and the cohesion in the adjacent soil.


TUTORIAL MANUAL

Table 3.1 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 unsat 16 17 kN/m3

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

Initial void ratio einit 1.0 - -

Parameters

Modified compression index 3.0 10-2 - -Modified swelling index 8.5 10-3 - -Secant stiffness in standard drained triaxial test E ref50 - 4.0 104 kN/m2Tangent stiffness for primary oedometer loading E refoed - 4.0 104 kN/m2Unloading / reloading stiffness E refur - 1.2 105 kN/m2Power 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 ' 25 32

Dilatancy angle 0.0 2.0

Poisson's ratio ur ' 0.15 0.2 -

Flow parameters

Permeability in horizontal direction kx 0.001 1.0 m/dayPermeability 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 ratio POP 5.0 0.0 -

For the sand layer, enter "Sand" for the Identification and select Hardening soil asthe Material model. The material type should be set to Drained.

Enter the properties of the sand layer, as listed in Table 3.1, 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.

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.

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.



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.

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.

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).

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 3.2. 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 3.2 Material properties of the diaphragm wall (Plate)


Type of behaviour Material type Elastic; Isotropic

Normal stiffness EA 7.5 106 kN/mFlexural rigidity EI 1.0 106 kNm2/mUnit weight w 10.0 kN/m/mPoisson's ratio 0.0 -

Set the Set type parameter in the Material sets window to Anchors and click New.Enter "Strut" as an Identification of the data set and enter the properties as given inTable 3.3. 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.

Mesh Generation

In this lesson a local mesh refinement procedure is used. Starting from a global coarsemesh, there are simple possibilities for local refinement within a cluster, on a line or


TUTORIAL MANUAL

Table 3.3 Material properties of the strut (anchor)


Type of behaviour Material type Elastic -

Normal stiffness EA 2106 kNSpacing 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 lessons in this Tutorial Manualare stored in the global database during the installation of the program. Tocopy an existing data set, click the Show global button of the Material setswindow. Drag the appropriate data set from the tree view of the globaldatabase to the project database and drop it. Now the global data set isavailable for the current project. Similarly, data sets created in the projectdatabase may be dragged and dropped in the global database.

around a point. These options are available from the Mesh menu. In order to generatethe proposed mesh, follow these steps:

From the Mesh menu, select the Global coarseness option. Set the Elementdistribution to Coarse and click OK.

Multi-select all the wall elements by keeping the key pressed while clickingon each of them.

From the Mesh menu, select the Refine line option. The resulting mesh is displayed.

Click the Close button to return to the Input program.

Hint: The Reset all option in the Mesh menu is used to restore the meshgeneration default setting (Global coarseness = Medium; no localrefinement).

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.



Figure 3.4 Resulting mesh

3.2 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 lesson 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 lesson only deals with the direct generation procedure.Generation based on groundwater flow is presented in Section 4.2.

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 4.2. Here only a general phreatic level is defined at 2.0 m below the groundsurface.


TUTORIAL MANUAL

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 leftmouse 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.

Click the Close button to go to the Input program.

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

Hint: An existing water level may be modified by using the Selection button. Ondeleting the General phreatic level (selecting it and pressing the 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 in



the 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.

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.

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.

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. Thestrut should turn black to indicate it is active.

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


TUTORIAL MANUAL

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 Mstage is increased from0.0 to 1.0. This parameter is displayed on the calculation info window. As soon asMstage has reached the value 1.0, the construction stage is completed and thecalculation phase is finished. If a Staged construction calculation finishes while Mstageis 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 Mstage multiplier,click the Multipliers tab and select the Reached values radio button. The Mstageparameter is displayed at the bottom of the Other box that pops up. Verify that this value



is equal to 1.0. You also might wish to do the same for the other calculation phases.

3.3 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 (Figure3.5).

Figure 3.5 Deformed mesh after submerged excavation

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 anindication 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 3.6).


TUTORIAL MANUAL

Figure 3.6 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 3.7).

Figure 3.7 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 - Mstage.

Click OK to accept the input and generate the load-displacement curve. As a resultthe curve of Figure 3.8 is plotted.

Figure 3.8 Load-displacement curve of deflection of wall

The curve shows the construction stages. For each stage, the parameter Mstagechanges 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.


TUTORIAL MANUAL


DRY EXCAVATION USING A TIE BACK WALL

4 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 4.1 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.

4.1 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

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, 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 4.2.

x

y

28 m 10 m 2 m

1 m1 m

20 m 40 m

3 m

3 m

4 m

5 m

13 m

(0; 0)

(0; 15)

(0; 27)

(0; 30)

Geogrid

Node-to-node anchors

Figure 4.2 Geometry model of building pit

To define the geometry:

Define the soil clusters as shown in Figure 4.2. 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.

A ground anchor can be modelled by a combination of a node-to-node anchor and ageogrid. The geogrid simulates the grout body whereas the node-to-node anchorsimulates the anchor rod. In reality there is a complex three-dimensional state of stressaround the grout body.

Define the node-to-node anchors according to Table 4.1.

Table 4.1 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 Geogrid button according to Table 4.2.

Table 4.2 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)

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.

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.

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 4.3.

Table 4.3 Properties of the diaphragm wall (plate)


Material type Type Elastic; Isotropic -Normal stiffness EA 1.2 107 kN/mFlexural rigidity EI 1.2 105 kNm2/mWeight w 8.3 kN/m/mPoisson's ratio 0.15 -

For the properties of the ground anchors, two material data sets are needed: One of theAnchor type and one of the Geogrid type. The Anchor data set contains the properties ofthe anchor rod and the Geogrid data set contains the properties of the grout body. Thedata are listed in Table 4.4 and 4.5.

Table 4.4 Properties of the anchor rod (node-to-node anchor)


Material type Type Elastic -

Normal stiffness EA 5.0 105 kNSpacing out of plane Ls 2.5 m


TUTORIAL MANUAL

Table 4.5 Properties of the grout body (geogrid)


Material type Type Elastic; Isotropic -Normal stiffness EA 2.0 105 kN/m

The soil consists of three distinct layers. Enter three data sets for soil and interfaces withthe parameters given in Table 4.6.

Table 4.6 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 unsat 16 17 17 kN/m3

Soil unit weight below phreatic level sat 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/m2Power for stress-level dependency ofstiffness

m 0.5 0.5 0.8 -

Cohesion cref ' 1.0 0.0 5.0 kN/m2

Friction angle ' 30 34 29

Dilatancy angle 0.0 4.0 0.0

Poisson's ratio ur ' 0.2 0.2 0.2 -

Flow parameters

Data set - USDA USDA USDA -

Model - VanGenuchten

VanGenuchten

VanGenuchten

-

Soil type - Silt Sand Loam -

> 2m - 6.0 4.0 20.0 %2m 50m - 87.0 4.0 40.0 %50m 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/dayPermeability 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 -

Initial

K0 determination Automatic Automatic Automatic -Over-consolidation ratio OCR 1.0 1.0 1.0 -Pre-overburden ratio POP 0.0 0.0 25.0 -

Mesh generation

The Default global coarseness (Medium) is convenient for this example.

Multiselect the soil clusters between the walls and refine them by selecting theRefine cluster option in the Mesh menu.

Multiselect the lines corresponding to the load and the grout bodies (5 lines) andrefine them by selecting the Refine line option in the Mesh menu.



4.2 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, including the dewatering of theexcavation. This involves a groundwater flow analysis to calculate the new pore waterdistribution, which is a part of the definition of the third calculation phase. In the Phase 5,the second anchor is installed and pre-stressed and the Phase 6 is a further excavation(and dewatering) of to the final depth of 10 m.

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 Stagedconstruction 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 geogrids and the surface loads are deactivated in theStaged construction mode.

In the Water conditions mode of the Input program, click the Phreatic level buttonand draw the phreatic level through (0; 27) and (100; 27).

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 the

interface 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.

Phase 2:



TUTORIAL MANUAL

Configuration of Phase 1 in the Staged construction mode

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


Phase 3:


In the Staged construction mode activate the upper geogrids.

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.


Phase 4:




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.

Deactivate the second 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 27.0 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 = 23.0 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; 27.0) and draw the phreatic level throug

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