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PLAXIS 2D

Tutorial Manual

2016

Build 8122

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 23

2 Submerged construction of an excavation 312.1 Input 322.2 Mesh generation 372.3 Calculations 382.4 Results 42

3 Dry excavation using a tie back wall 473.1 Input 473.2 Mesh generation 523.3 Calculations 523.4 Results 58

4 Construction of a road embankment 614.1 Input 614.2 Mesh generation 654.3 Calculations 654.4 Results 694.5 Safety analysis 714.6 Using drains 764.7 Updated mesh + Updated water pressures analysis 77

5 Settlements due to tunnel construction 795.1 Input 795.2 Mesh generation 845.3 Calculations 855.4 Results 87

6 Excavation of an NATM tunnel 916.1 Input 916.2 Mesh generation 956.3 Calculations 956.4 Results 98

7 Stability of dam under rapid drawdown 1017.1 Input 1017.2 Mesh generation 1027.3 Calculation 1037.4 Results 111

8 Dry excavation using a tie back wall - ULS 1158.1 Input 1158.2 Calculations 1178.3 Results 118

PLAXIS 2D 2016 | Tutorial Manual 3

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9 Flow through an embankment 1219.1 Input 1219.2 Mesh generation 1229.3 Calculations 1239.4 Results 127

10 Flow around a sheet pile wall 13110.1 Input 13110.2 Mesh generation 13110.3 Calculations 13210.4 Results 133

11 Potato field moisture content 13511.1 Input 13511.2 Mesh generation 13711.3 Calculations 13811.4 Results 141

12 Dynamic analysis of a generator on an elastic foundation 14312.1 Input 14312.2 Mesh generation 14512.3 Calculations 14612.4 Results 150

13 Pile driving 15313.1 Input 15313.2 Mesh generation 15613.3 Calculations 15713.4 Results 159

14 Free vibration and earthquake analysis of a building 16314.1 Input 16314.2 Mesh generation 16814.3 Calculations 16914.4 Results 171

15 Thermal expansion of a navigable lock 17515.1 Input 17515.2 Mesh generation 17815.3 Calculations 17915.4 Results 183

16 Freeze pipes in tunnel construction 18716.1 Input 18716.2 Mesh generation 19216.3 Calculations 19216.4 Results 193

Appendix A - Menu tree 195

4 Tutorial Manual | PLAXIS 2D 2016

INTRODUCTION

INTRODUCTION

PLAXIS is a finite element package that has been developed specifically for the analysisof deformation, stability and flow in geotechnical engineering projects. The simplegraphical input procedures enable a quick generation of complex finite element models,and the enhanced output facilities provide a detailed presentation of computationalresults. The calculation itself is fully automated and based on robust numericalprocedures. This concept enables new users to work with the package after only a fewhours 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. Please note that minor differences inresults maybe found, depending on hardware and software configuration.

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 an axisymmetric model

• Creating soil stratigraphy using the Borehole feature.

• 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.

• 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 GEOMETRY 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 ofthree tabsheets, Project, Model and Constants (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 "Lesson 1" in the Title box and type "Settlement of acircular footing" in the Comments box.

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

• In the Type group the type of the model (Model) and the basic element type(Elements) are specified. Since this tutorial concerns a circular footing, select theAxisymmetry and the 15-Noded options from the Model and the Elementsdrop-down menus respectively.

• In the Contour group set the model dimensions to xmin = 0.0, xmax = 5.0, ymin = 0.0and ymax = 4.0.

• Keep the default units in the Constants tabsheet.

Figure 1.4 Model tabsheet of the Project properties window


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• Click OK button to confirm the settings.

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.

Definition of soil stratigraphy

When you click the OK button the Project properties window will close and the Soil modeview will be shown where the soil stratigraphy can be defined.

Hint: The modelling process is completed in five modes. More information onmodes is available in the Section 3.4 of the Reference Manual.

Information on the soil layers is entered in boreholes. Boreholes are locations in the drawarea at which the information on the position of soil layers and the water table is given. Ifmultiple boreholes are defined, PLAXIS 2D will automatically interpolate between theboreholes. The layer distribution beyond the boreholes is kept horizontal. In order toconstruct the soil stratigraphy follow these steps:

Click the Create borehole button in the side (vertical) toolbar to start defining the soilstratigraphy.

• Click at x = 0 in the draw area to locate the borehole. The Modify soil layers windowwill appear.

• In the Modify soil layers window add a soil layer by clicking the Add button.

• Set the top boundary of the soil layer at y = 4 and keep the bottom boundary at y = 0m.

• By default the Head value (groundwater head) in the borehole column is set to 0 m.Set the Head to 2.0 m (Figure 1.5).

The creation of material data sets and their assignment to soil layers is described in thefollowing section.

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 soil layers. Forstructures (like walls, plates, anchors, geogrids, etc.) the system is similar, but differenttypes of structures have different parameters and therefore different types of materialdata sets. PLAXIS 2D distinguishes between material data sets for Soil and interfaces,Plates, Geogrids, Embedded beam rows and Anchors.



Figure 1.5 Modify soil layers window

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

Open the Material sets window by clicking the Materials button in the Modify soillayers window. The Material sets window pops up (Figure 1.6).

Figure 1.6 Material sets window

• Click the New button at the lower side of the Material sets window. A new windowwill appear with six tabsheets: General, Parameters, Groundwater, Thermal,


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Interfaces and 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. Keep parameters that are not mentioned inthe table at their default values.

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

• 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.

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 ◦

• The soil material is drained, the geometry model does not include interfaces and thedefault thermal and initial conditions are valid for this case, therefore the remainingtabsheets can be skipped. Click OK to confirm the input of the current material dataset. Now the created data set will appear in the tree view of the Material sets



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

window.

• Drag the set Sand from the Material sets window (select it and hold down the leftmouse button while moving) to the graph of the soil column on the left hand side ofthe Modify soil layers window and drop it there (release the left mouse button).

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

• Click OK to close the Modify soil layers window.

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 clickingthe corresponding button in the side toolbar.

» 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 global database can be shown in the Materialsets window by clicking the Show global button. The data sets of all tutorialsin the Tutorial Manual are stored in the global database during the installationof the program.

» The material assigned to a selected entity in the model can be changed inthe Material drop-down menu in the Selection explorer. Note that all thematerial datasets assignable to the entity are listed in the drop-down menu.However, only the materials listed under Project materials are listed, and notthe ones listed under Global materials.

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

Visibility of a grid in the draw area can simplify the definition of geometry. The grid


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provides a matrix on the screen that can be used as reference. It may also be used forsnapping to regular points during the creation of the geometry. The grid can be activatedby clicking the corresponding button under the draw area. To define the size of the gridcell and the snapping options:

Click the Snapping options button in the bottom toolbar. The Snapping window popsup where the size of the grid cells and the snapping interval can be specified. Thespacing of snapping points can be further divided into smaller intervals by theNumber of snap intervals value. Use the default values in this example.

Definition of structural elements

The structural elements are created in the Structures mode of the program where auniform indentation will be created to model a very stiff and rough footing.

• Click the Structures tab to proceed with the input of structural elements in theStructures mode.

Click the Create prescribed displacement button in the side toolbar.

Select the Create line displacement option in the expanded menu (Figure 1.9).

Figure 1.9 The Create line displacement option in the Prescribed displacement menu

• In the draw area move the cursor to point (0 4) and click the left mouse button

• Move along the upper boundary of the soil to point (1 4) and click the left mousebutton again.

• Click the right mouse button to stop drawing.

• In the Selection explorer set the x-component of the prescribed displacement(Displacementx ) to Fixed.

• Specify a uniform prescribed displacement in the vertical direction by assigning avalue of -0.05 to uy ,start ,ref , signifying a downward displacement of 0.05 m (Figure1.10).

The geometry of the model is complete.

Mesh generation

When the geometry model is complete, the finite element mesh can be generated.PLAXIS 2D allows for a fully automatic mesh generation procedure, in which thegeometry 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 model,so that the exact position of layers, loads and structures is accounted for in the finiteelement mesh. The generation process is based on a robust triangulation principle that



Figure 1.10 Prescribed displacement in the Selection explorer

searches for optimised triangles. In addition to the mesh generation itself, atransformation of input data (properties, boundary conditions, material sets, etc.) from thegeometry model (points, lines and clusters) to the finite element mesh (elements, nodesand stress points) is made.

In order to generate the mesh, follow these steps:

• Proceed to the Mesh mode by clicking the corresponding tab.

Click the Generate mesh button in the side toolbar. The Mesh options window popsup.

• The Medium option is by default selected as element distribution.

• Click OK to start the mesh generation.

Figure 1.11 The Mesh options window

As the mesh is generated, click the View mesh button. A new window is openeddisplaying the generated mesh (Figure 1.12). Note that the mesh is automaticallyrefined under the footing.

Click on the Close tab to close the Output program and go back to the Mesh modeof the Input program.

1.2.2 PERFORMING CALCULATIONS

Once the mesh has been generated, the finite element model is complete.


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

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

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

Figure 1.12 The generated mesh in the Output window

Initial conditions

The 'Initial phase' always involves the generation of initial conditions. In general, the initialconditions comprise the initial geometry configuration and the initial stress state, i.e.effective stresses, pore pressures and state parameters, if applicable.

Click the Staged construction tab to proceed with the definition of calculation phases.The Flow conditions mode may be skipped. When a new project has been defined, a firstcalculation phase named "Initial phase", is automatically created and selected in thePhases explorer (Figure 1.13). All structural elements and loads that are present in thegeometry are initially automatically switched off; only the soil volumes are initially active.

In this tutorial lesson the properties of the Initial phase will be described. Below anoverview is given of the options to be defined even though the default values of theparameters are used.



Figure 1.13 Phases explorer

The Phases window (Figure 1.14) is displayed by clicking the Edit phase button orby double clicking on the phase in the Phases explorer.

Figure 1.14 The Phases window for Initial phase

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

The Staged construction option is available as Loading type.

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

The Ignore temperature option is selected by default as the Thermal calculation type.

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

Hint: The K0 procedure should be primarily used for horizontally layeredgeometries with a horizontal ground surface and, if applicable, a horizontalphreatic level. See Section 7.3 of the Reference Manual for more informationon the K0 procedure.

For deformation problems two types of boundary conditions exist: Prescribeddisplacement and prescribed forces (loads). In principle, all boundaries must have oneboundary condition in each direction. That is to say, when no explicit boundary conditionis given to a certain boundary (a free boundary), the natural condition applies, which is aprescribed force equal to zero and a free displacement.


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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 the Model explorer expand the Model conditions subtree.

• Expand the Deformations subtree. Note that the box is checked by default. Bydefault, a full fixity is generated at the base of the geometry, whereas roller supportsare assigned to the vertical boundaries (BoundaryXMin and BoundaryXMax arenormally fixed, BoundaryYMin is fully fixed and BoundaryYMax is free).

• Expand the Water subtree. The water level generated according to the Head valueassigned to boreholes in the Modify soil layers window (BoreholeWaterLevel_1) isautomatically assigned to GlobalWaterLevel (Figure 1.15).

Figure 1.15 The Deformations and Water subtrees in the Model explorer

The initial water level has been entered already in the Modify soil layers window.

• The water level defined according to the Head specified for boreholes is displayed(Figure 1.16). Note that only the global water level is displayed in both Phasedefinition modes. All the water levels are displayed in the model only in the Flowconditions mode.

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



Figure 1.16 Initial phase in the Staged construction mode

will be added in the Phases explorer.

• Double-click Phase_1 to open the Phases window.

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

• The current phase starts from the Initial phase, which contains the initial stressstate. The default options and values assigned are valid for this phase (Figure 1.17).

Figure 1.17 The Phases window for the Indentation phase

• Click OK to close the Phases window.

• Click the Staged construction tab to enter the corresponding mode.

• Right-click the prescribed displacement in the draw area and select the Activateoption in the appearing menu (Figure 1.18).

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


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Figure 1.18 Activation of the prescribed displacement in the Staged construction mode

Execution of calculation

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

Click the Calculate button to start the calculation process. Ignore the warning thatno nodes and stress points have been selected for curves. During the execution of acalculation, a window appears which gives information about the progress of theactual calculation phase (Figure 1.19).

Figure 1.19 Active task window displaying the calculation progress

The information, which is continuously updated, shows the calculation progress, thecurrent step number, the global error in the current iteration and the number of plasticpoints in the current calculation step. It will take a few seconds to perform the calculation.When a calculation ends, the window is closed and focus is returned to the main window.



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

Save the project before viewing results.

Viewing calculation results

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

To check the applied load that results from the prescribed displacement of 0.05 m:

• Open the Phases window.

• For the current application the value of Force-Y in the Reached values subtree isimportant. This value represents the total reaction force corresponding to theapplied prescribed vertical displacement, which corresponds to the total force under1.0 radian of the footing (note that the analysis is axisymmetric). In order to obtainthe total footing force, the value of Force-Y should be multiplied by 2π (this gives avalue of about 588 kN).

The results can be evaluated in the Output program. In the Output window you can viewthe displacements and stresses in the full geometry as well as in cross sections and instructural elements, if applicable. The computational results are also available intabulated form. To view the results of the footing analysis, follow these steps:

• Select the last calculation phase in the Phases explorer.

Click the View calculation results button in the side toolbar. As a result, the Outputprogram is started, showing the deformed mesh at the end of the selectedcalculation phase (Figure 1.20). The deformed mesh is scaled to ensure that thedeformations are visible.

• 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 hand side 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.

• In the Stresses menu point to the Principal effective stresses and select theEffective principal stresses option from the appearing menu. The plot shows theeffective principal stresses at the stress points of each soil element with anindication of their direction and their relative magnitude (Figure 1.21).


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Figure 1.20 Deformed mesh

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.

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

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



Figure 1.21 Effective principal stresses

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

• In the Input program select the Save project as option of the File menu. Enter anon-existing name for the current project file and click the Save button.

• Go back to the Structures mode.

Right-click the prescribed displacement. In the right mouse button menu point to theLine displacement option. In the expanded menu click on the Delete option (Figure1.22).

• In the model right-click the line at the location of the footing. Point on Create andselect the Plate option in the appearing menu (Figure 1.23). A plate is created whichsimulates the flexible footing.

• In the model right-click again the line at the location of the footing. Point on Createand select the Line load option in the appearing menu (Figure 1.24).


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Figure 1.22 Delete Prescribed displacement

Figure 1.23 Assignment of Plate to line

Figure 1.24 Assignment of Line load to line

• In the Selection explorer the default input value of the distributed load is -1.0 kN/m2



in the y-direction. The input value will later be changed to the real value when theload is activated.

Adding material properties for the footing

Click the Materials button in the side toolbar.

• 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. Keep parameters that are not mentionedin the table at their default values.

• 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

• Proceed to the Mesh mode.

Create the mesh. Use the default option for the Element distribution parameter(Medium).

View the mesh.

• Click on the Close tab to close the Output program.


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

Calculations

• Proceed to the Staged construction mode.

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

• Double-click the following phase (Phase_1) and enter an appropriate name for thephase ID. Keep Plastic as Calculation type and keep Staged construction as loadingtype.

• Close the Phases window.

• In the Staged construction mode activate the load and plate. The model is shown inFigure 1.25.

Figure 1.25 Active plate and load in the model

• In the Selection explorer assign −188 kN/m2 to the vertical component of the lineload (Figure 1.26). Note that this gives a total load that is approximately equal to thefooting force that was obtained from the first part of this tutorial. (188 kN/m2 · π·(1.0m)2 ≈ 590 kN).

• No changes are required in the Flow conditions tabsheet.

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 in the side 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 (0.0 4.0) for the coordinates of the point of interestand click Search closest. The nodes and stress points located near that specific



Figure 1.26 Definition of the load components in the Selection explorer

location are listed.

• Select the node at exactly (0.0 4.0) by checking the box in front of it. The selectednode is indicated by ’A’ in the model when the Selection labels option is selected inthe Mesh 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 Input program.

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

Click the Calculate button to start the calculation.

Save the project after the calculation has finished.

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 menuto view the forces in the footing.


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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 1.28, follow these steps:

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

Figure 1.27 Curve generation window

• In the Charts tabsheet, click New. The Curve generation window pops up (Figure1.27).

• For the x−axis, select 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. ΣMstage is the proportion of the specifiedchanges that has been applied. Hence the value will range from 0 to 1, whichmeans that 100% of the prescribed load has been applied and the prescribedultimate state has been fully reached.

• Click OK to accept the input and generate the load-displacement curve. As a resultthe curve of Figure 1.28 is plotted.



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.

Figure 1.28 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 submergedexcavation is carried out in order to construct a tunnel by the installation of prefabricatedtunnel segments which are 'floated' into the excavation and 'sunk' onto the excavationbottom. The excavation is 30 m wide and the final depth is 20 m. It extends in longitudinaldirection for a large distance, so that a plane strain model is applicable. The sides of theexcavation are supported by 30 m long diaphragm walls, which are braced by horizontalstruts at an interval of 5 m. Along the excavation a surface load is taken into account.The load is applied from 2 m from the diaphragm wall up to 7 m from the wall and has amagnitude 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.


TUTORIAL MANUAL

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.

• 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 title.

• In the Model tabsheet keep the default options for Model (Plane strain), andElements (15-Node).

• Set the model dimensions to xmin = 0.0 m, xmax = 65.0 m, ymin = -30.0 m and ymax =20.0.

• Keep the default values for units and constants and press OK to close the Projectproperties window.


To define the soil stratigraphy:

Create a borehole at x = 0. The Modify soil layers window pops up.

• Add the top soil layer and specify its height by setting the top level to 20 m and thebottom level to 0 m.

• Add the bottom soil layer and specify its height by keeping the top level at 0 m andby setting the bottom level to -30 m.

• Set the Head in the borehole to 18.0 m.

Two data sets need to be created; one for the clay layer and one for the sand layer. Tocreate the material data sets, follow these steps:

Click the Materials button in the Modify soil layers window. The Material sets windowpops up where the Soil and interfaces option is selected by default as the Set type.

• Click the New button in the Material sets window 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 in Table 2.1, in the General,



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 0.5 -

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 -

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 -

K0-value for normal consolidation K nc0 0.5774 0.4701 -

Groundwater

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

Parameters and Flow parameters tabsheets.

• 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 (wallfrictions) and interface cohesion (adhesion) compared to the friction angle and thecohesion in the adjacent soil.

• In the Initial tabsheet keep the default option for the K0 determination and thedefault value for the overconsolidation ratio (OCR). Set the pre-overburden pressure(POP) value to 5.0.

• 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 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 value


TUTORIAL MANUAL

of 0.67 for the parameter Rinter . Close the data set.

• Assign the material datasets to the corresponding soil layers.

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 6.1.5 of the Reference Manual).

» Instead of accepting the default data sets of interfaces, data sets can directlybe assigned to interfaces by selecting the proper data set in the Materialmode drop-down menu in the Object explorers.

2.1.1 DEFINITION OF STRUCTURAL ELEMENTS

The creation of diaphragm walls, strut, surface load and excavation levels is describedbelow.


To define the diaphragm wall:

Click the Create structure button in the side toolbar.

In the expanded menu select the Create plate option (Figure 2.2).

Figure 2.2 The Create plate option in the Create structures menu

• In the draw area move the cursor to position (50.0 20.0) at the upper horizontal lineand click. Move 30 m down (50.0 -10.0) and click. Click the right mouse button tofinish the drawing.

Click the Show materials button in the side toolbar. Set the Set type parameter inthe Material sets window to Plates and click the New button. Enter "Diaphragm wall"as an Identification of the data set and enter the properties 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.

• Click OK to close the Material sets window.

To define interfaces:



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


Hint: 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. More information is available in Section5.2.4 of the Reference Manual.

• Right-click the plate representing the diaphragm wall. Point to Create and click onthe Positive interface option in the appearing menu (Figure 2.3). In the same wayassign a negative interface as well.

Figure 2.3 Positive interface assignment to existing geometry

Hint: In order to identify interfaces at either side of a geometry line, a positive sign(⊕) or negative sign () is added. This sign has no physical relevance orinfluence on the results.

» 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, select the interface in the draw area and specifythe value to the Virtual thickness factor parameter in the Selection explorer.Non-experienced users are advised not to change the default value. Formore information about interface properties see the Reference Manual.


TUTORIAL MANUAL

To define the excavation levels:

Click the Create line button in the side toolbar.

• To define the first excavation stage move the cursor to position (50.0 18.0) at thewall and click. Move the cursor 15 m to the right (65.0 18.0) and click again. Clickthe right mouse button to finish drawing the first excavation stage.

• To define the second excavation stage move the cursor to position (50.0 10.0) andclick. Move to (65.0 10.0) and click again. Click the right mouse button to finishdrawing the second excavation stage.

• The third excavation stage is automatically defined as it corresponds to theboundary between the soil layers (y = 0.0).

To define the strut:

Click the Create structure button in the side toolbar and select the Create fixed-endanchor button in the expanded menu.

• Move the cursor to (50.0 19.0) and click the left mouse button. A fixed-end anchor isis added, being represented by a rotated T with a fixed size.

Click the Show materials button in the side toolbar. Set the Set type parameter inthe Material sets window to Anchor and click the New button. Enter "Strut" as anIdentification of the data set and enter the properties as given in Table 2.3. Click OKto close the data set.

• Click OK to 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

• Make sure that the fixed-end anchor is selected in the draw area.

• In the Selection explorer assign the material data set to the strut by selecting thecorresponding option in the Material drop-down menu.

• The anchor is oriented in the model according to the Directionx and Directionyparameters in the Selection explorer. The default orientation is valid in this tutorial.

• Enter an Equivalent length of 15 m corresponding to half the width of the excavation(Figure 2.4).

Hint: The Equivalent length is the distance between the connection point and theposition in the direction of the anchor rod where the displacement is zero.

To define the distributed load:

Click the Create load button in the side toolbar

Select the Create line load option in the expanded menu to define a distributed load(Figure 2.5).



Figure 2.4 Parameters for fixed-end anchors in the Selection explorer

Figure 2.5 The Create line load option in the Create load menu

• Move the cursor to (43.0 20.0) and click. Move the cursor 5 m to the right to (48.020.0) and click again. Right-click to finish drawing.

• In the Selection explorer assign a value of -5 kN/m/m to the y-component of the load(qy ,start ,ref ) (Figure 2.6).

Figure 2.6 Components of the distributed load in the Selection explorer

2.2 MESH GENERATION



View the mesh. The resulting mesh is displayed in Figure 2.7.



TUTORIAL MANUAL

Figure 2.7 The generated mesh

2.3 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 loading typeavailable in the General subtree of the Phases window. It enables the activation ordeactivation of weight, stiffness and strength of selected components of the finite elementmodel. Note that modifications in the Staged construction mode of the program arepossible only for this type of loading. The current tutorial explains the use of this powerfulcalculation option for the simulation of excavations.

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

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

Phase 1: External load

In the Phases explorer click the Add phase button to introduce a new phase.

• The default settings are valid for this phase. In the model the full geometry is activeexcept for the wall, interfaces, strut and load.

Click the Select multiple objects button in the side toolbar. In the appearing menupoint to Select line and click on the Select plates option (Figure 2.8).

• In the draw area define a rectangle including all the plate elements (Figure 2.9).

• Right-click the wall in the draw area and select the Activate option from theappearing menu. The wall is now visible in the color that is specified in the materialdataset.



Figure 2.8 The Select plates option

Figure 2.9 Multi-selection of plates in the draw area

• Right-click the distributed load to activate it and select the Activate option from theappearing menu. The load has been defined in the Structures mode as −5 kN/m/m.The value can be checked in the Selection explorer.

• Make sure all the interfaces in the model are active.

Phase 2: First excavation stage



TUTORIAL MANUAL

Hint: The selection of an interface is done by right-clicking the correspondinggeometry line and subsequently selecting the corresponding interface(positive or negative) from the appearing menu.

• A new calculation phase appears in the Phases explorer. Note that the programautomatically presumes that the current phase should start from the previous oneand that the same objects are active.

Hint: To copy the settings of the parent phase, select the phase in the Phasesexplorer and then click the Add phase button. Note that the settings of theparent phase are not copied when it is specified by selecting it in the Startfrom phase drop-down menu in the Phases window.

• The default settings are valid for this phase. In the Staged construction mode all thestructure elements except the fixed-end anchor are active.

• In the draw area right-click the top right cluster and select the Deactivate option inthe appearing menu. Figure 2.10 displays the model for the first excavation phase.

Figure 2.10 Model view for the first excavation phase

Phase 3: Installation of strut

Add a new phase.

• Activate the strut. The strut should turn black to indicate it is active.

Phase 4: Second (submerged) excavation stage

Add a new phase.

• Deactivate the second cluster from the top on the right side of the mesh. It shouldbe the topmost active cluster (Figure 2.11).



Figure 2.11 Model view for the second excavation phase

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

Add a new phase.

• 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 (Figure 2.12).

Figure 2.12 Model view for the third excavation phase

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 in the side toolbar. The connectivity plot is


TUTORIAL MANUAL

displayed 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 on the Update tab to close the Output program and go back to the Inputprogram.

Calculate the project.

During a Staged construction calculation phase, a multiplier called ΣMstage is increasedfrom 0.0 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.

2.4 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 (Figure2.13).

Figure 2.13 Deformed mesh after the third excavation stage

• 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, which indicates the forming of a



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.

'mechanism' of soil movement behind the wall.

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 theeffective principal stresses at the three middle stress points of each soil elementwith an indication of their direction and their relative magnitude. Note that the Centerprincipal 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 2.14).

Figure 2.14 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 2.15).

• 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) is shown in the


TUTORIAL MANUAL

Figure 2.15 Bending moments in the wall

displayed table.

• 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 2.16 is plotted.

Figure 2.16 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 indicates



that 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

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.

• 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




• Set the model dimensions to xmin = 0.0 m, xmax = 100.0 m, ymin = 0.0 m, ymax = 30.0m.

• Keep the default values for units and the constants and press OK to close theProject properties window.




• Add three soil layers to the borehole. Locate the ground level at y = 30 m byassigning 30 to the Top level of the uppermost layer. The bottom levels of the layersare located at 27, 15 and 0 m, respectively.

• Set the Head to 23 m. The layer stratigraphy is shown in Figure 3.2.

Figure 3.2 The Modify soil layers window

Define three data sets for soil and interfaces with the parameters given in Table 3.1.

• Assign the material data sets to the corresponding soil layers (Figure 3.2).



Table 3.1 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 -

K0-value for normal consolidation K nc0 0.5 0.4408 0.5152 -

Groundwater

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


In the Structures mode, model the diaphragm walls as plates passing through (40.030.0) - (40.0 14.0) and (60.0 30.0) - (60.0 14.0).

• Multi-select the plates in the model.

• In the Selection explorer click on Material. The view will change displaying adrop-down menu and a plus button next to it (Figure 3.3).

Click the plus button. A new empty material set is created for plates.

• Define the material data set for the diaphragm walls according to the properties arelisted in Table 3.2. The concrete has a Young's modulus of 35 GN/m2 and the wall is0.35 m thick.


TUTORIAL MANUAL

Figure 3.3 Material assignment in the Selection explorer

Table 3.2 Properties of the diaphragm wall (plate)



End bearing − Yes -



Weight w 8.3 kN/m/m


• Assign positive and negative interfaces to the geometry lines created to representthe diaphragm walls.

The soil is excavated in three stages. The first excavation layer corresponds to the bottomof the silt layer and it is automatically created. To define the remaining excavation stages:

Define the second excavation phase by drawing a line through (40.0 23.0) and (60.023.0).

Define the third excavation phase by drawing a line through (40.0 20.0) and (60.020.0).

A ground anchor can be modelled by a combination of a node-to-node anchor and anembedded beam. The embedded pile simulates the grouted part of the anchor whereasthe node-to-node anchor simulates the free length. In reality there is a complexthree-dimensional state of stress around the grout body which cannot be simulated in a2D model.

Define the node-to-node anchors according to Table 3.3.

Table 3.3 Node to node anchor coordinatesAnchor location First point Second point

TopLeft (40.0 27.0) (31.0 21.0)

Right (60.0 27.0) (69.0 21.0)

BottomLeft (40.0 23.0) (31.0 17.0)

Right (60.0 23.0) (69.0 17.0)

Create an Anchor material data set according to the parameters specified in Table3.4.

• Multi-select the anchors in the draw area. Assign the material data set by selectingthe corresponding option in the Material drop-down menu in the Selection explorer.

Define the grout body using the Embedded beam row button according to Table 3.5.

Create the Grout material data set according to the parameters specified in Table3.6.



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 Grout coordinatesGrout location First point Second point

TopLeft (31.0 21.0) (28.0 19.0)

Right (69.0 21.0) (72.0 19.0)

BottomLeft (31.0 17.0) (28.0 15.0)

Right (69.0 17.0) (72.0 15.0)

Table 3.6 Properties of the grout body (embedded beam rows)


Stiffness E 7.07·106 -

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 resistanceTskin,start ,max 400 kN/m

Tskin,end ,max 400 kN/m

Base resistance Fmax 0 kN/m

Interface stiffness factor - Default values -

• Set the connection of the embedded beam rows to Free (Figure 3.4). This is neededto set the top free from the underlying soil element. The connection with the anchorwill be automatically established.

Figure 3.4 Embedded beam rows in the Selection explorer

• Multi-select (keep the <Ctrl> key pressed while selecting) the top node-to-nodeanchors and embedded beams. Right-click and select the Group option in theappearing menu.

• In the Model explorer expand the Groups subtree. Note that a group is createdcomposed of the elements of the top ground anchors.

• Click on Group_1 in the Model explorer and type a new name (e.g'GroundAnchor_Top').


TUTORIAL MANUAL

• Follow the same steps to create a group and to rename the bottom ground anchors.

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.

Create a line load between (28.0 30.0) and (38.0 30.0).

3.2 MESH GENERATION





3.3 CALCULATIONS

The calculation of this project consists of six phases. In the initial phase (Phase 0), theinitial stresses are generated. In Phase 1, the walls are constructed and the surfaceloads are activated. In Phase 2, the first 3 m of the pit is excavated without connection ofanchors to the wall. At this depth the excavation remains dry. In Phase 3, the first anchoris installed and pre-stressed. Phase 4 involves further excavation to a depth of 7 m. Atthis depth the excavation still remains dry. In Phase 5, the second anchor is installed andpre-stressed. Phase 6 is a further excavation to the final depth of 10 m including thedewatering of the excavation.

Before defining the calculation phases, the water levels to be considered in thecalculation can be defined in the Flow conditions mode. The water level is lowered in thefinal excavation phase. At the side boundaries, the groundwater head remains at a levelof 23.0 m. The bottom boundary of the problem should be closed. The flow ofgroundwater is triggered by the fact that the pit is pumped dry. At the bottom of theexcavation the water pressure is zero, which means that the groundwater head is equal tothe vertical level (head = 20.0 m). This condition can be met by drawing a new generalphreatic level and performing a groundwater flow calculation. Activating the interfacesduring the groundwater flow calculation prevents flow through the wall.



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 and loads are inactive. Hence, make sure that theplates, the node-to-node anchors, the embedded beam rows and the surface loadsare deactivated.

• In the Phases explorer double-click the initial phase. The default parameters for theinitial phase will be used. The Phreatic option is selected as Pore pressurecalculation type. Note that when the pore pressures are generated by phreatic level,the full geometry of the defined phreatic level is used to generate the pore pressures.



• Expand the Water subtree. The water level created according to the head valuespecified in the borehole, (BoreholeWaterLevel_1), is automatically assigned toGlobalWaterLevel (Figure 3.6).

Figure 3.6 Configuration of the initial phase

Phase 1

Add a new phase.

• In the Staged constructions mode activate all walls and interfaces by clicking on thecheckbox in front of them in the Model explorer. The active elements in the projectare indicated by a green check mark.

• Activate the distributed load.

• After selecting the line load assign a value of -10 to qy ,start ,ref in the Selectionexplorer (Figure 3.7).

Figure 3.7 Line load in the Selection explorer


TUTORIAL MANUAL

• The model for the phase 1 in the Staged construction mode is displayed in Figure3.8.

Figure 3.8 Configuration of Phase 1 in the Staged construction mode

Phase 2

Add a new phase.

• In the Staged construction mode de-activate the upper cluster of the excavation(Figure 3.9).


Phase 3

Add a new phase.

• Activate the upper ground anchors by clicking on the checkbox in front ofGroundAnchors_Top under the Groups subtree in the Model explorer.

Multi-select the top node-to-node anchors.

• In the Selection explorer set the Adjust prestress parameter to True and assign apre-stress force of 500 kN.

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.

• The model for the phase 3 in the Staged construction mode is displayed in Figure



3.10.


Phase 4

Add a new phase.

• Deactivate the second cluster of the excavation. The model for the phase 4 in theStaged construction mode is displayed in Figure 3.11. Note that the anchors are notpre-stressed anymore.


Phase 5

Add a new phase.

• Activate the lower ground anchors.

Select the bottom node-to-node anchors.

• In the Selection explorer set the Adjust prestress parameter to True and assign apre-stress force of 1000 kN.

• The model for the phase 5 in the Staged construction mode is displayed in Figure3.12.

Phase 6

Add a new phase.

In the General subtree of the Phases window select the Steady state groundwaterflow option as Pore pressure calculation type. The default values of the remainingparameters is valid.


TUTORIAL MANUAL


• Deactivate the third cluster of the excavation.

• Click the Flow conditions tab to display the corresponding mode.

• In the Model explorer expand the Attributes library.

• Expand the Water levels subtree.

Click the Create water level button in the side toolbar and draw a new phreatic level.Start at (0.0 23.0) and draw the phreatic level through (40.0 20.0), (60.0 20.0) andend in (100.0 23.0).

• In the Model explorer expand the User water levels subtree. Click onUserWaterLevel_1 and type 'LoweredWaterLevel' to rename the water level createdin the Flow conditions mode (Figure 3.13).

Figure 3.13 Water levels in the Model explorer

• Expand the GroundwaterFlow subtree under the Model conditions in the Modelexplorer. The default boundary conditions (Figure 3.14) are valid.

• In the Water subtree assign the LoweredWaterLevel to GlobalWaterLevel. Themodel and the defined water levels are displayed in Figure 3.15.



Figure 3.14 The GroundwaterFlow subtree under the Model conditions in the Model explorer

Figure 3.15 Configuration of Phase 6 in the Flow conditions mode

Hint: Note that for Groundwater flow (steady or transient) the intersection points ofthe water level with the active model boundaries are important. The programcalculates flow boundary conditions in terms of a groundwater headcorresponding to the water level. The 'internal' part of the water level is notused and will be replaced by the phreatic level resulting from thegroundwater flow calculation. Hence, the water level tool is just a convenienttool to create boundary conditions for a flow calculation.

Select some characteristic points for curves (for example the connection points ofthe ground anchors on the diaphragm wall, such as (40.0 27.0) and (40.0 23.0)).

Calculate the project by clicking the Calculate button in the Staged constructionmode.



TUTORIAL MANUAL

3.4 RESULTS

Figures 3.16 to 3.20 show the deformed meshes at the end of calculation phases 2 to 6.

Figure 3.16 Deformed mesh (scaled up 50.0 times) - Phase 2




Figure 3.21 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 seen



Figure 3.20 Deformed mesh (scaled up 50.0 times) - Final phase

that there are stress concentrations around the grout anchors.

Figure 3.21 Principal effective stresses (final stage)

Figure 3.22 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 3.22 Bending moments in the diaphragm walls in the final stage

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

• Safety analysis (phi-c reduction)

• Updated mesh analysis (large deformations)

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 mis peat and the lower 3.0 m is clay. The phreatic level is located 1 m below the originalground surface. Under the soft soil layers there is a dense sand layer of which 4.0 m areconsidered in the model.

General settings



• In the Model tabsheet make sure that Model is set to Plane strain and that Elementsis set to 15-Noded.


TUTORIAL MANUAL

• Define the limits for the soil contour as xmin = 0.0, xmax = 60.0, ymin = −10.0 andymax = 4.0.


The sub-soil layers are defined using a borehole. The embankment layers are defined inthe Structures mode. To define the soil stratigraphy:


• Define three soil layers as shown in Figure 4.2.

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

Open the Material sets window.

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

• Close the Modify soil layers window and proceed to the Structures mode to definethe embankment and drains.

Figure 4.2 Soil layer distribution

Hint: The initial void ratio (einit ) and the change in permeability (ck ) should bedefined to enable the modelling of a change in the permeability in aconsolidation analysis due to compression of the soil. This option isrecommended when using advanced 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 material behaviour Type Drained Drained Undrained(A)

Undrained(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 drained triaxialtest

E ref50 2.5· 104 3.5· 104 - - kN/m2

Tangent stiffness forprimary oedometer loading

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 to default Yes Yes Yes Yes Yes Yes

Groundwater

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 0.05 0.04752 m/day

Change in permeability ck 1· 1015 1· 1015 1.0 0.2 -

Interfaces

Interface strength − Rigid Rigid Rigid Rigid -

Strength reduction factor 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-overburden pressure POP 0.0 0.0 5.0 0.0 kN/m2


TUTORIAL MANUAL

4.1.1 DEFINITION OF EMBANKMENT AND DRAINS

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

Click the Create soil polygon button in the side toolbar and select the Create soilpolygon option in the appearing menu.

• Define the embankment in the draw area by clicking on (0.0 0.0), (0.0 4.0), (8.0 4.0)and (20.0 0.0).

• Right-click the created polygon and assign the Embankment data set to the soilpolygon (Figure 4.3).

Figure 4.3 Assignment of a material dataset to a soil cluster in the draw area

To define the embankment construction level click the Cut polygon in the sidetoolbar and define a cutting line by clicking on (0.0 2.0) and (14.0 2.0). Theembankment cluster is split into two sub-clusters.

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

Click the Create hydraulic conditions button in the side toolbar and select the Createdrain option in the appearing menu (Figure 4.4).

Figure 4.4 The Create drain option in the Create hydraulic conditions menu

Drains are defined in the soft layers (clay and peat; y = 0.0 to y = -6.0). The distancebetween two consecutive drains is 2 m. Considering the symmetry, the first drain islocated at 1 m distance from the model boundary. 10 drains will be created in total(Figure 4.5). The head is defined at 0.0 m.



Hint: The modelling of drains in a plane strain model actually involves the use ofan equivalent (lateral) permeability in the surrounding soil based on the drainpattern. The latter has been omitted in this simplified example. Moreinformation can be in found in literaturea.

a CUR (1997). Achtergronden bij numerieke modellering van geotechnische constructies, deel 2. CUR191. Stichting CUR, GoudaIndraratna, B.N., Redana, I.W., Salim, W. (2000), Predicted and observed behaviour of soft clayfoundations stabilised with vertical drains. Proc. GeoEng. 2000, Melbourne

Figure 4.5 Final geometry of the model

4.2 MESH GENERATION


Generate the mesh. Use the default option for the Element distribution parameter(Medium).

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



4.3 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.


TUTORIAL MANUAL

Initial phase: Initial conditions

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 deactivate 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 (Figure 4.7).

Figure 4.7 Configuration of the initial phase

The initial water pressures are fully hydrostatic and based on a general phreatic levellocated at y = -1. Note that a phreatic level is automatically created at y = -1, according tothe value specified for Head in the borehole. 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 except for the bottom boundary are draining so that water can freely flow outof these boundaries and excess pore pressures can dissipate. In the current situation,however, the left vertical boundary must be closed because this is a line of symmetry, sohorizontal flow should not occur. The remaining boundaries are open because the excesspore pressures can be dissipated through these boundaries. In order to define theappropriate consolidation boundary conditions, follow these steps:


• Expand the GroundwaterFlow subtree and set BoundaryXMin to Closed andBoundaryYMin to Open (Figure 4.8).

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 stepping procedurethat takes this critical time step into account. Within this procedure there are three mainpossibilities:

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

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



Figure 4.8 The boundary conditions of the problem

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.

Add a new phase.

In the Phases window select the Consolidation option from the Calculation typedrop-down menu in the General subtree.

Make sure that the Staged construction option is selected for the Loading type.

• Enter a Time interval of 2 days. The default values of the remaining parameters willbe used.

• In the Staged construction mode activate the first part of the embankment (Figure4.9).

Figure 4.9 Configuration of the phase 1

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.

Add a new phase.


TUTORIAL MANUAL



• Enter a Time interval of 30 days. The default values of the remaining parameters willbe used.

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

Add a new phase.



• Enter a Time interval of 1 day. The default values of the remaining parameters willbe used.

• In the Staged construction mode activate the second part of the embankment(Figure 4.10).

Figure 4.10 Configuration of the phase 3

Phase 4: The fourth phase is a Consolidation analysis to a minimum excess porepressure.

Add a new phase.

In the General subtree select the Consolidation as calculation type.

Select the Minimum excess pore pressure option in the Loading input drop-downmenu and accept the default value of 1 kN/m2 for the minimum pressure. Thedefault values of the remaining parameters will be used.

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 4.11).

In addition to the multipliers, a parameter Pexcess,max occurs, which indicates the currentmaximum excess pore pressure. This parameter is of interest in the case of a Minimumexcess pore pressure consolidation analysis, where all pore pressures are specified toreduce below a predefined value.



Figure 4.11 Calculation progress displayed in the Active tasks window

4.4 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 4.12). Consideringthe results of the third phase, the deformed mesh shows the uplift of the embankment toeand hinterland due to the undrained behaviour.

Figure 4.12 Deformed mesh after undrained construction of embankment (Phase 3)

• In the Deformations menu select the Incremental displacements→ |∆u|.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 4.13).

• 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.


TUTORIAL MANUAL

Figure 4.13 Displacement increments after undrained construction of embankment

Click the Center principal directions. The principal directions of excess pressuresare displayed at the center of each soil element. The results are displayed in Figure4.14. It is clear that the highest excess pore pressure occurs under the embankmentcentre.

Figure 4.14 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.

Figure 4.15 Excess pore pressure contours after consolidation to Pexcess < 1.0 kN/m2

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.Figure 4.15 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:

Create a new curve.



• 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 4.16 should appear.

Figure 4.16 Development of excess pore pressure under the embankment

Figure 4.16 clearly shows the four calculation phases. During the construction phasesthe excess 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 asmall time interval. From the curve it can be seen that more than 50 days are needed toreach full consolidation.

• Save the chart before closing the Output program.

4.5 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 a


TUTORIAL MANUAL

centrifuge 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:

• Select Phase 1 in the Phases explorer.

Add a new calculation phase.

• Double-click on the new phase to open the Phases window.

• In the Phases window the selected phase is automatically selected in the Start fromphase drop-down menu.

In the General subtree, select Safety as calculation type.

The Incremental multipliers option is already selected in the Loading input box. Thefirst increment of the multiplier that controls the strength reduction process, Msf, isset to 0.1.

Note that the Use pressures from the previous phase option in the Pore pressurecalculation type drop-down menu is automatically selected and grayed out indicatingthat this option cannot be changed

• In order to exclude existing deformations from the resulting failure mechanism,select the Reset displacements to zero option in the Deformation control parameterssubtree.

• In the Numerical control parameters subtree deselect Use default iter parametersand set the number of Max steps to 50. The first safety calculation has now beendefined.



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

Hint: The default value of Max steps in a Safety calculation is 100. In contrast toan Staged construction calculation, the specified number of steps is alwaysfully executed. In most Safety calculations, 100 steps are sufficient to arriveat a state of failure. If not, the number of steps can be increased to amaximum 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.

Figure 4.17 Phases explorer displaying the Safety calculation phases

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 4.18). The magnitude of thedisplacement increments is not relevant.

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 the


TUTORIAL MANUAL

Figure 4.18 Shadings of the total displacement increments indicating the most applicable failuremechanism of the embankment in the final stage

parameter 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.

• Right-click on the chart and select the Settings option in the appearing menu. TheSettings window pops up.

• In the tabsheet corresponding to the curve click the Phases button.

• In the Select phases window select Phase 5 (Figure 4.19).

Figure 4.19 The Select phases window

• Click OK to close the Select phases window.

• In the Settings window change the titles of the curve in the corresponding tabsheet.

• Click the Add curve button and select the Add from current project option in theappearing menu. Define curves for phases 6, 7 and 8 by following the describedsteps.

• In the Settings window click the Chart tab to open the corresponding tabsheet.



• In the Chart tabsheet specify the chart name.

• Set the scaling of the x-axis to Manual and set the value of Maximum to 1 (Figure4.20).

Figure 4.20 The Chart tabsheet in the Settings window

• Click Apply to update the chart according to the changes made and click OK toclose the Settings window.

• To modify the location of the legend right-click on the legend.

• In the appearing menu point at View and select the Legend in chart option (Figure4.21).

Figure 4.21 Enabling legend in chart

• The legend can be relocated in the chart by dragging it. The plot is shown in Figure4.22.

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.


TUTORIAL MANUAL

Figure 4.22 Evaluation of safety factor

4.6 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. Thefirst of these new phases should start from the initial phase. The differences in the newphases are:

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

• The Time interval in the first three of the consolidation phases (9 to 11) is 1 day. Thelast phase is set to Minimum excess pore pressure and a value of 1.0 kN/m2 isassigned to the minimum pressure (|P-stop|).

After the calculation is finished save the project, select the last phase and click theView calculation results button. The Output window now shows the deformed mesh

after the drained construction of the final part of the embankment. In order to comparethe effect of the drains, 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 change the titles of the curves in the corresponding



tabsheets.

• In the Chart tabsheet specify the chart name.

• Click Apply to preview the generated cure and click OK to close the Settingswindow. The chart (Figure 4.23) gives a clear view of the effect of drains in the timerequired for the excess pore pressures to dissipate.

Figure 4.23 Effect of drains

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

4.7 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 meter 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.

• Select the initial phase in the Phases explorer.


• Define the new phase in the same way as Phase 1. In the Deformation controlparameters subtree check the Updated mesh and Updated water pressures options.

• Define in the same way the other 3 phases.

When the calculation has finished, compare the settlements for the two different


TUTORIAL MANUAL

calculation 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.

• 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 4.24.

Figure 4.24 Effect of Updated mesh and water pressures analysis on resulting settlements

In Figure 4.24 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.


SETTLEMENTS DUE TO TUNNEL CONSTRUCTION

5 SETTLEMENTS DUE TO TUNNEL CONSTRUCTION

In this tutorial the construction of a shield tunnel in medium soft soil and the influence ona pile foundation is considered. A shield tunnel is constructed by excavating soil at thefront of a tunnel boring machine (TBM) and installing a tunnel lining behind it. In thisprocedure the soil is generally over-excavated, which means that the cross sectional areaoccupied by the final tunnel lining is always less than the excavated soil area. Althoughmeasures are taken to fill up this gap, one cannot avoid stress re-distributions anddeformations in the soil as a result of the tunnel construction process. To avoid damageto existing buildings or foundations on the soil above, it is necessary to predict theseeffects and to take proper measures. Such an analysis can be performed by means ofthe finite element method. This tutorial shows 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

Objectives:

• Modelling of the tunnel boring process

• Modelling undrained behaviour using the Undrained (B) option

5.1 INPUT

The tunnel considered in this tutorial has a diameter of 5.0 m and is located at an averagedepth of 20 m. To create the geometry model, follow these steps:


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General settings



• In the Model tabsheet keep the default options for Model (Plane strain), andElements (15-Noded).

• Set the model dimensions to xmin = 0.0 m, xmax = 35.0 m, ymin = -30.0 m and ymax =3.0 m.

• Keep the default values for units and constants and press OK to close the Projectproperties window.


The soil profile indicates four distinct layers: The upper 13 m consists of soft clay typesoil with stiffness that increases approximately linearly with depth. Under the clay layerthere is a 2.0 m thick fine sand layer. This layer is used as a foundation layer for oldwooden piles on which traditional brickwork houses were built. The pile foundation ofsuch a building is modelled next to the tunnel. Displacements of these piles may causedamage to the building, which is highly undesirable. Below the sand layer there is a 5.0 mthick deep loamy clay layer.



• Create the soil stratigraphy as shown in Figure 5.2.

Figure 5.2 The soil stratigraphy in the Modify soil layers window

• Keep the Head in the borehole at 0.0 m.


• Create data sets under the Soil and interfaces set type according to the information



given in Table 5.1.

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

Power for stress-leveldependency of stiffness

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

Groundwater

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 -

Over-consolidation ratio OCR - 1.0 - 1.0 -

Pre-overburden ratio POP - 0.0 - 0.0 -

For the upper clay layer the stiffness and shear strength increase with depth. Thereforevalues for E 'inc and su,inc are entered in the Advanced subtree. The values of E 'ref andsu,ref become the reference values at the reference level yref . Below yref , the actualvalues of E ' and su, increase with depth according 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 default


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values. Enter four data sets with the properties as listed in Table 5.1 and assign them tothe corresponding clusters in the geometry model.


The tunnel considered here is the right half of a circular tunnel. After generating the basicgeometry, follow these steps to design the circular tunnel:

In the Structures mode click the Create tunnel button in the side toolbar and click at(0.0 -17.0) in the draw area. The Tunnel designer window pops up displaying theGeneral tabsheet of the Cross section mode.

• Select the Circular option in the Shape type drop-down menu.

• Select the Define right half option in the Whole or half tunnel drop-down menu.

• In the Offset to begin point group set Axis 2 to -2.5. No change is required for theorientation axes.

• Click the Segments tab to proceed to the corresponding tabsheet. A segment isautomatically created. A new box is shown under the segment list where theproperties of the segment can be defined.

• In the Segment box set Radius to 2.5 m. The generated segment is shown in Figure5.3.

Figure 5.3 The geometry of the tunnel segment

• Click the Properties tab to proceed to the corresponding tabsheet.

• Right-click the segment in the display area and select the Create plate option in theappearing menu.

Create a new material dataset. Specify the material parameters for lining accordingto Table 5.2.



Hint: In the tunnel as considered here the segments do not have a specificmeaning as the tunnel lining is homogeneous and the tunnel will beconstructed at once. In general, the meaning of segments becomessignificant when:• It is desired to excavate or construct the tunnel (lining) in different

stages.• Different tunnel segments 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).

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 -

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

• Right-click the segment in the display area and select the Create negative interfaceoption in the appearing menu.

• Right-click the segment in the display area and select the Create line contractionoption in the appearing menu. In the polycurve box specify a value of 0.5% for Cref .The tunnel model is shown in Figure 5.4.

Hint: A line contraction of the tunnel contour of 0.5% corresponds approximately toa value loss of 1% of the tunnel volume.

• Click on Generate to include the defined tunnel in the model.

• Close the Tunnel designer window.

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.

Create a material set for the building according to Table 5.2 and assign it to the plate.

Draw two piles (embedded beam rows) from (5.0 3.0) to (5.0 -11.0) and from (15.03.0) to (15.0 -11.0).

Create a material set for the foundation piles according to Table 5.3 and assign it to


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Figure 5.4 Tunnel model in the Properties mode

the corresponding geometric entities in the model.

Table 5.3 Material properties of the piles

Parameter Name Foundation piles 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 resistanceTskin,start ,max 1.0 kN/m

Tskin,end ,max 100.0 kN/m

Base resistance Fmax 100.0 kN

Interface stiffness factors - Default kN

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.

5.2 MESH GENERATION

The default global coarseness parameter (Medium) can be accepted in this case. Notethat the structural elements (plate and embedded beams) are internally automaticallyrefined by a factor of 0.25.



View the mesh.



• In the Output program click on the Fixities option in the Geometry menu to displaythem in the model. The generated mesh is shown in (Figure 5.5).



5.3 CALCULATIONS

To simulate the construction of the tunnel it is clear that a staged construction calculationis needed.


• The initial phase has already been introduced. Keep its calculation type as K0procedure. The water pressures can be generated on the basis of a general phreaticlevel at a level of y = 0.0 m as already defined in the borehole. Make sure that thebuilding, foundation piles and tunnel lining are deactivated.

Phase 1: Building

The first calculation phase is used to activate the building.


• In the Phases window rename the phase as 'Building'.

• In the Deformation control parameters subtree select the Ignore undr. behaviour(A,B) option. The default values of the remaining parameters are valid for this phase.

• In the draw area activate the plate and the foundation piles.


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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 Waterconditions of the two soil clusters in the tunnels must be set to Dry in the Objectexplorers. The calculation phases are Plastic analyses, Staged construction. To createthe input, follow these steps.

Phase 2: Tunnel


• In the Phases window select the Reset displacements to zero option in theDeformation control parameters subtree.

• In Staged construction multi-select the clusters inside the tunnel. In the Selectionexplorer deactivate the two soil clusters and set the Water conditions to Dry.

• Activate the tunnel lining and the negative interfaces. Note that contraction is notactive in this phase.

Phase 3: Contraction

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:


• Multi-select the plates. In the Selection explorer activate the contraction.

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

» 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 Phases window do NOT select the Reset displacements to zero option in theDeformation control parameters subtree.

• In the Staged construction mode deactivate the tunnel lining (plates, negativeinterfaces and contraction).



• Multi-select the clusters inside the tunnel. In the Selection explorer activateWaterConditions.

• Select the User-defined option in the Condition drop-down menu and set pref to -230kN/m2. The pressure distribution in the tunnel is constant.

Phase 5: Final lining


• In the Phases window, do NOT select the Reset displacements to zero option in theParameters subtree.

• In the Staged construction set the clusters inside the tunnel to Dry.

• Activate the tunnel lining (plates) and the negative interfaces in the tunnel.

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).



5.4 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 5.6).

Figure 5.6 Deformed mesh after construction of the tunnel (Phase 5; scaled up 20.0 times)

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 some


TUTORIAL MANUAL

deformation. 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 5·10-3 and 0.02 respectively (Figure 5.7).

Figure 5.7 Axial forces and Bending moments in the lining after the second phase

The plot of effective stresses, Figure 5.8, 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.

Figure 5.8 Effective principal stresses after the construction of the tunnel

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 5.9).



Figure 5.9 Distance measurement information window


TUTORIAL MANUAL


EXCAVATION OF AN NATM TUNNEL

6 EXCAVATION OF AN 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.

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.

6.1 INPUT

General settings



• In the Model tabsheet make sure that Model is set to Plane strain and that Elementsis set to 15-Noded.

• Define the limits for the soil contour as xmin = −50.0, xmax = 50.0, ymin = 0.0 andymax = 35.0.


The basic stratigraphy will be created using the Borehole feature. In the model 11 m ofthe Clay-limestone layer is considered. The bottom of this layer is considered asreference in y direction (ymin = 0). To define the soil stratigraphy:

Create the first borehole x = -22.0.

• In the Modify soil layers window create three soil layers. The layer number 1 has adepth equal to zero in Borehole_1. Assign 24.00 to Top and Bottom of the layer 1.The layer number 2 lies from Top = 24.00 to Bottom = 11.00. The layer number 3lies from Top = 11.00 to Bottom = 0.00.

• Click the Boreholes button at the bottom of the Modify soil layers window.


TUTORIAL MANUAL

• In the appearing menu select the Add option. The Add borehole window pops up.

• Specify the location of the second borehole (X = -14).

• Note that the soil layers are available for Borehole_2. The layer number 1 has adepth equal to zero in Borehole_2. However as the depth of layer 2 is higher assign30.00 to Top and Bottom of the layer 1. The layer number 2 lies from Top = 30.00 toBottom = 11.00. The layer number 3 lies from Top = 11.00 to Bottom = 0.00.

• Create a new borehole (Borehole_3) at X = -7.

• In Borehole_3 the layer number 1 has a non-zero thicknesss and lies from Top =35.00 to Bottom = 30.00. The layer number 2 lies from Top = 30.00 to Bottom =11.00. The layer number 3 lies from Top = 11.00 to Bottom = 0.00.

• In all the boreholes the water level is located at y = 0 m.

• Specify the soil layer distribution as shown in Figure 6.2.

• Create soil material data sets according to Table 6.1 and assign them to thecorresponding layers (Figure 6.2).

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

Table 6.1 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 phreatic level γunsat 20 25 24 kN/m3

Soil unit weight below phreatic level γsat 22 25 24 kN/m3

Initial void ratio einit 0.5 0.5 0.5 -

Parameters

Secant stiffness in standard drained triaxialtest

E ref50 4.0·104 - - kN/m2

Tangent stiffness for primary oedometerloading

E refoed 4.0·104 - - kN/m2

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

Power for stress-level dependency ofstiffness

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 intact rock 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 -



Figure 6.2 Soil layer distribution

6.1.1 DEFINITION OF TUNNEL

In the Structures mode click the Create tunnel button in the side toolbar and click on(0.0 16.0) in the draw area to specify the location of the tunnel. The Tunnel designerwindow pops up.

• The default shape option (Free) will be used. The default values of the rest of theparameters defining the location of the tunnel in the model are valid as well.

• Click on the Segments tab.

Click the Add button in the side toolbar.

• In the segment info box set the Segment type to Arc. Set Radius to 10.4 m and theSegment angle to 22◦. The default values of the remaining parameters are valid.

Add a new arc segment. Set Radius to 2.4 m and the Segment angle to 47◦. Thedefault values of the remaining parameters are valid.

Add a new arc segment. Set Radius to 5.8 m and the Segment angle to 50◦. Thedefault values of the remaining parameters are valid.

Click the Extend to symmetry axis option to complete the right half of the tunnel. Anew arc segment is automatically added closing the half of the tunnel.

Click the Symmetric close button to complete the tunnel. Four new arc segment areautomatically added closing the tunnel.

• Click on the Subsections tab.

Add a new subsection. This subsection will be used to separate the top heading(upper excavation cluster) from the invert (lower excavation cluster).

• Set Offset 2 to 3 m. Select the Arc option from the Segment type drop-down menu.Set Radius to 11 m and Segment angle to 360 ◦.


TUTORIAL MANUAL

Figure 6.3 Segments in the tunnel cross section

Select all the geometric entities in the slice.

Click the Intersect button.

Delete the part of the subsection outside of the slice by selecting it in the displayarea and clicking the Delete button in the side toolbar.

• Proceed to the Properties mode.

• Multi-select the polycurves in the display area and select the Create plate option inthe appearing menu.

• Press <Ctrl> + <M> to open the Material sets window. Create a new materialdataset for the created plates according to Table 6.2.

• Multi-select the created plates and in the Selection explorer, assign the materialLining to the selected plates.

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


• Assign negative interfaces to the lines defining the shape of the tunnel (not theexcavation levels). The final tunnel view in the Tunnel designer window is given inFigure 6.4.

• Click on Generate to update the tunnel in the model and press Close.



Figure 6.4 Final tunnel

6.2 MESH GENERATION

The default global coarseness parameter (Medium) can be accepted in this case.



View the mesh. The generated mesh is shown in Figure 6.5.



6.3 CALCULATIONS

To simulate the construction of the tunnel it is clear that a staged construction calculationis needed.


TUTORIAL MANUAL


The initial phase has already been introduced. Note that the soil layers are nothorizontal. As a result, the K0 procedure cannot be used to generate the initialeffective stresses in this example. Instead Gravity loading should be used. Thisoption is available in the General subtree of the Phases window.

• Water will not be considered in this example. The general phreatic level shouldremain at the model base.

• Make sure that the tunnel is inactive.

6.3.1 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)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 Phases window define a value of 0.6 for ΣMstage in the General subtree. Thiscorresponds 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. The model for Phase 1 is displayed in Figure 6.6.

Figure 6.6 Configuration of Phase 1

Phase 2


• In the Staged construction mode activate the lining and interfaces of the part of the



tunnel excavated in the previous phase (Figure 6.7).

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


Phase 3


• In the Phases window define a value of 0.6 for ΣMstage in the General subtree. Thiscorresponds to a β-value of 1-ΣMstage = 0.4.

• In the Staged construction mode deactivate the lower cluster (invert) and thetemporary lining in the middle of the tunnel (Figure 6.8).


Phase 4


• Activate the remaining lining and interfaces. All the plates and interfaces around thefull tunnel are active (Figure 6.9).

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

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




TUTORIAL MANUAL


6.4 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 6.10).

Figure 6.10 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 6.11) andpress View. Note that the tunnel lining is displayed in the Structures view.

Figure 6.11 Select structures window

• From the Forces menu select the Bending moment M option. The result, scaled by afactor of 0.5 is displayed in Figure 6.12.



Figure 6.12 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. The data ofthe dam materials and the sub-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:

• Defining time-dependent hydraulic conditions (Flow functions)

• Defining transient flow conditions using water levels

7.1 INPUT

• Start the Input program and select the Start a new project from the Quick selectdialog box.

• In the Project properties window enter an appropriate title.

• Keep the default units and constants and set the model dimensions to xmin = -130.0,xmax = 130.0, ymin = -30.0 and ymax = 30.0.

7.1.1 DEFINITION OF SOIL STRATIGRAPHY

In order to define the underlying foundation soil, a borehole needs to be added andmaterial properties must be assigned. A layer of 30 m overconsolidated silty sand isconsidered as sub-soil in the model.



TUTORIAL MANUAL

• Add a soil layer extending from ground surface (y = 0.0) to a depth of 30 m (y =-30.0).


• Create data sets under Soil and interfaces set type according to the informationgiven in Table 7.1. Note that the Thermal, Interfaces and Initial tabsheets are notrelevant (no thermal properties, no interfaces or K0 procedure are used).

• Assign the Subsoil material dataset to the soil layer in the borehole.

Table 7.1 Material properties of the dam and sub-soil

Parameter Name Core Fill Subsoil Unit

General

Material model Model Mohr-Coulomb Mohr-Coulomb Mohr-Coulomb -

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


Groundwater

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 1.00 0.01 m/day

Vertical permeability ky 1.0·10-4 1.00 0.01 m/day

7.1.2 DEFINITION OF THE EMBANKMENT

The embankment will be defined in the Structures mode.

Define a polygon by specifying points located at (-80.0 0.0), (92.5 0.0), (2.5 30.0)and (-2.5 30.0).

To create the sub-clusters in the embankment define two cutting lines from (-10.00.0) to (-2.5 30.0) and from (10.0 0.0) to (2.5 30.0).

• Assign the corresponding material datasets to the soil clusters.

7.2 MESH GENERATION


Create the mesh. Use the Fine option for the Element distribution parameter.

View the generated mesh. The generated mesh is shown in Figure 7.2.




Figure 7.2 Finite element mesh

7.3 CALCULATION

The following cases will be considered:

• long term situation with water level at 25 m.

• water level drops quickly from 25 to 5 m.

• water level drops slowly from 25 to 5 m.

• long term situation with water level at 5 m.

In addition to Initial phase, the calculation consists of eight phases. In the initial phase,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. The first andsecond phases both start from the initial phase (i.e. a dam with a reservoir level at 25 m)and the water level is lowered to 5 m. A distinction is made in the time interval at whichthis is done (i.e. different speeds of water level reduction; rapid drawdown and slowdrawdown). In both cases the water pressure distribution is calculated using a transientgroundwater flow calculation. The third calculation phase also starts from the initial phaseand considers the long-term behaviour of the dam at the low reservoir level of 5 m, whichinvolves a steady-state groundwater flow calculation to calculate the water pressuredistribution. Finally, for all the water pressure situations the safety factor of the dam iscalculated by means of phi-c reduction.

Note that only the water conditions will be defined for different calculation phases. Themodel requires no changes in the geometry. Water levels can be defined in the Flowconditions mode.

• Proceed to the Flow conditions mode by clicking the corresponding tab.

Initial phase: Gravity loading

By default the initial phase is added in the Phases explorer.

• In the Phases explorer double-click Initial phase.

• In the General subtree specify the name of the phase (e.g. High reservoir).

Select the Gravity loading option as calculation type.

Select the Steady state groundwater flow option as Pore pressure calculation type

• The Phases window is displayed (Figure 7.3). Click OK to close the Phases window.


TUTORIAL MANUAL

Figure 7.3 The Phases window

Hint: Note that by default Undrained behaviour (A) and (B) are ignored for aGravity loading calculation type. The corresponding option is available in theDeformation control parameters subtree in the Phases window.

Define the water level corresponding to the level of water in the reservoir prior to thedrawdown. The water level consists of four points; starting at the very left side at alevel of 25 m above the ground surface (-132.0 25.0); the second point is just insidethe dam at a level of 25 m (-10.0 25.0); the third point is near the dam toe (93.0-10.0) and the forth point just outside the right boundary at a level of 10 m below theground surface (132.0 -10.0). The defined water level is shown in Figure 7.4.

• Right-click the created water level and select the Make global option in theappearing menu. Note that the global water level can also be specified by selectingthe corresponding option in the GlobalWaterLevel menu in the Water subtree in theModel conditions.

Hint: Straight lines can be defined by keeping the <Shift> key pressed whiledefining the geometry.

Figure 7.4 High water level in the reservoir

• In the Model explorer expand the Attributes library.



• Expand the Water levels subtree. The levels created in the Flow conditions modeare grouped under User water levels.

• Expand the User water levels subtree. The created water level can be seen namedas 'UserWaterLevel_1'. The location of the water levels in Model explorer is shownin Figure 7.5.

Figure 7.5 Water levels in Model explorer

• Double-click on the created water level and rename it as 'FullReservoir_Steady'.This is a distinctive name that satisfies the naming requirements (no invalidcharacters).

• Expand the Model conditions subtree.

• Expand the GroundWaterFlow subtree. Note that by default the boundary at thebottom of the model is set to Closed. This is relevant for this example (Figure 7.6).

Figure 7.6 GroundwaterFlow boundary conditions in Model explorer


TUTORIAL MANUAL

Phase 1: Rapid drawdown

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


• In Phases explorer double-click the newly added phase. The Phases window isdisplayed.

• In the General subtree specify the name of the phase (e.g. Rapid drawdown). Notethat the High reservoir phase is automatically selected in the Start from phasedrop-down menu.

Select the Fully coupled flow-deformation option as calculation type.

• Assign a value of 5 days to the Time interval parameter.

• Make sure that the Reset displacements to zero and Reset small strain options areselected in the Deformation control parameters subtree.


• Due to the global nature of the water levels, if an attribute is assigned to a waterlevel in the model it will affect it in all phases. The water level in this phase has thesame geometry with the one previously defined, however it is time dependent and afunction needs to be assigned to it. As a result, it is required to create a new waterlevel with the same geometry and different attributes. In Model explorer right-clickon FullReservoir_Steady and select the Duplicate option in the appearing menu(Figure 7.7). A copy of the water level is created.

Figure 7.7 Copying water levels in Model explorer

• Rename the newly created water level as 'FullReservoir_Rapid'.



The behaviour of the water levels can be described by specifying Flow functions. Notethat Flow functions are global entities and are available under the Attributes library inModel explorer. To define the flow functions:

• Right-click the Flow functions option in the Attributes library in the Model explorerand select the Edit option in the appearing menu. The Flow functions window isdisplayed.

In the Head functions tabsheet add a new function by clicking the correspondingbutton. The new function is highlighted in the list and options to define the functionare displayed.

• Specify a proper name to the function for the rapid drawdown (e.g. Rapid).

• Select the Linear option from the Signal drop-down menu.

• Specify a time interval of 5 days.

• Assign a value of -20 m to ∆Head, representing the amount of the head decrease.A graph is displayed showing the defined function (Figure 7.8).

Figure 7.8 The flow function for the rapid drawdown case

• Click OK to close the Flow functions window.

• In the Model explorer right-click on FullReservoir_Rapid and select the Use asglobal phreatic level option in the appearing menu.

• Expand the FullReservoir_Rapid subtree. Note that the water level is composed of 3water segments. Select the water segment in the upstream shoulder (left from thedam, at the reservoir side).

• Expand the subtree of the selected segment and select the Time dependent optionfor the TimeDependency parameter.

• Select the Rapid option for the HeadFunction parameter. Figure 7.9 shows the


TUTORIAL MANUAL

selected water segment in Model explorer.

Figure 7.9 Properties of the lowering water segment

• In the Water subtree under the Model conditions in the Model explorer note that thenew water level (FullReservoir_Rapid) is assigned to GlobalWaterLevel.

The configuration of the phase is shown in Figure 7.10. Note that the shadow under thewater level segment in the upstream shoulder indicates the variation of the water levelduring the phase.

Figure 7.10 Configuration of the rapid drawdown phase

Phase 2: Slow drawdown

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

• Select the High reservoir phase in the Phases explorer.





• In the General subtree specify the name of the phase (e.g. Slow drawdown). TheHigh reservoir phase is automatically selected for the Start from phase parameter.

Select the Fully coupled flow deformation option as calculation type.

• Assign a value of 50 days to the Time interval parameter.

• Make sure that the Reset displacements to zero and Reset small strain options areselected in the Deformation control parameters subtree.


• Create a new duplicate of the high water level. The newly created water level will beused as Global water level in the slow drawdown phase. Even though the waterlevel in this phase has the same geometry as the previously defined ones, the flowfunction for the time dependency is different.

• Rename the newly created water level as 'FullReservoir_Slow'.

Add a new flow function following the steps described for the previous phase.

• Specify a proper name to the function for the slow drawdown (e.g. Slow).

• Select the Linear option from the Signal drop-down menu.

• Specify a time interval of 50 days.

• Assign a value of -20 m to ∆Head, representing the amount of the head decrease.A graph is displayed showing the defined function (Figure 7.11).


Figure 7.11 The flow function for the slow drawdown case

• In the Model explorer right-click on FullReservoir_Slow and select the Use as globalphreatic level option in the appearing menu.

• Expand the FullReservoir_Slow subtree. Select the water segment in the upstream


TUTORIAL MANUAL

shoulder (left from the dam, at the reservoir side). The segment selected in Modelexplorer is indicated by a red colour in the model.

• Expand the subtree of the selected segment and select the Time dependent optionfor the TimeDependency parameter.

• Select the Slow option for the HeadFunction parameter.

• In the Water subtree under the Model conditions in the Model explorer note that thenew water level (FullReservoir_Slow) is assigned to GlobalWaterLevel.

Phase 3: Low level

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

• Select the High reservoir phase in the Phases explorer.



• In the General subtree specify the name of the phase (e.g. Low level). The Highreservoir phase is automatically selected for the Start from phase parameter.

Make sure that the Plastic option is selected as calculation type.

Make sure that the Steady state groundwater flow option is selected as Porepressure calculation type

• In the Deformation control subtree, select Ignore und. behaviour (A,B) and makesure that the Reset displacements to zero and Reset small strain options areselected in the Deformation control parameters subtree.


Define the water level corresponding to the level of water in the reservoir after thedrawdown. The water level consists of four points; starting at the very left side at alevel of 5 m above the ground the surface (-132.0 5.0); the second point is inside thedam at a level of 5 m (-60.0 5.0); third point at (93.0 -10.0) and the fourth point justoutside the right boundary at a level of 10 m below the ground surface (132.0 -10.0).

• Rename the newly created water level as 'LowLevel_Steady'.

• In the Water subtree under the Model conditions in the Model explorer assign thenew water level (LowLevel_Steady) to GlobalWaterLevel. All the defined waterlevels are shown in Figure 7.12.

Figure 7.12 Model for the low level case in the Flow conditions mode



Phase 4 to 7:

In Phases 4 to 7 stability calculations are defined for the previous phases.

• Select the parent phase in the Phases explorer.

Add a new calculation phase and proceed to the Phases window.

Set Calculation type to Safety.

• In the Deformation control subtree, select Reset displacements to zero.

• In the Numerical control parameters subtree set the Max steps parameter to 30 forPhase 4 and to 50 for phases 5 to 7. The final view of Phases explorer is given inFigure 7.13.

Figure 7.13 The final view of Phases explorer


Select nodes located at the crest (-2.5 30.0) and at the toe of the dam (-80.0 0.0).

Start the calculation process by clicking the Calculate button in the Stagedconstruction mode.


7.4 RESULTS

The results of the four groundwater flow calculations in terms of pore pressure distributionare shown in Figures 7.14 to 7.17. Four different situations were considered:

• The steady-state situation with a high (standard) reservoir level (Figure 7.14).

• The pore pressure distribution after rapid drawdown of the reservoir level (Figure7.15).


TUTORIAL MANUAL

Figure 7.14 Pore pressure distribution, (pactive), for high reservoir level

Figure 7.15 Pore pressure distribution, (pactive), after rapid drawdown

• The pore pressure distribution after slow drawdown of the reservoir level (Figure7.16).

Figure 7.16 Pore pressure distribution, (pactive), after slow drawdown

• The steady-state situation with a low reservoir level (Figure 7.17).

Figure 7.17 Pore pressure distribution, (pactive), for low reservoir level

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 the first four calculation phases.Here, attention is focused on the variation of the safety factor of the dam for the differentsituations. Therefore, the development of ΣMsf is plotted for the phases 4 to 7 as afunction of the displacement of the dam crest point (see Figure 7.18).



Figure 7.18 Safety factors for different situations

Rapid drawdown of a reservoir level can reduce the stability of a dam significantly. Fullycoupled flow-deformation and stability analysis can be performed with PLAXIS 2D toeffectively analyze such situations


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.

• Select the Design approaches option in the Soil or Structures menu. Thecorresponding window is displayed.

• Click the Add button. A new design approach is added in the list.

• 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).Click the design approach in the list and specify a representative name (ex:'Eurocode 7 - DA 3').

• In the lower part of the window the partial factors can be defined for loads andmaterials. Set the partial factor for Variable unfavourable 1.3.

Figure 8.1 Partial factors for loads

• Click the Materials tab.

• Assign a value of 1.25 to Effective friction angle and Effective cohesion.


TUTORIAL MANUAL

Figure 8.2 Partial factors for materials

• Click the Materials button. The Material sets window pops up.

• Open the Loam material data set. Note that the view has changed. In the currentview it is possible to assign factors to different soil parameters, as well as to see theeffect of these factors on the soil parameters.

• Click the Parameters tab. In the Parameters tabsheet select the correspondinglabels for c'ref and ϕ' (Figure 8.3)

• Do the same for the remaining soil data sets.

• Close the Design approaches window.

Figure 8.3 Assignment of partial factors to material parameters



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

8.2 CALCULATIONS

There are two main schemes to perform design calculations in relation to serviceabilitycalculations (Section 5.8 of the Reference Manual). The first approach is used in thistutorial.


• Click Phase_1 in the Phases explorer.

Add a new phase.

• Double-click the newly added phase to open the Phases window.

• In the General subtree of the Phases window select the defined design approach inthe corresponding drop-down menu.

• In the Model explorer expand the Line loads and all the subtrees under it.

• Select the Variable unfavourable option in the LoadFactorLabel drop-down menu ofthe static component of the load (Figure 8.4).

Figure 8.4 Assignment of factor label to loads in the Selection explorer

• Follow the same steps to define ULS phases for all the remaining SLS phases.Make sure that the Phase 7 starts from Phase 1, Phase 8 from Phase 2, Phase 9from Phase 3 and so on.


TUTORIAL MANUAL

Select some characteristic points for curves (for example the connection points ofthe ground anchors on the diaphragm wall, such as (40.0 27.0) and (40.0 23.0)).



8.3 RESULTS

The results obtained for the design approach phases can be evaluated in Output. Figure8.5 displays the ΣMstage - |u| plot for the node located at (40.0 27.0).

Figure 8.5 Σ−Mstage - |u| plot for the ULS phases

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 8.6 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 8.6 ΣMsf - |u| plot for the last calculation phase and the corresponding ULS phase


TUTORIAL MANUAL


FLOW THROUGH AN EMBANKMENT

9 FLOW THROUGH AN EMBANKMENT

In this chapter the flow through an embankment will be considered. The crest of theembankment has a width of 2.0 m. Initially the water in the river is 1.5 m deep. Thedifference 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:

• Performing Flow only analysis

• Using cross section curves

9.1 INPUT


General settings




• Set the model dimensions to xmin = 0.0 m, xmax = 23.0 m, ymin = 0.0 m and ymax =6.0 m.

• Keep the default values for units, constants and the general parameters and pressOK to close the Project properties window.





TUTORIAL MANUAL

• Specify the head value as 4.5.

• Add a soil layer in the borehole. Set the top level to 3. No change is required for thebottom boundary of the layer.

• Create the rest of the required boreholes according to the information given in Table9.1.

Table 9.1 Information on the boreholes in the model

Borehole number Location (x) Head Top Bottom

1 2.0 4.5 3.0 0.0

2 8.0 4.5 6.0 0.0

3 10.0 4.0 6.0 0.0

4 20.0 1.0 1.0 0.0

Define the soil material according to the Table 9.2 and assign the material dataset tothe cluster. Skip the Interfaces and Initial tabsheets as these parameters are notrelevant.

Table 9.2 Properties of the embankment material (sand)

Parameter Name Sand Unit

General

Material model Model Linear elastic -


Soil unit weight above phreaticlevel

γunsat 20 kN/m3

Soil unit weight below phreaticlevel

γsat 20 kN/m3

Parameters

Stiffness E ' 1.0· 104 kN/m2


Groundwater

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

• After assigning the material to the soil cluster close the Modify soil layers window.

9.2 MESH GENERATION


Refine the lines shown in Figure 9.2 by specifying a Coarseness factor of 0.5.

Click the Generate mesh button in order to generate the mesh. The Mesh optionswindow appears.

• Select the Fine option in the Element distribution drop-down menu and generate themesh.




Figure 9.2 Indication of the local refinement of the mesh in the model



9.3 CALCULATIONS

In this project only the flow related behaviour will be analysed. The calculation processconsists of three phases that will be defined in the Staged construction mode. In theinitial phase, the groundwater flow in steady state is calculated for an average river level.In Phase 1, the transient groundwater flow is calculated for a harmonic variation of thewater level. In Phase 2, the calculation is similar as in Phase 1, but the period is longer.

• Click the Staged construction tab to proceed to the corresponding mode. A globallevel is automatically created according to the head values specified for eachborehole (Table 9.1). The model in the Staged construction mode is shown in Figure9.4.

Figure 9.4 The model in the Staged construction mode

Hint: Note that the 'internal' part of the global water level will be replaced by theresult of the groundwater flow calculation.


TUTORIAL MANUAL

Initial phase

• Double-click the initial phase in the Phases explorer.

• In the General subtree select the Flow only option as the Calculation type.

• The default values of the remaining parameters are valid for this phase. Click OK toclose the Phases window.


• In the Model conditions expand the GroundwaterFlow subtree. The defaultboundary conditions (Figure 9.5) are relevant for the initial phase. Check that onlythe bottom boundary is closed.

Figure 9.5 The groundwater flow boundary conditions for the initial phase

• In the Model explorer expand the Groundwater flow BCs subtree. The boundaryconditions at the extremities of the model are automatically created by the programand listed under the GWFlowBaseBC.

Hint: Note that when the boundary conditions under the Groundwater flow BCssubtree are active, the model conditions specified in the GroundwaterFloware ignored.

Phase 1


• In the Phases explorer double-click the current phase.

• In the General subtree select the Transient groundwater flow option as porepressure calculation type.

• Set the Time interval to 1.0 day.



• In the Numerical control parameters subtree set the Max number of steps storedparameter to 50. The default values of the remaining parameters will be used.


Click the Select multiple objects button in the side toolbar.

Point to the Select lines option and click on the Select water boundaries option inthe appearing menu (Figure 9.6).

Figure 9.6 The Select water boundaries option in the Select multiple objects menu

• Select the hydraulic boundaries as shown in Figure 9.7.

• Right-click and select the Activate option in the appearing menu.

Figure 9.7 The time dependent boundaries in the model

• In the Selection explorer set the Behaviour parameter to Head.

• Set href to 4.5.

• Select the Time dependent option in the Time dependency drop-down menu.

• Click on the Head function parameter.


TUTORIAL MANUAL

Add a new head function.

• In the Flow functions window select the Harmonic option in the Signal drop-downmenu. Set the amplitude to 1.0 m, the phase angle to 0 ◦ and the period to 1.0 day(Figure 9.8).

Figure 9.8 The flow function for the rapid case


Phase 2


• In the Phases explorer double-click the current phase.

• In the General subtree select the Initial phase in the Start from phase drop-downmenu.

• Select the Transient groundwater flow option as pore pressure calculation type.

• Set the Time interval to 10.0 day.

• In the Numerical control parameters subtree set the Max number of steps storedparameter to 50. The default values of the remaining parameters will be used.


• In the Selection explorer click on the Head function parameter.

Add a new head function.

• In the Flow functions window select the Harmonic option in the Signal drop-downmenu. Set the amplitude to 1.0 m, the phase angle to 0 ◦ and the period to 10.0 day(Figure 9.9).




Figure 9.9 The flow function for the slow case

To select points to be considered in curves:

In the Staged construction mode click the Select point for curves button in the sidetoolbar. The Connectivity plot is displayed in the Output program.

• In the Select points window select nodes located nearest to (0.0 3.0) and (8.0 2.5) tobe considered in curves.

• Click Update to close the output program.



9.4 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.

• 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.

• Deselect the initial phase and Phase 2, such that only Phase 1 is included in theanimations and rename the animation accordingly. The Create animation window isshown in Figure 9.10.

To view the results in a cross section:


TUTORIAL MANUAL

Figure 9.10 Create animation window

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 (2.0 3.0) and (20.0 1.0). The results in the crosssection are 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 Phase 1. The variation of the results in the cross section is displayed in anew window.

• Do the same for Phase 2. This may take about 30 seconds,

• The variation of the results due to different time intervals in harmonic variation at aspecific cross section can be compared (Figure 9.11 and Figure 9.12).

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 9.11 Active pore pressure variation in the cross section in Phase 1

Figure 9.12 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 (e.g. 'Flow around a sheet pile wall'). Thematerial parameters remain unchanged. The used groundwater parameters areshown in Table 10.1.

Table 10.1 Flow parameters

Parameter Name Silt Sand Loam Unit

Groundwater

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

In the Structures mode click the Create hydraulic conditions button in the sidetoolbar.

Select the Create well option in the appearing menu.

• Draw the first well by clicking on (42.0 23.0) and (42.0 20.0).

• Draw the second well by clicking on (58.0 23.0) and (58.0 20.0).

10.2 MESH GENERATION






TUTORIAL MANUAL


10.3 CALCULATIONS

• Proceed to the Staged construction mode. In this project only groundwater flowanalysis will be performed.

In the Phases explorer remove the existing phases (Phases 1 to 6).

Initial phase

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

• In the General subtree of the Phases window select the Flow only option in theCalculation type drop-down menu.

• The standard settings for the remaining parameters are valid for this phase.

• The default groundwater flow boundary conditions are valid. Only the bottomboundary of the model (BoundaryYMin) is Closed whereas the rest of theboundaries are Open.

• The water level created according to the head specified in the borehole is assignedas GlobalWaterLevel.

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.

Add a new phase.

• In the Phases window the calculation type is by default defined as Flow only.

• The default option (Steady state groundwater flow) will be used as Pore pressurecalculation type.

• In the Staged construction mode activate the interface elements along the wall.

• Multi-select the wells in the model and activate them.

• In the Selection explorer the behaviour of the wells is by default set to Extraction.

• Set the discharge value to 0.7 m3/day/m.

• Set the hmin value to 20.0m. This means that water will be extracted as long as thegroundwater head at the wall location is at least 20 m. Figure 10.2 shows theparameters assigned to the wells in the Selection explorer.


FLOW AROUND A SHEET PILE WALL

Figure 10.2 Well properties

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

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


10.4 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 6 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.


TUTORIAL MANUAL

a. Active pore pressures (Phase 6 in Chapter 3)

b. Active pore pressures (Phase 1 in the current project)

Figure 10.4 Comparison of the resulting active pore pressures.


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. 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 m0.50 m

1.25 m

Figure 11.1 Potato field geometry

Objectives:

• Defining precipitation

11.1 INPUT

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.


General settings




• Set the model dimensions to xmin = 0.0 m, xmax = 15.0 m, ymin = 0.0 m and ymax =5.0 m.

• Keep the default values for units, constants and the general parameters and pressOK to close the Project properties window.


TUTORIAL MANUAL


Due to the geometry of the model, the options for snapping should be changed.

Click the Snapping options button in the bottom toolbar.

• In the appearing window set the Number of snap intervals to 100 (Figure 11.2).

• Click OK to close the Snapping window.

Figure 11.2 Modification of the Number of snap intervals


Create two boreholes located at x = 0.75 and x = 2.00 respectively.

• In the Modify soil layers window add two soil layers.

• In the first borehole set Top = 3.75 and Bottom = 3.00 for the uppermost soil layer.Set Bottom = 0 for the lowest soil layer.

• In the second borehole set Top = 5.00 and Bottom = 3.0 for the uppermost soil layer.Set Bottom = 0 for the lowest soil layer.

• For both boreholes the Head is located at y = 4.25. Figure 11.3 shows the soilstratigraphy defined in the Modify water levels window.

Figure 11.3 Soil stratigraphy in the Modify soil layers window



Create the material data sets according to Table 11.1.

• Assign the material data set to the corresponding 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 -

Soil unit weight above p.l. γunsat 19 20 kN/m3

Soil unit weight below p.l. γsat 19 20 kN/m3

Parameters

Young's modulus E ' 1.0·103 1.0·104 kN/m2

Poisson's ratio ν ' 0.3 0.3 -

Groundwater

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



• Multi-select the line segments composing the upper boundary of the model (Figure11.4).

Figure 11.4 The upper boundary of the model

• In the Selection explorer set the Coarseness factor parameter to 0.5.


View the mesh. The resulting mesh is displayed in (Figure 11.5).



TUTORIAL MANUAL

Figure 11.5 Potato field mesh

11.3 CALCULATIONS

The calculation process consists of two phases. In the initial phase, the groundwater flowin steady state is calculated. In Phase 1, the transient groundwater flow is calculated.

Initial phase

• Proceed to the Staged construction mode. In this project only groundwater flowanalysis will be performed.

• In the Phases window select the Flow only option as the Calculation type in theGeneral subtree.

• The default values of the remaining parameters are valid for this phase. Click OK toclose the Phases window.

Right-click the bottom boundary of the model and select the Activate option in theappearing menu.

• In the Selection explorer select the Head option in the Behaviour drop-down menuand set href to 3.0 (Figure 11.6).

Figure 11.6 Boundary conditions at the bottom of the geometry model


• Expand the GroundwaterFlow subtree. Set BoundaryXMin and BoundaryXMax toClosed.

• Expand the Water subtree. The borehole water level is assigned toGlobalWaterLevel.

Transient phase

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



Hint: Note that the conditions explicitly assigned to groundwater flow boundariesare taken into account. In this tutorial the specified Head will be consideredfor the bottom boundary of the model, NOT the Closed condition specified inthe GroundwaterFlow subtree under the Model conditions.


• In General subtree of the Phases window select the Transient groundwater flow asPore pressure calculation type.

• Set the Time interval to 15 days.

• In the Numerical control parameters subtree set the Max number of steps stored to250. The default values of the remaining parameters will be used.


To define the precipitation data a discharge function should be defined.

• In the Model explorer expand the Attributes library subtree.

• Right-click on Flow functions and select the Edit option in the appearing menu. TheFlow functions window pops up.

• In the Discharge functions tabsheet add a new function.

• Specify a name for the function and select the Table option in the Signal drop-downmenu.

• Click the Add row button to introduce a new row in the table. Complete the datausing the values given in the Table 11.2.

Table 11.2 Precipitation data

ID Time [day] ∆Discharge [m3/day/m]

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

• Figure 11.7 shows the defined function for precipitation. Close the windows byclicking OK.

• In the Model explorer expand the Precipitation subtree under Model conditions andactivate it. The default values for discharge (q) and condition parameters (ψmin =


TUTORIAL MANUAL

Figure 11.7 The Flow function window displaying the precipitation data and plot

-1.0 m and ψmax = 0.1m) are valid.

• For the precipitation select the Time dependent option in the correspondingdrop-down menu and assign the defined function (Figure 11.8).



Figure 11.8 Precipitation in the Model explorer

Hint: Negative values of precipitation indicate evaporation.



11.4 RESULTS

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

• From the Stresses menu select Groundwater flow → Saturation.

• Double click the legend. The Legend settings window pops up. Define the settingsas shown in Figure 11.9.

Figure 11.9 Value for settings

• Figure 11.10 shows the spatial distribution of the saturation for the last time step.

Figure 11.10 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 dynamic soil-structure interaction. Here theinfluence of a vibrating source on its surrounding soil is studied. The vibrating source is agenerator founded on a 0.2 m thick concrete footing of 1 m in diameter, see Figure 12.1.Oscillations caused by the generator are transmitted through the footing into the subsoil.

sandy clay

1m

generator

Figure 12.1 Generator founded on elastic subsoil

The physical damping due to the viscous effects is taken into consideration via theRayleigh damping. Also, due to axisymmetry 'geometric damping' can be significant inattenuating the 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.

Objectives:

• Defining a Dynamic calculation.

• Defining Dynamic loads.

• Defining material damping by means of Rayleigh damping.

12.1 INPUT


General settings



• Due to the three dimensional nature of the problem, an axisymmetric model is used.In the Model tabsheet select the Axisymmetric option for Model and keep thedefault option for Elements (15-Noded).

• Keep the default values for units and constants and set the model dimensions toxmin = 0.0 m, xmax = 20.0 m, ymin = 0.0 m, ymax = 20.0 m.


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Hint: The model boundaries should be sufficiently far from the region of interest, toavoid disturbances due to possible reflections. Although special measuresare adopted in order to avoid spurious reflections (viscous boundaries), thereis always a small influence and it is still a good habit to put boundaries faraway. In a dynamic analysis, model boundaries are generally taken furtheraway than in a static analysis.


The subsoil consists of one layer with a depth of 10 m. The ground level is defined at y =0. Note that water conditions are not considered in this example. To define the soilstratigraphy:

Create a borehole at x = 0.

• Create a soil layer extending from ground surface (y = 0.0) to a depth of 10 m (y =-10.0).

• Keep the Head in the borehole at 0.0 m.

The soil layer consists of sandy clay, which is assumed to be elastic. Create a dataset under the Soil and interfaces set type according to the information given in Table12.1. The specified Young's modulus seems relatively high. This is because thedynamic stiffness of the ground is generally considerably larger than the staticstiffness, since dynamic loadings are usually fast and cause very small strains. Theunit weight suggests that the soil is saturated; however the presence of thegroundwater is neglected.

Table 12.1 Material properties of the subsoil


General

Material model Model Linear elastic -


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 -

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 6.1.2 of the Reference Manual.




The generator is defined in the Structures mode.

Create a plate extending from (0.0 0.0) to (0.5 0.0) to represent the footing.

Define a material data set for the footing according to the information given in Table12.2. The footing is assumed to be elastic and has a weight of 5 kN/m2.

Table 12.2 Material properties of the footing





Weight w 5.0 kN/m/m


• Apply a distributed load on the footing to model the weight of the generator as wellas the vibrations that it produces. The actual value of the load will be defined later.The model is shown in Figure 12.2.

Figure 12.2 Model layout



Generate the mesh. Use the default option for the Element distribution parameter(Medium).

View the generated mesh. The resulting mesh is shown in Figure 12.3. Note that themesh is automatically refined under the footing.



TUTORIAL MANUAL


12.3 CALCULATIONS

The calculation consists of 4 phases and it will be defined in the Staged constructionmode.

Initial phase

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

• The initial phase has already been introduced. The default settings of the initialphase will be used in this tutorial.

Phase 1

Add a new calculation phase. The default settings of the added phase will be usedfor this calculation phase.

• Activate the footing.

• Activate the static component of the distributed load. In the Selection explorer setqy ,start ,ref value to -8 kN/m/m. Do not activate the dynamic component of the load(Figure 12.4).

Figure 12.4 Specification of the static load component in the Selection explorer

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 total time interval of 0.5 sec are considered.


In the General subtree in the Phases window, select the Dynamic option ascalculation type.

• Set the Dynamic time interval parameter to 0.5 s.

• In the Deformation control parameters subtree in the Phases window select theReset displacements to zero parameter. The default values of the remainingparameters will be used for this calculation phase.

• In the Model explorer expand the Attributes library subtree.

• Right-click the Dynamic multipliers subtree and select the Edit option from theappearing menu. The Multipliers window pops up.

• Click the Load multipliers tab.

Click the Add button to introduce a multiplier for the loads.

• Define a Harmonic signal with an Amplitude of 10, a Phase of 0◦ and a Frequencyof 10 Hz and as shown in Figure 12.5.

Figure 12.5 Definition of a Harmonic multiplier

In the Selection explorer, activate the dynamic component of the load(DynLineLoad_1).

• Specify the components of the load as (qx ,start ,ref , qy ,start ,ref ) = (0.0, -1.0). ClickMultiplier_y in the dynamic load subtree and select the LoadMultiplier_1 optionfrom the drop-down menu (Figure 12.6).

Hint: The dynamic multipliers can be defined in the Geometry modes as well as inthe Calculation modes.


TUTORIAL MANUAL

Figure 12.6 Specification of the dynamic load component in the Selection explorer

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, viscous boundaries are specified at Xmax and Ymin. The dynamicboundaries can be specified in the Dynamics subtree located under the Model conditionsin the Model explorer (Figure 12.7).

Figure 12.7 Boundary conditions for Dynamic calculations



Phase 3

Add a new phase (Phase_3).

In the General subtree in the Phases window, select the Dynamic option ascalculation type.

• Set the Dynamic time interval parameter to 0.5 s.

• In the Staged construction mode deactivate the dynamic component of the surfaceload. Note that the static load is still active. The dynamic boundary conditions of thisphase should be the same as in the previous phase.

Select nodes located at the ground surface (ex: (1.4 0.0), (1.9 0.0), (3.6 0.0)) toconsider in curves.


Save the project.

12.3.1 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:

• Save the project under another name.

• Open the material data set of the soil.

• In the General tabsheet click the box next to the Rayleigh α parameter. Note that thedisplay of the General tabsheet has changed displaying the Single DOF equivalencebox.

• In order to introduce 5% of material damping, set the value of the ξ parameter to 5%for both targets and set the frequency values to 1 and 10 for the Target 1 and Target2 respectively.

• Click on one of the definition cells of the Rayleigh parameters. The values of α andβ are automatically calculated by the program.

• Click OK to close the data base.

• Check whether the phases are properly defined (according to the information givenbefore) and start the calculation.


TUTORIAL MANUAL

Figure 12.8 Input of Rayleigh damping

12.4 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 the x-axis and uy to they-axis. Figure 12.9 shows the response of the pre-selected points at the surface of thestructure. It can be seen that even with no damping, the waves are dissipated which canbe attributed to the geometric damping.

The presence of damping is clear in Figure 12.10. 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 12.10 (without damping)with Figure 12.10 (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. Figure12.11 shows the total accelerations in the soil at the end of phase 2 (t = 0.5 s).



Figure 12.9 Vertical displ.- time on the surface at different distances to the vibrating source (withoutdamping)

Figure 12.10 Vertical displ.- time on the surface at different distances to the vibrating source (withdamping)


TUTORIAL MANUAL

Figure 12.11 Acceleration (|a|) 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


General settings


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

• In the Model tabsheet select the Axisymmetry option for Model and keep the defaultoption for Elements (15-Noded).

• Keep the default units and constants and set the model dimensions to xmin = 0, xmax= 30, ymin = 0 and ymax = 18.


The subsoil is divided into an 11 m thick clay layer and a 7 m thick sand layer. Thephreatic level is assumed to be at the ground surface. Hydrostatic pore pressures aregenerated in the whole geometry according to this phreatic line. To define the soil


TUTORIAL MANUAL

stratigraphy:

Create a borehole at x = 0.

• Create two soil layers extending from y = 18.0 to y = 7.0 and from y = 7.0 to y = 0.0.

• Set the Head in the borehole at 18.0 m.

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 interfacestrength reduction factor should be taken equal to unity (rigid).

Create the material data sets according to the information given 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 -


PILE DRIVING


The pile is defined as a column of 0.2 m width. The Interface elements are placed alongthe pile to model the interaction between the pile and the soil. The interface should beextended to about half a meter into the sand layer (see Figure 13.2). Note that theinterface should be defined only at the side of the soil. A proper modelling of the pile-soilinteraction is important to include the material damping caused by the sliding of the soilalong the pile during penetration and to allow for sufficient flexibility around the pile tip.

Hint: Use the Zoom in feature to create the pile and the interface.

Pile

Interface

Clay

Extended interface

Sand

(0.0, 7.0)(0.2, 7.0)

(0.2, 6.6)

Figure 13.2 Extended interface

To define the concrete pile:


Select the Create polygon feature in the side toolbar and click on (0.0 18.0), (0.218.0), (0.2 7.0) and (0.0 7.0).

Create a negative interface to model the interaction of the pile with the surroundingsoil by clicking on (0.2 6.6) and (0.2 18.0).

The pile is made of concrete, which is modelled by means of the linear elastic modelconsidering non-porous behaviour (Table 13.1). In the beginning, the pile is not present,so initially the clay properties are also assigned to the pile cluster.

In order to model the driving force, a distributed unit load is created on top of the pile. Tocreate a dynamic load:

Define a distributed load by clicking on (0.0 18.0) and (0.2 18.0).

• The load components will be defined in the Selection explorer. Note that the staticcomponent of the load will not be used in this project. The program will neglect thestatic components of the load if it (static load) is not activated.

• Expand the Dynamic load subtree and specify a unit load in the gravity direction.

Click the Multiplier_y drop down menu and click on the appearing plus button. TheMultipliers window pops up and a new load multiplier is automatically added.

• Define a Harmonic signal with an Amplitude of 5000, a Phase of 0◦ and aFrequency of 50 Hz and as shown in Figure 13.3.


TUTORIAL MANUAL

Figure 13.3 Definition of a Harmonic multiplier

Hint: Note that dynamic multipliers can be defined by right-clicking the Dynamicmultipliers subtree under Attributes library in the Model explorer.

» Note that dynamic multipliers are attributes and as such it is possible todefine them in all the program modes.

The final geometry model is shown in Figure 13.4.

Figure 13.4 The geometry model



Generate the mesh. Use the default option for the Element distribution parameter


PILE DRIVING

(Medium).




13.3 CALCULATIONS

The calculation consists of 3 phases. In the Initial phase, the initial stress conditions aregenerated. In the Phase 1 the pile is created. In the Phase 2 the pile is subjected to asingle stroke, which is simulated by activating half a harmonic cycle of load. In the Phase3 the load is kept zero and the dynamic response of the pile and soil is analysed in time.The last two phases involve dynamic calculations.

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


• In the General subtree in the Phases window, the Plastic option is selected asCalculation type.

• The Staged construction option is by default selected as Loading type.

• In the Staged construction mode assign the pile properties to the pile cluster.

• Activate the interface in the Sand layer. The model for the Phase 1 in the Staged


TUTORIAL MANUAL

construction mode is displayed in Figure 13.6.


Phase 2


• In the General subtree in the Phases window, select the Dynamic option asCalculation type.

• Set the Dynamic time interval to 0.01 s.

• In the Deformation control parameters subtree select Reset displacements to zero.

• In the Staged construction mode activate the dynamic component of the distributedload. The activated dynamic component of the load in Selection explorer is shown inFigure 13.7.

Figure 13.7 The dynamic load component in the Selection explorer


PILE DRIVING

• Expand the Dynamics subtree under Model conditions in the Model explorer.

• Specify viscous boundaries at xmax and ymin (Figure 13.8).


The result of this phase is half a harmonic cycle of the external load. At the end of thisphase, the load is back to zero.

Phase 3


• In the General subtree in the Phases window, select the Dynamic option asCalculation type.

• Set the Dynamic time interval to 0.19 s.

• In the Staged construction mode de-activate the dynamic load.

Select a node at the top of the pile for load displacement curves.


Save the project.

13.4 RESULTS

Figure 13.9 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 13mm. However, the final settlement is almost 10 mm.


TUTORIAL MANUAL

• 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 13.9 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 13.10 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.

Figure 13.10 Maximum shear stresses in the interface at t = 0.01 s.


PILE DRIVING

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.


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


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

• In the Model tabsheet keep the default options for Model (Plane strain) andElements (15-Noded).

• Keep the default units and constants and set the model dimensions to xmin = -80.0,xmax = 80.0, ymin = -40.0 and ymax = 15.0.

x

y15 m

15 m

25 m

75 m75 m 10 m

2 m

Figure 14.1 Geometry of the project


The subsoil is divided into an 15 m thick clayey layer and a 25 m thick sandy layer. Thephreatic level is assumed to be at y = -15.0 m. Hydrostatic pore pressures are generatedin the whole geometry according to this phreatic line.


• Add two soil layers extending from y = 0.0 to y = -15.0 and from y = -15.0 to y = -40.

• Set the Head in the borehole at -15.0 m.

The upper layer consists of mostly clayey soil and the lower one is sandy. Both have HSsmall model properties. The presence of the groundwater is neglected. The soil layers


TUTORIAL MANUAL

with HS small model properties have inherent hysteretic damping.


• Create data sets under Soil and interfaces set type according to the informationgiven in Table 14.1.

• Assign the material datasets to the corresponding soil layers in the borehole.

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 14.2 and 14.3 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.

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 14.4 and 14.5 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 the



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 14.2 Modulus reduction curves for the upper clayey layer

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 14.3 Modulus reduction curve for the lower sandy layer

modulus reduction curve to the damping curve can be found in the literature∗.


The structural elements of the model are defined in the Structures mode. To define thestructure:

Create the vertical walls of the building passing through (-5.0 0.0) to (-5.0 15.0) andthrough (5.0 0.0) to (5.0 15.0).

• Use the same feature to define the vertical walls of the basement passing through(-5.0 -2.0) to (-5.0 0.0) and through (5.0 -2.0) to (5.0 0.0).

• Define the floors and the basement of the building as plates passing through (-5.0

∗ 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


TUTORIAL MANUAL

0

0.2

0.15

0.1

0.05Dam

ping

ratio

Cyclic shear strain0.00001 0.0001 0.001 0.01

Figure 14.4 Damping curve for the upper clayey layer

0

0.2

0.15

0.1

0.05

Dam

ping

ratio

Cyclic shear strain0.00001 0.0001 0.001 0.01

Figure 14.5 Damping curve for the lower sandy layer

-2.0) to (5.0 -2.0), (-5.0 0.0) to (5.0 0.0), (-5.0 3.0) to (5.0 3.0), (-5.0 6.0) to (5.0 6.0),(-5.0 9.0) to (5.0 9.0), (-5.0 12.0) to (5.0 12.0) and (-5.0 15.0) to (5.0 15.0).

The plates, representing the walls and the floors in the building, are considered to belinear elastic. Note that two different material datasets are used, one for the basementand the other for the rest of the building. The physical damping in the building issimulated by means of Rayleigh damping. A description of Rayleigh damping parametersis given in Section 6.1.1 or the Reference Manual.

Define the material datasets for the structural elements in the building according toTable 14.3.

Table 14.3 Material properties of the building (plate properties)

Parameter Name Rest of building Basement Unit

Material type Type Elastic; Isotropic Elastic; Isotropic -

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 -

• Assign the Basement material dataset to the vertical plates (2) and the lowesthorizontal plate (all under the ground level) in the model.

• Assign the Rest of the building material dataset to the remaining plates in the model.



Use the Node-to-node anchor feature to define the column at the centre of thebuilding connecting consecutive floors, (0.0 -2.0) to (0.0 0.0), (0.0 0.0) to (0.0 3.0),(0.0 3.0) to (0.0 6.0), (0.0 6.0) to (0.0 9.0), (0.0 9.0) to (0.0 12.0) and (0.0 12.0) to(0.0 15.0).

• Define the properties of the anchor according to Table 14.4 and assign the materialdataset to the anchors in the model.

Table 14.4 Material properties of the node-to-node anchor

Parameter Name Column Unit

Material type Type Elastic -

Normal stiffness EA 2.5· 106 kN

Spacing out of plane Lspacing 3.0 m

Define an interface to model the interaction between soil and building around thebasement floor.

Create a point load at the top left corner of the building.

• Specify the components of the load as (10.0 0.0).

The earthquake is modelled by imposing a prescribed displacement at the bottomboundary. To define the prescribed displacement:

Define a prescribed displacement at the bottom of the model, through (-80.0 -40.0)and (80.0 -40.0).

• Set the x-component of the prescribed displacement to Prescribed and assign avalue of 1.0. The y-component of the prescribed displacement is Fixed. The defaultdistribution (Uniform) is valid.

To define the dynamic multipliers for the prescribed displacement:

• Expand the Dynamic displacement

Click the Multiplier_x drop down menu and click on the appearing plus button. TheMultipliers window pops up and a new displacement multiplier is automaticallyadded.

• From the Signal drop-down menu select the Table option.

• The file containing the earthquake data is available in the PLAXIS knowledge base(http://kb.plaxis.nl/search/site/smc). Copy all the data to a text editor file (e.g.Notepad) and save the file in your computer.

• Open the page in the web browser and copy all the data.

In the Multipliers window click the Paste button. In the Import data window select theStrong motion CD-ROM files option from the Parsing method drop-down menu andpress OK to close the window.

• Select the Acceleration option in the Data type drop-down menu.

• Select the Drift correction options and click OK to finalize the definition of themultiplier. The defined multiplier is displayed (Figure 14.6).

The geometry of the model is shown in Figure 14.7.


TUTORIAL MANUAL

Figure 14.6 Dynamic multipliers window

Figure 14.7 Geometry of the model



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






14.3 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

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

• The initial phase has already been introduced. The default settings of the initialphase will be used in this tutorial.

• In the Staged construction mode check that the building and load are inactive(Figure 14.9).

Figure 14.9 Initial phase

Phase 1

Add a new phase (Phase_1). The default settings of the added phase will be usedfor this calculation phase.

• In the Staged construction mode construct the building (activate all the plates, theinterfaces and the anchors) and deactivate the basement volume (Figure 14.10).

Phase 2


• In the Phases window select the Reset displacement to zero in the Deformationcontrol parameters subtree. The default values of the remaining parameters will be


TUTORIAL MANUAL

Figure 14.10 Construction of the building

used in this calculation phase.

• In the Staged construction mode activate the load. The value of the load is alreadydefined in the Structures mode.

Phase 3


In the Phases window select the Dynamic option as Calculation type.

• Set the Dynamic time interval parameter to 5 sec.

• In the Staged construction mode deactivate the point load.


• Expand the Dynamics subtree. Set BoundaryYMin to viscous (Figure 14.11).




Hint: For a better visualisation of the results, animations of the free vibration andearthquake can be created. If animations are to be created, it is advised toincrease the number of the saved steps by assigning a proper value to theMax steps saved parameter in the Parameters tabsheet of the Phaseswindow.

Phase 4


• In the Phases window set the Start from phase option to Phase 1 (construction ofbuilding).

Select the Dynamic option as Calculation type.

• Set the Dynamic time interval parameter to 20 sec.

• Select the Reset displacement to zero in the Deformation control parameterssubtree. The default values of the remaining parameters will be used in thiscalculation phase.

• In the Model explorer activate the Prescribed displacement and its dynamiccomponent. The Ymin boundary is NOT viscous in this phase.

Select a point at the top of the building for curves (0.0 15.0).


Save the project.

14.4 RESULTS

Figure 14.12 shows the deformed structure at the end of the Phase 2 (application ofhorizontal load).

Figure 14.12 Deformed mesh of the system

Figure 14.13 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.

In the Chart tabsheet of the Settings window select the Use frequency representation(spectrum) and Standard frequency (Hz) options in the Dynamics box. The plot is shown


TUTORIAL MANUAL

Figure 14.13 Time history of displacements at selected points

in Figure 14.14. From this figure it can be evaluated that the dominant building frequencyis around 1 Hz.

Figure 14.14 Frequency representation (spectrum)

Figure 14.15 shows the time history of the lateral acceleration of the selected points A (015) for the earthquake phase (dynamic analysis). For a better visualisation of the resultsanimations of the free vibration and earthquake can be created.



Figure 14.15 Variation of acceleration in dynamic time


TUTORIAL MANUAL


THERMAL EXPANSION OF A NAVIGABLE LOCK

15 THERMAL EXPANSION OF A NAVIGABLE LOCK

A navigable lock is temporarily 'empty' due to maintenance. After some time there issignificant increase of the air temperature, which causes thermal expansion of the innerside of the lock, while the soil-side of the concrete block remains relatively cold. Thisleads to backward bending of the wall and, consequently, to increased lateral stress inthe soil behind the wall and increased bending moments in the wall itself.

50 m

16m

5m

6m

12 m

10 m

Excavation

Concrete lock

Sand

Figure 15.1 Concrete lock

This example demonstrates the use of the Thermal module to analyse this kind ofsituations.

Objectives:

• Defining a thermal temperature function

• Use of thermal expansion

• Performing a fully coupled analysis for THM calculation

15.1 INPUT

General settings

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


• In the Model tabsheet, the default options for Model and Elements are used for thisproject. Also the default options for the units are used in this tutorial.

• Set the model dimensions to xmin = 0.0 m, xmax = 25.0 m, ymin = -16.0 m and ymax =0.0 m.

• Click Ok to exit the Project properties window.




TUTORIAL MANUAL

• Create a single soil layer with top level at 0.0 m and bottom level at -16.0 m. Set thehead at -4.0 m.

Click the Materials button in the Modify soil layers window.

Two data sets need to be created; one for the sand layer and one for the concrete block.

• Define a data set for the Sand layer with the parameters given in Table 15.1, for theGeneral, Parameters, Groundwater, Thermal and Initial tabsheets.

• Create another dataset for Concrete according to the Table 15.1.

• Assign the material dataset Sand to the borehole soil layer.

Table 15.1 Soil properties of the sand

Parameter Name Sand Concrete Unit

General

Material model Model HS small Linear elastic -

Type of material behaviour Type Drained Non-porous -

Soil unit weight above phreatic level γunsat 20.0 24.0 kN/m3

Soil unit weight below phreatic level γsat 20.0 - kN/m3

Initial void ratio einit 0.5 0.5 -

Parameters

Young’s modulus E' - 25·106 kN/m2

Poisson’s ratio ν - 0.15 -

Secant stiffness in standard drained triaxial test E ref50 40·103 - kN/m2

Tangent stiffness for primary oedometer loading E refoed 40·103 - kN/m2

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

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

Cohesion cref ' 2.0 - kN/m2

Angle of internal friction φ' 32.0 - ◦

Dilatancy angle ψ 2.0 - ◦

Shear strain at which Gs = 0.722G0 γ0.7 0.1·10−3 - -

Shear modulus at very small strains Gref0 8·104 - kN/m2

Groundwater

Data set - USDA - -


- -

Soil type - Sandy clay - -

Set parameters to defaults - Yes - -

Thermal

Specific heat capacity cs 860 900 kJ/t/K

Thermal conductivity λs 4.0·10−3 1.0·10−3 kW/m/K

Soil density ρs 2.6 2.5 t/m3

X-component of thermal expansion αx 0.5·10−6 0.1·10−4 1/K

Y-component of thermal expansion αy 0.5·10−6 0.1·10−4 1/K

Z-component of thermal expansion αz 0.5·10−6 0.1·10−4 1/K

Interfaces

Interface strength - Rigid Manual -

Strength reduction factor inter. Rinter 1.0 0.67 -

Initial

K0 determination - Automatic Automatic


The lock will be modelled as a concrete block during the staged construction.

• Proceed to Structures mode.



Click the Create soil polygon button in the side toolbar and select the Create soilpolygon option in the appearing menu.

• Define the lock in the draw area by clicking on (0.0 -5.0), (5.0 -5.0), (5.0 0.0), (5.50.0), (6.0 -6.0), (0.0 -6.0) and (0.0 -5.0).

Hint: The Snapping options can be selected, and the Spacing can be set to 0.5 toeasily create the polygon.

The Concrete material will be assigned later in the Staged construction.


Select the Create thermal flow bc option in the expanded menu (Figure 15.2).

• Create thermal boundaries at vertical boundaries and the bottom boundary (Xmin,Xmax and Ymin).

Figure 15.2 The Create thermal bc option in the Create line menu

• The vertical boundaries have the default option of Closed for the Behaviour.

• Select the bottom boundary, in the Selection explorer set the Behaviour toTemperature.

• Set the reference temperature, Tref to 283.4 K (Figure 15.3).

Figure 15.3 Thermal boundary condition in the Selection explorer

The geometry of the model is now complete (Figure 15.4).


TUTORIAL MANUAL




• Select the polygon representing the concrete block, and in the Selection explorer setthe Coarseness factor to 0.25.

Click the Generate mesh button. The default element distribution of Medium is usedfor this example.






15.3 CALCULATIONS

The calculations for this tutorial is carried out in three phases. The concrete lock isactivated in a plastic calculation, after which the temperature increase is defined as a fullycoupled flow deformation analysis.

Initial phase

• Proceed to Staged construction mode.

• Double click on Initial phase in the Phases explorer.

• The default options for Calculation type and Pore pressure calculation type are usedin this example.

• Select Earth gradient for the Thermal calculation type option and close the Phaseswindow.

• In the Staged construction activate the ThermalFlow under the Model conditionssubtree and set the value for Tref to 283 K. The default values for href and Earthgradient are valid (Figure 15.6).

Figure 15.6 Thermal flow in the Selection explorer



TUTORIAL MANUAL

Phase 1


• Double click on Phase_1 in the Phases explorer.

In the Phases window, enter an appropriate name for the phase ID and selectSteady state groundwater flow as Pore pressure calculation type.

Set the Steady state thermal flow for the Thermal calculation type.

• Note that both Reset displacements to zero and Ignore suction are selected.

• In the Staged construction mode, assign the Concrete dataset to the createdpolygon which represents the navigable lock (Figure 15.8).

Figure 15.8 Assigning Concrete soil data set to the navigable lock

Right click the soil cluster which is cut-off by the polygon and select the optionDeactivate from the appearing menu.

• In the Selection explorer, set the WaterConditions of this cluster to Dry.

• Multi-select the vertical and bottom horizontal wall of the excavation.

• In the Selection explorer, activate the Groundwater flow boundary condition.

• Set the Behaviour to Head and the href to -5.0 m (Figure 15.9). This will simulate an'empty' lock.

• In the Model explorer, activate all the Thermal flow boundary conditions.

• In the Model explorer, activate the Climate condition under the subtree Modelconditions.

• Set the Air temperature to 283.0 K and the Surface transfer to 1.0 kW/m2 (Figure15.10). This will define the thermal conditions at the ground surface and the insideof the lock.

• Deactivate the ThermalFlow option. This is because the thermal flow boundary



Figure 15.9 Groundwater flow boundary condition in the Selection explorer

conditions, including climate condition, are used in a steady state thermal flowcalculation, instead of the earth gradient option.

• Figure 15.11 shows the model at the end of Phase_1.

Figure 15.10 Model conditions for Phase_1

Phase 2


• Double click on Phase_2 in the Phases explorer.

Set the Calculation type to Fully coupled flow deformation.

The Thermal calculation type is set to Use temperatures from previous phase. Thisis to indicate that temperature needs to be considered and that the initialtemperature is taken from the previous phase.

• The Time interval is set to 10 days.

• Reset displacements to zero and Ignore suction should be selected for this example.

A temperature function is defined for the Time dependency in Climate which is used forthis phase. Follow these steps to create a temperature function.

• Right-click the Thermal functions option in the Attributes library in the Modelexplorer and select Edit option in the appearing menu. The Thermal functions


TUTORIAL MANUAL

Figure 15.11 The model at the end of Phase_1

window is displayed.

In the Temperature functions tabsheet add a new function by clicking on thecorresponding button. The new function is highlighted in the list and options todefine the function are displayed.

• The default option of Harmonic is used for this signal.

• Assign a value of 15.0 for the Amplitude and 40 days for the Period. A graph isdisplayed showing the defined function (Figure 15.12). Since the time interval of thephase is 10 days, only a quarter of a temperature cycle is considered in this phase,which means that after 10 days the temperature has increased by 15 K.

• Click OK to close the Thermal functions window.

• Expand the subtree Model conditions in the Model explorer.

• In the Climate option, set the Time dependency to Time dependent and assign thethe temperature function which was created (Figure 15.13).

The calculation definition is now complete. Before starting the calculation it is suggestedthat you select nodes or stress points for a later generation of curves.

Click the Select points for curves button in the side toolbar. Select somecharacteristic points for curves (for example at the top of the excavation, (5.0, 0.0)).





Figure 15.12 The temperature function

Figure 15.13 Model conditions for Phase_2

15.4 RESULTS

In the Phases explorer, select the Initial phase and click the View calculation resultsbutton on the toolbar. In the Output program, select Temperature from the Heat flowoption in the Stresses menu.

Figure 15.14 shows the initial temperature distribution, which is obtained from thereference temperature at the ground surface and the earth gradient. This gives atemperature of 283.0 K at the ground surface and 283.4 at the bottom of the model.

Figure 15.15 shows the temperature distribution obtained from Phase_1 using asteady-state thermal flow calculation. In fact, the temperatures at the top and bottom areequal to the temperatures as defined in the Initial phase; however, since the temperature


TUTORIAL MANUAL

Figure 15.14 Initial temperature distribution

at the ground surface is now defined in terms of Climate conditions (air temperature), thistemperature is also applied at the inner side of the lock and affects the temperaturedistribution in the ground.

Figure 15.15 Steady-state temperature distribution in Phase_1

The most interesting results are obtained in Phase_2 in which the air temperature in theClimate condition increases gradually from 283 K to 298 K (defined by a quarter of aharmonic cycle with an amplitude of 15K). Figure 15.16 shows the temperature at theground surface as a function of time.



Figure 15.16 Temperature distribution in Point A as a function of time

As a result of the short increase in temperature at the inside of the concrete block, whilethe outer side (soil side) remains 'cold', the wall will bend towards the soil. Figure 15.17shows the deformed mesh at the end of Phase_2. As a result of this backward bending,the lateral stresses in the soil right behind the concrete block will increase, tendingtowards a passive stress state (Figure 15.18). Note that the visualisation is different forFigure 15.18, because it displays the stresses in the porous materials. This can bechanged in the Settings window under the tab Results (Section 8.5.2 of the ReferenceManual).

Figure 15.17 Deformed mesh at the end of Phase_2


TUTORIAL MANUAL

Figure 15.18 Effective principal stresses at the end of Phase_2


FREEZE PIPES IN TUNNEL CONSTRUCTION

16 FREEZE PIPES IN TUNNEL CONSTRUCTION

This tutorial illustrates change in coupling of groundwater flow and thermal flow as aresult of ground freezing. A tunnel is constructed with the use of freeze pipes. By firstinstalling freeze pipes in the soil, the soil freezes and becomes watertight so that tunnelconstruction can take place. This method of construction requires a lot of energy for thecooling of the soil, so by being able to model the cooling behaviour while groundwaterflow is present an optimal freezing system can be designed.

In this tutorial a tunnel with a radius of 3.0 m will be constructed in a 30 m deep soil layer(Figure 16.1). A groundwater flow from left to right is present, influencing the thermalbehaviour of the soil. First the soil will be subjected to the low temperatures of the freezepipes, and once the soil has frozen sufficiently, tunnel construction can take place. Thelatter is not included in this tutorial.

Because groundwater flow causes an asymmetric temperature distribution, the wholegeometry needs to be modelled, where in previous examples only half of the geometrywas sufficient.

Objectives:

• Modelling soil freezing, coupling between thermal flow and groundwater flow

• Modelling unfrozen water content.

• Using the command line for structure definition.

Figure 16.1 Input geometry

16.1 INPUT

General settings

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


• In the Model tabsheet, the default options for Model and Elements are used for thisproject. Also the default options for the units are used in this tutorial. Note that theunit of Mass is set automatically to tonnes.

• Set the model dimensions to xmin = 0.0 m, xmax = 85.0 m, ymin = -30.0 m and ymax =


TUTORIAL MANUAL

0.0 m.

• In the Constants tabsheet, set Twater and Tref to 283 K , other constants keep theirdefault values. A description of constants can be found in the Reference Manual.Click Ok to exit the Project properties window.



• Create a single soil layer with top level at 0.0 m and bottom level at -30.0 m. Set thehead at ground level (0.0 m).

Click the Materials button in the Modify soil layers window.

• Define a data set for soil with the parameters given in Table 16.1, for the General,Parameters and Groundwater tabsheets.

Table 16.1 Soil properties of the sand

Parameter Name Sand Unit

General

Material model Model Mohr-Coulomb -


Soil unit weight above phreatic level γunsat 18.0 kN/m3

Soil unit weight below phreatic level γsat 18.0 kN/m3

Initial void ratio einit 0.5 -

Parameters

Young’s modulus E' 1·105 kN/m2

Poisson’s ratio ν 0.3 -

Cohesion cref ' 0.0 kN/m2

Angle of internal friction φ' 37.0 ◦

Dilatancy angle ψ 0.0 ◦

Groundwater

Data set - Standard -

Type - Medium -

Horizontal permeability kx 1.00 m/day

Vertical permeability ky 1.00 m/day

Change of permeability ck 1.0·1015 -

Thermal

Specific heat capacity cs 860 kJ/t/K

Thermal conductivity λs 4.0·10−3 kW/m/K

Soil density ρs 2.6 t/m3

X-component of thermal expansion αx 5.0·10−6 1/K

Y-component of thermal expansion αy 5.0·10−6 1/K

Z-component of thermal expansion αz 5.0·10−6 1/K

Unfrozen water content - Table 16.2 -

Interfaces

Interface strength - Rigid -

Thermal resistance R 0 m2K/kW

Initial

K0 determination - Automatic -

To model the amount of (fluid) water available to flow through the soil at certaintemperatures, a curve for unfrozen water content needs to be determined by defining atable with values for unfrozen water content at certain temperatures. The same curve canbe applied in other projects, hence the table can be saved and loaded into the soil



properties of other projects. For more information, refer Section 6.1.4 of the ReferenceManual.

• Click the Thermal tab. Enter the values as given in the Table 16.1.

• Click the checkbox for the option Unfrozen water content at the bottom of thetabsheet.

Add rows to the table by clicking the Add row button to introduce a new row in thetable. Complete the data using the values given in the Table 16.2.

• Enter the values for Interfaces and Initial tabsheets as given in Table 16.1.

• Click OK to close the dataset.

• Assign the material dataset to the soil layer.

Hint: The table can be saved by clicking the Save button in the table. The file mustbe given an appropriate name. For convenience, save the file in the samefolder as the project is saved.

Table 16.2 Input for unfrozen water content curve for sand

# Temperature [K] Unfrozen water content [-]

1 273.0 1.00

2 272.0 0.99

3 271.6 0.96

4 271.4 0.90

5 271.3 0.81

6 271.0 0.38

7 270.8 0.15

8 270.6 0.06

9 270.2 0.02

10 269.5 0.00


The freeze pipes are modelled by defining lines with a length similar to the freeze pipediameter (10 cm), containing a convective boundary condition. For simplicity, in thistutorial only 12 cooling elements are defined, while in reality more elements may beimplemented in order to achieve a sufficient share of frozen soil.

• Proceed to Structures mode.


• Click the command line and type "line 45.141 -13.475 45.228 -13.425". Press<Enter> to create the first freezing pipe. For more information regarding commandline, see Section 3.6 of the Reference Manual.

• Similarly create the remaining freeze pipes according to Table 16.3.

Multi select the created lines using the Select lines from the side toolbar.

Right click the selected lines and select Thermal flow BC to create the thermal flowboundary conditions for the freeze pipes.


TUTORIAL MANUAL

Hint: A file containing the commands for the definition of the lines, is available inthe PLAXIS knowledgebase(http://kb.plaxis.nl/search/site/LineCoordinatesCommands.txt). This canbe downloaded and copied in the Commands runner, to get the pipes.

• For the selected freeze pipes, in the Selection explorer expand the subtree for theThermalFlowBC.

• The Behaviour is set to Convection, the Tfluid to 250 K and the Transfer coefficientto 1.0 kW/m2/K.

Table 16.3 Coordinates of the end points of the freezing pipes, modelled as lines

Line number Xpoint1 Ypoint1 Xpoint2 Ypoint2

1 45.141 -13.475 45.228 -13.425

2 44.025 -12.359 44.075 -12.272

3 42.500 -11.950 42.500 -11.850

4 40.975 -12.359 40.925 -12.272

5 39.859 -13.475 39.772 -13.425

6 39.450 -15.000 39.350 -15.000

7 39.859 -16.525 39.772 -16.575

8 40.975 -17.641 40.925 -17.728

9 42.500 -18.050 42.500 -18.150

10 44.025 -17.641 44.075 -17.728

11 45.141 -16.525 45.228 -16.575

12 45.550 -15.000 45.650 -15.000


Figure 16.2 The Create thermal and groundwater flow bc option in the Create line menu

Select the Create thermal flow BC option in the expanded menu. In the draw areacreate a thermal boundary condition from (0.0 0.0) to (85.0 0.0) (Figure 16.2).

Click the Create line button in the side toolbar, select the Create groundwater flowBC option in the expanded menu. In the draw area create a groundwater flowboundary condition from (0.0 0.0) to (85.0 0.0) (Figure 16.2).



• Similarly follow the above steps to create thermal and groundwater flow boundaryfor the following lines (85.0 0.0) to (85.0 -30.0); (85.0 -30.0) to (0.0 -30.0) and finally(0.0 -30.0) to (0.0 0.0).

PLAXIS allows different types of Thermal boundary conditions to be applied. In thistutorial the freeze pipes will be modelled as convective boundary conditions.

• Multi select the created boundaries.

• For the ThermalFlowBC, set the Behaviour to Temperature and Tref to 283 K.

To assign the groundwater boundary conditions, the following steps are followed:

• Multi select the top and bottom boundary.

• For the GWFlowBC, set the Behaviour to Closed.

• Select the left boundary, set the Behaviour to Inflow with a qref value of 0.1 m/day.

• The right boundary has the default behaviour of Seepage.

The tunnel is created with the help of the Tunnel designer. Because deformations are notconsidered in this calculation, there is no need to assign a plate material to the tunnel.The generated tunnel will only be used for generating a more dense and homogeneousmesh around the freezing pipes. The tunnel will not be activated during any calculationphase, but PLAXIS will detect the line elements and will generate the mesh according tothese elements. Changing the coarseness factor of the pipe elements will cause adenser, but not a more homogeneous mesh.

• Click the Create tunnel button in the side toolbar and click on (42.5 -18) in the drawarea.

• The option Circular is selected for Shape type. Note that the default option is Free.

• The default option of Define whole tunnel is used in this example.

• Proceed to the Segments tab and set Radius to 3.0 m to the two multi selectedsegments.

• Click on Generate to generate the defined tunnel in the model. Close the Tunneldesigner window.

The geometry of the model is shown in Figure 16.3.



TUTORIAL MANUAL



Click the Generate mesh button. The default element distribution of Medium is usedfor this example.




16.3 CALCULATIONS

The calculations for this tutorial are carried out in the Flow only mode.

Initial phase

• Proceed to Staged construction mode.

• Double click on Initial phase in the Phases explorer.

• In the Phases window select the Flow only option from the Calculation typedrop-down menu.

• Choose the Earth gradient option for the Thermal calculation type.

• In the Staged construction activate the ThermalFlow under the Model conditionssubtree and set the value for Tref to 283 K, href to 0 m and 0 K/m for the Earthgradient.

Phase 1

Add a new phase.

• Double click the new phase in the Phases explorer.

• In the Phases window, enter an appropriate name for the phase ID (For eg:"Transient calculation").

Set Transient groundwater flow as the option for the Pore pressure calculation type.

Set Transient thermal flow as the option for the Thermal calculation type.

• Set Time interval to 180 days and the Max number of steps stored to 100. This is tobe able to view intermediate time steps after the calculation.




• In Staged construction mode, activate all the thermal boundary conditions byclicking the check box for the Thermal flow BCs in the Model explorer.

• In the Model explorer, activate the four groundwater flow boundary conditionscorresponding to the left, top, right and bottom boundary conditions in theGroundwater flow BCs subtree.

• In the Model explorer, deactivate the ThermalFlow condition under the Modelconditions subtree.

The calculation definition is now complete. Before starting the calculation it is suggestedthat you select nodes or stress points for a later generation of curves.

Click the Select points for curves button in the side toolbar. Select somecharacteristic points for curves (for example between two freezing pipes).



16.4 RESULTS

Interesting results from this calculation can be the point in time when there is nogroundwater flow in between two freezing pipes, groundwater flow over the whole modeland temperature distribution for both steady state and transient calculations.

To view the results in the Output program:

Click the View calculation results button on the toolbar.

• From the Stresses menu, select Heat flow → Temperature.

• Figure 16.6 shows the spatial distribution of the temperature for transient calculationin the final step.

• From the Stresses menu, select Groundwater flow → |q|.Select the Arrows option in the View menu or click the corresponding button in thetoolbar to display the results arrows.

In the Output program, it is possible to view the results for the intermediate saved steps.


TUTORIAL MANUAL

Figure 16.6 Temperature distribution for transient phase

More information is available in Section 8.4.9 of the Reference Manual. It is possible toview the progression of the freezing of the tunnel.

• Figure 16.7 shows the distribution of the of groundwater flow field for anintermediate step for the transient calculation (around 80 days).

• Figure 16.8 shows the groundwater flow field for the last time step for the transientflow calculation. Here it is clearly noticeable that the entire tunnel area is frozen andno flow occurs.

Figure 16.7 Groundwater flow field for transient phase for an intermediate step (t ≈ 38 days)

Figure 16.8 Groundwater flow field after 180 days


APPENDIX A - MENU TREE


A.1 INPUT MENUIN

PU

TM

EN

U1

File

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