Tutorial Lesson2 2D

PLAXIS 2D - SUBMERGED CONSTRUCTION OF AN EXCAVATION

3 SUBMERGED CONSTRUCTION OF AN EXCAVATION

This lesson illustrates the use of PLAXIS for the analysis of submergedconstruction of an excavation. Most of the program features that were used inLesson 1 will be utilised here again. In addition, some new features will beused, such as the use of interfaces and anchor elements, the generation ofwater pressures and the use of multiple calculation phases. The new featureswill be described in full detail, whereas the features that were treated inLesson 1 will be described in less detail. Therefore it is suggested thatLesson 1 should be completed before attempting this exercise.

This lesson concerns the construction of an excavation close to a river. Theexcavation is carried out in order to construct a tunnel by the installation ofprefabricated tunnel segments. The excavation is 30 m wide and the finaldepth is 20 m. It extends in longitudinal direction for a large distance, so thata plane strain model is applicable. The sides of the excavation are supportedby 30 m long diaphragm walls, which are braced by horizontal struts at aninterval of 5.0 m. Along the excavation a surface load is taken into account.The load is applied from 2 meter from the diaphragm wall up to 7 meter fromthe wall and has a magnitude of 5 kN/m2/m (Figure 3.1).

The subsoil consists of a stiff sand layer, which extends to a large depth. 50m of this sand layer are considered in the model.

Since the geometry is symmetric, only one half (the left side) is considered inthe analysis. The excavation process is simulated in three separateexcavation stages. The diaphragm wall is modelled by means of a plate, suchas used for the footing in the previous lesson. The interaction between thewall and the soil is modelled at both sides by means of interfaces. Theinterfaces allow for the specification of a reduced wall friction compared to thefriction in the soil. The strut is modelled as a spring element for which thenormal stiffness is a required input parameter.

Objectives:

• Modelling soil-structure interaction using the Interface feature.

• Advanced soil model (Hardening Soil model).

• Defining Fixed-end-anchor.

PLAXIS Introductory 2010 | Tutorial Manual 43

TUTORIAL MANUAL

x

y

43 m43 m 5 m5 m 2 m2 m 30 m

1 m

19 m

10 m

20 m

Sand

Diaphragm wall

to be excavated

Strut

5 kN/m2/m5 kN/m2/m

Figure 3.1 Geometry model of the situation of a submerged excavation

• Creating and assigning material data sets for anchors.

• Refining mesh around lines.

• Simulation of excavation (cluster de-activation).

3.1 INPUT

To create the geometry model, follow these steps:

General settings

• Start the Input program and select Start a new project from the Quickselect dialog box.

• In the Project tabsheet of the Project properties window, enter anappropriate title and make sure that Model is set to Plane strain and thatElements is set to 15-Node.

• Keep the default units and set the model dimensions to Xmin = 0.0 m,

44 Tutorial Manual | PLAXIS Introductory 2010


Xmax = 65.0 m, Ymin = -30.0 m and Ymax = 20.0 m. Keep the defaultvalues for the grid spacing (Spacing = 1 m; Number of intervals = 1).

Geometry contour, layers and structures

To define the geometry contour:

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

To define the diaphragm wall:

Click the Plate button in the toolbar. Move the cursor to position (50.0;20.0) at the upper horizontal line and click. Move 30 m down (50.0;-10.0) and click. Click the right mouse button to finish the drawing.

To define the excavation levels:

• Select the Geometry line button again. Move the cursor to position(50.0; 18.0) at the wall and click. Move the cursor 15 m to the right (65.0;18.0) and click again. Click the right mouse button to finish drawing thefirst excavation stage. Now move the cursor to position (50.0; 10.0) andclick. Move to (65.0; 10.0) and click again. Click the right mouse buttonto finish drawing the second excavation stage. In the same way, definethe third excavation stage by drawing a line between (50.0; 0.0) and(65.0; 0.0).

To define interfaces:

Click the Interface button on the toolbar or select the Interface optionfrom the Geometry menu. The shape of the cursor will change into across with an arrow in each quadrant. The arrows indicate the side atwhich the interface will be generated when the cursor is moved in acertain direction.

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


TUTORIAL MANUAL

Hint: Within the geometry input mode it is not strictly necessary toselect the buttons in the toolbar in the order that they appearfrom left to right. In this case, it is more convenient to create thewall first and then enter the separation of the excavation stagesby means of a Geometry line.» When creating a point very close to a line, the point is usuallysnapped onto the line, because the mesh generator cannothandle non-coincident points and lines at a very small distance.This procedure also simplifies the input of points that areintended to lie exactly on an existing line.» If the pointer is substantially mispositioned and instead ofsnapping onto an existing point or line a new isolated point iscreated, this point may be dragged (and snapped) onto theexisting point or line by using the Selection button.» In general, only one point can exist at a certain coordinate andonly one line can exist between two points. Coinciding points orlines will automatically be reduced to single points or lines. Theprocedure to drag points onto existing points may be used toeliminate redundant points (and lines).

Hint: In general, it is a good habit to extend interfaces around cornersof structures to allow for sufficient freedom of deformation and toobtain a more accurate stress distribution. When doing so, makesure that the strength of the extended part of the interface isequal to the soil strength and that the interface does notinfluence the flow field, if applicable. The latter can be achievedby switching off the extended part of the interface beforeperforming a groundwater flow analysis.

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



side of the wall. Move back to (50.0; 20.0) and click again. Click the rightmouse button to finish drawing.

Hint: Interfaces are indicated as dotted lines along a geometry line. Inorder to identify interfaces at either side of a geometry line, apositive sign (⊕) or negative sign () is added. This sign has nophysical relevance or influence on the results.

To define the strut:

Click the Fixed-end anchor button in the toolbar or select thecorresponding option from the Geometry menu. Move the cursor to aposition 1 metre below point 6 (50.0; 19.0) and click the left mousebutton. The Fixed-end-anchor window pops up (Figure 3.2).

Figure 3.2 Fixed-end anchor window

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

To define the surface load:

Click the Distributed load - load system A button.

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

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


TUTORIAL MANUAL

Hint: A fixed-end anchor is represented by a rotated T with a fixedsize. This object is actually a spring of which one end isconnected to the mesh and the other end is fixed. Theorientation angle and the equivalent length of the anchor must bedirectly entered in the properties window. The equivalent lengthis the distance between the connection point and the position inthe direction of the anchor rod where the displacement is zero.By default, the equivalent length is 1.0 unit and the angle is zerodegrees (i.e. the anchor points in the positive x-direction).» Clicking the 'middle bar' of the corresponding T selects anexisting fixed-end anchor.

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

Boundary Conditions

To create the boundary conditions, click the Standard fixities button onthe toolbar. As a result, the program will generate full fixities at thebottom and vertical rollers at the vertical sides. These boundaryconditions are in this case appropriate to model the conditions ofsymmetry at the right hand boundary (center line of the excavation). Thegeometry model so far is shown in Figure 3.3.

Material properties

After the input of boundary conditions, the material properties of the soilclusters and other geometry objects are entered in data sets. Interfaceproperties are included in the data sets for soil (Data sets for Soil andinterfaces). In addition to the soil data set for the sand layer, a data set of thePlate type is created for the diaphragm wall and a data set of the Anchor typeis created for the strut. To create the material data sets, follow these steps:

Click the Material sets button on the toolbar. Select Soil and interfacesas the Set type. Click the New button to create a new data set.

• Enter "Sand" for the Identification and select Hardening soil as the



Figure 3.3 Geometry model in the Input window

Material model.

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

• Click the Interfaces tab. Select the Manual option in the Strengthdrop-down menu. Enter a value of 0.67 for the parameter Rinter . Thisparameter relates the strength of the soil to the strength in the interfaces,according to the equations:

tanϕinterface = Rinter tanϕsoil and cinter = Rinter csoil

where:csoil = cref (see Table 3.1)

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

• Close the data set.

• Drag the 'Sand' data set to each of the four clusters of the geometry anddrop it there.

• Set the Set type parameter in the Material sets window to Plates and


TUTORIAL MANUAL

Table 3.1 Material properties of the sand layer and the interfaces

Parameter Name Sand Unit

General

Material model Model Hardening soil -

Type of material behaviour Type Drained -

Soil unit weight above phreatic level γunsat 17 kN/m3

Soil unit weight below phreatic level γsat 20 kN/m3

Parameters

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) c'ref 0.0 kN/m2

Friction angle ϕ' 32 ◦

Dilatancy angle ψ 2.0 ◦

Poisson's ratio νur ' 0.2 -

Flow parameters

Permeability in horizontal direction kx 1.0 m/day

Permeability in vertical direction ky 1.0 m/day

Interfaces

Interface strength − Manual -

Strength reduction factor inter. Rinter 0.67 -

Initial

K0 determination − Automatic -

Over-consolidation ratio OCR 1.0 -

Pre-overburden ratio POP 0.0 -



Hint: Due to the limitations of the Introductory version, it is notpossible to make a separate material data set for the extendedinterface part below the wall.

Hint: Instead of accepting the default data sets of interfaces, data setscan directly be assigned to interfaces in their properties window.This window appears after double clicking the correspondinggeometry line and selecting the appropriate interface from theSelect dialog box. On clicking the Change button behind theMaterial set parameter, the proper data set can be selected fromthe Material sets tree view.

Hint: A Virtual thickness factor can be defined for interfaces. This is apurely numerical value, which can be used to optimise thenumerical performance of the interface. To define it, double clickthe structure and select the option corresponding to the interfacefrom the appearing window. The Interface window pops upwhere this value can be defined. Non-experienced users areadvised not to change the default value. For more informationabout interface properties see the Reference Manual.

Hint: When the Rigid option is selected in the Strength drop-down, theinterface has the same strength properties as the soil(Rinter = 1.0).

click the New button. Enter "Diaphragm wall" as an Identification of thedata set and enter the properties as given in Table 3.2. Click OK toclose the data set.

• Drag the Diaphragm wall data set to the wall in the geometry and drop it


TUTORIAL MANUAL

as soon as the cursor indicates that dropping is possible.

Table 3.2 Material properties of the diaphragm wall (Plate)

Parameter Name Value Unit

Type of behaviour Material type Elastic

Normal stiffness EA 7.5 · 106 kN/m

Flexural rigidity EI 1.0 · 106 kNm2/m

Unit weight w 10.0 kN/m/m

Poisson's ratio ν 0.0 -

• Set the Set type parameter in the Material sets window to Anchors andclick New. Enter "Strut" as an Identification of the data set and enter theproperties as given in Table 3.3. Click the OK button to close the dataset.

• Drag the Strut data set to the anchor in the geometry and drop it as soonas the cursor indicates that dropping is possible. Close the Material setswindow.

Table 3.3 Material properties of the strut (anchor)

Parameter Name Value Unit

Type of behaviour Material type Elastic -

Normal stiffness EA 2·106 kN

Spacing out of plane Lspacing 5.0 m

Mesh Generation

In this lesson a local mesh refinement procedure is used. Starting from aglobal coarse mesh, there are simple possibilities for local refinement within acluster, on a line or around a point. These options are available from theMesh menu. In order to generate the proposed mesh, follow these steps:

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

• Multi-select all the wall elements by keeping the <Shift> key pressedwhile clicking on each of them.

• From the Mesh menu, select the Refine line option. The resulting meshis displayed.



Click the Close button to return to the Input program.

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

Hint: The mesh settings are stored together with the rest of the input.On re-entering an existing project and not changing thegeometry configuration and mesh settings, the same mesh canbe regenerated by just clicking the Generate mesh button on thetoolbar. However, any slight change of the geometry will result ina different mesh.

Figure 3.4 Resulting mesh


TUTORIAL MANUAL

3.2 CALCULATIONS

In practice, the construction of an excavation is a process that can consist ofseveral phases. First, the wall is installed to the desired depth. Then someexcavation is carried out to create space to install an anchor or a strut. Thenthe soil is gradually removed to the final depth of the excavation. Specialmeasures are usually taken to keep the water out of the excavation. Propsmay also be provided to support the retaining wall.

In PLAXIS, these processes can be simulated with the Staged constructioncalculation option. Staged construction enables the activation or deactivationof weight, stiffness and strength of selected components of the finite elementmodel. The current lesson explains the use of this powerful calculation optionfor the simulation of excavations.

Click the Calculations tab. The calculation process for this example will beperformed in the Classical mode.

Phase 0: Initial phase

The initial conditions of the current project require the generation of waterpressures, the deactivation of structures and loads and the generation ofinitial stresses. Water pressures (pore pressures and water pressures onexternal boundaries) can be generated in two different ways: A directgeneration based on the input of phreatic levels and groundwater heads or anindirect generation based on the results of a groundwater flow calculation.The current lesson only deals with the direct generation procedure.Generation based on groundwater flow is only available in the Professionalversion.

Within the direct generation option there are several ways to prescribe thewater conditions. The simplest way is to define a general phreatic level, underwhich the water pressure distribution is hydrostatic, based on the input of aunit water weight. The general phreatic level is automatically assigned to allclusters for the generation of pore pressures. It is also used to generateexternal water pressures, if applicable. Instead of the general phreatic level,individual clusters may have a separate phreatic level or an interpolated porepressure distribution. Here only a general phreatic level is defined at 2.0 mbelow the ground surface.



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

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

• In the Parameters tabsheet, click the Define button to enter the Stagedconstruction mode.

• In the Water conditions mode the General water level is generated at thebottom of the geometry.

Click the Phreatic level button. Move the cursor to position (0; 18.0) andclick the left mouse button. Move to the right (65; 18.0) and click again.Click the right mouse button to finish drawing. The plot now indicates anew General phreatic level 2.0 m below the ground surface.

The Generate by phreatic level option is selected in the drop-down menuat the left of the Water pressures button.

Click the Water pressures button to generate the water pressures. Thepressure distribution is displayed in the Output program.

Click the Close button to go to the Input program.

Hint: The water weight can be modified after selecting the Wateroption in the Geometry menu of the Input program opened forStaged construction.

• Make sure that the structural elements (structures, interfaces and loads)are not active in the Staged construction mode. The programautomatically deactivates them for the initial phase.

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

Phase 1: External load

• Click Next to add a new phase.

• In the General tabsheet, accept all defaults.


TUTORIAL MANUAL

Hint: An existing water level may be modified by using the Selectionbutton. On deleting the General phreatic level (selecting it andpressing the <Delete> key on the keyboard), the default generalphreatic level will be created again at the bottom of the geometry.The graphical input or modification of water levels does not affectthe existing geometry.» To create an accurate pore pressure distribution in the geometry,an additional geometry line can be included corresponding withthe level of the groundwater head or the position of the phreaticlevel in a project.

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

• In the Staged construction mode the full geometry is active except for thewall, strut and load. Click the wall to activate it (the wall should becomeblue).

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

• Make sure all the interfaces in the model are active. In the Waterconditions mode note that the interfaces below the wall are not activated(not indicated by the orange colour). This is correct because there is noimpermeability below the wall.

Hint: The selection of an interface is done by selecting thecorresponding geometry line and subsequently selecting thecorresponding interface (positive or negative) from the Selectdialog box.

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



Hint: You can also enter or change the values of the load at this timeby double clicking the load and entering a value. If a load isapplied on a structural object such as a plate, load values can bechanged by clicking the load or the object. As a result a windowappears in which you can select the load. Then click the Changebutton to modify the load values.

Phase 2: First excavation stage


• A new calculation phase appears in the list. Note that the programautomatically presumes that the current phase should start from theprevious one.

• In the General tabsheet, accept all defaults. Enter the Parameterstabsheet and click Define.

• In the Staged construction mode all the structure elements except thefixed end anchor are active. Click the top right cluster in order todeactivate it and simulate the first excavation step.

• Click the Update button to finish the definition of the first excavationphase.

Phase 3: Installation of strut


• In the Parameters tabsheet click Define.

• In the Staged construction mode activate the strut by clicking thehorizontal line. The strut should turn black to indicate it is active.

• Click Update to return to the calculation program and define anothercalculation phase.

Phase 4: Second (submerged) excavation stage



TUTORIAL MANUAL

• Keep all default settings and enter the Input program. This phase willsimulate the excavation of the second part of the building pit. In theStaged construction mode deactivate the second and third clusters fromthe top on the right side of the mesh. It should be the two topmost activeclusters.

• Click Update to return to the Calculations program.

Hint: Note that in PLAXIS the pore pressures are not automaticallydeactivated when deactivating a soil cluster. Hence, in this case,the water remains in the excavated area and a submergedexcavation is simulated.

Hint: In the Professional version, the excavation of the building pit inthe last calculation phase is done in two separate calculationphases as the number of calculation phases is not limited.

The calculation definition is now complete. Before starting the calculation it issuggested that you select nodes or stress points for a later generation ofload-displacement curves or stress and strain diagrams. To do this, follow thesteps given below.

Click the Select points for curves button on the toolbar. The connectivityplot is displayed in the Output program and the Select points window isactivated.

• Select some nodes on the wall at points where large deflections can beexpected (e.g. 50.0; 10.0). The nodes located near that specific locationare listed. Select the convenient one by checking the box in front of it inthe list. Close the Select points window.

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

Calculate the project.

During a Staged construction calculation, a multiplier called ΣMstage is



increased from 0.0 to 1.0. This parameter is displayed on the calculation infowindow. As soon as ΣMstage has reached the value 1.0, the constructionstage is completed and the calculation phase is finished. If a Stagedconstruction calculation finishes while ΣMstage is smaller than 1.0, theprogram will give a warning message. The most likely reason for not finishinga construction stage is that a failure mechanism has occurred, but there canbe other causes as well. See the Reference Manual for more informationabout Staged construction.

In this example, all calculation phases should successfully finish, which isindicated by the green check marks in the list. In order to check the values ofthe ΣMstage multiplier, click the Multipliers tab and select the Reachedvalues radio button. The ΣMstage parameter is displayed at the bottom ofthe Other box that pops up. Verify that this value is equal to 1.0. You alsomight wish to do the same for the other calculation phases.

3.3 RESULTS

In addition to the displacements and the stresses in the soil, the Outputprogram can be used to view the forces in structural objects. To examine theresults of this project, follow these steps:

• Click the final calculation phase in the Calculations window.

Click the View calculation results button on the toolbar. As a result, theOutput program is started, showing the deformed mesh (scaled up) atthe end of the selected calculation phase, with an indication of themaximum displacement (Figure 3.5).

Hint: In the Output program, the display of the loads, fixities andprescribed displacements applied in the model can be toggledon/off by clicking the corresponding options in the Geometrymenu.

• Select |∆u| from the side menu displayed as the mouse pointer islocated on the Incremental displacements option of the Deformations


TUTORIAL MANUAL

Figure 3.5 Deformed mesh after submerged excavation

menu. The plot shows colour shadings of the displacement increments.

Click the Arrows button in the toolbar. The plot shows the displacementincrements of all nodes as arrows. The length of the arrows indicates therelative magnitude.

• In the Stresses menu point to the Principal effective stresses and selectthe Effective principal stresses option from the appearing menu. Theplot shows the average effective principal stresses at the center of eachsoil element with an indication of their direction and their relativemagnitude. Note that the Central principal stresses button is selected inthe toolbar. The orientation of the principal stresses indicates a largepassive zone under the bottom of the excavation and a small passivezone behind the strut (Figure 3.6).

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

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

• Select the bending moment M from the Forces menu. The bendingmoment in the wall is displayed with an indication of the maximummoment (Figure 3.7).



Figure 3.6 Principal stresses after excavation

Figure 3.7 Bending moments in the wall

• Select Shear forces Q from the Forces menu. The plot now shows theshear forces in the wall.

• Select the first window (showing the effective stresses in the fullgeometry) from the Window menu. Double-click the strut. The strutforce (in kN/m) is shown in the displayed table. This value must be


TUTORIAL MANUAL

Hint: The Window menu may be used to switch between the windowwith the forces in the wall and the stresses in the full geometry.This menu may also be used to Tile or Cascade the twowindows, which is a common option in a Windows environment.

multiplied by the out of plane spacing of the struts to calculate theindividual strut forces (in kN).

• Click the Curves manager button on the toolbar. As a result, the Curvesmanager window 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 treeselect Deformations - Total displacements - |u|.

• For the y-axis keep the Project option in the drop-down menu. In thetree select Multiplier - ΣMstage.

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

Figure 3.8 Load-displacement curve of deflection of wall



The curve shows the construction stages. For each stage, the parameterΣMstage changes from 0.0 to 1.0. The decreasing slope of the curve in thelast stage indicates that the amount of plastic deformation is increasing. Theresults of the calculation indicate, however, that the excavation remains stableat the end of construction.


TUTORIAL MANUAL


Documents

Tutorial Lesson2 2D