example applications : 14 : dewatered construction of a...

Dewatered Construction of a Braced Excavation 14 - 1

14 Dewatered Construction of a Braced Excavation

14.1 Problem Statement

A braced excavation is constructed in saturated ground. The excavation is dewatered during con-struction and is supported by diaphragm walls that are braced at the top by horizontal struts. Thepurpose of the FLAC analysis is to evaluate (1) the deformation of the ground adjacent to the wallsand at the bottom of the excavation, and (2) the performance of the walls and struts, throughout theconstruction stages. The analysis starts from the stage after the walls have been constructed, butprior to any excavation. Dewatering, excavation and installation of struts are simulated in separateconstruction stages. In addition, two different material models, the Mohr-Coulomb model and theCysoil model, are used to represent the behavior of the soils and demonstrate the difference indeformational response produced by these models when subjected to this construction sequence.

In practice, the construction may involve several stages of dewatering, excavation and adding ofsupport. For simplicity, in this example, only three construction stages are analyzed: (1) dewateringto a 20 m depth in the region to be excavated; (2) excavation to a 2 m depth; and (3) installationof a horizontal strut and excavation to a 10 m depth. Additional excavation stages can readily beincorporated in the FLAC analysis, as required.

Figure 14.1 shows the geometry for this example. The excavation is 20 m wide and the final depthis 10 m. The diaphragm walls extend to a 30 m depth and are braced at the top by horizontal strutsat a 2 m interval. The ground consists of two soil layers: a 20 m thick soft clay underlain by a stiffsand layer that extends to a great depth. The initial water table is at the ground surface.

Figure 14.1 Geometry for braced excavation example

FLAC Version 6.0

14 - 2 Example Applications

The properties selected in this example to simulate the behavior of the diaphragm wall and the strutsare listed in Tables 14.1 and 14.2. The thickness of the diaphragm wall varies, and an equivalentthickness is estimated to be 1.26 m. Note that for the two-dimensional FLAC analysis, the Young’smodulus of the wall should be divided by (1 − ν2) to convert the plane-stress formulation for thestructural elements to the plane-strain condition of a continuous wall. Thus, a value of 5.95 GPa isinput to FLAC for the wall elastic modulus.

The strut properties are listed in Table 14.2. The spacing of the struts is 2 m. A simple way tosimulate the three-dimensional effect of the strut spacing in the FLAC model is with linear scalingof the material properties of the struts by dividing by the strut spacing. (See Section 1.9.4 inStructural Elements.) For this example, by using elastic beam elements, it is only necessary toscale the elastic modulus and the density of the struts. This is done in FLAC automatically whenthe parameter spacing is specified.

The soil/wall interface is relatively smooth. The interface friction angle is 12.5◦ and the interfacecohesion is 2500 Pa.

The hydraulic conductivity of the soils is assumed to be a constant value of 10−6 m/sec (whichcorresponds to approximately 10−10 m2/(Pa-sec) for the mobility coefficient).

Table 14.1 Properties of the diaphragm wall

Equivalent thickness (m) 1.26Density (kg/m3) 2000Young’s modulus (GPa) 5.712Poisson’s ratio 0.2Moment of inertia (m4) 0.167

Table 14.2 Properties of the strut

Cross-sectional area (m2) 1.0Spacing (m) 2.0Density (kg/m3) 3000Young’s modulus (GPa) 4.0Moment of inertia (m4) 0.083

FLAC Version 6.0


14.1.1 Deformational Behavior of the Soils

The deformation of the soils during excavation is of particular interest in this example, specificallythe heave at the bottom of the excavation and the surface settlement adjacent to the excavationwall. Two different material models, the Mohr-Coulomb model and the Cysoil model, are used toillustrate the effect of the material model on the calculated deformational response of the soil. It isnoted that for uniform elastic properties, the linear elastic/perfectly plastic Mohr-Coulomb modelmay predict unrealistically large deformations in soils subjected to loading and unloading, such asheave induced at the bottom of excavations. A more realistic calculation may be obtained with thenonlinear elastic/plastic Cysoil model.

The Mohr-Coulomb properties chosen for this example are similar to those in Example 4 of thePlaxis Tutorial manual (2002), and the Cysoil properties are derived from properties for the PlaxisHardening Soil model described in Section 10.7 of the Plaxis Material Models manual (2002). Theproperties for the Mohr-Coulomb model and the Hardening Soil model in the Plaxis manual weredeveloped for the same soil types (clay and sand).

The Mohr-Coulomb properties are adapted from Table 4.1 of the Plaxis Tutorial manual (2002).The drained material properties associated with the sand and clay are summarized in Table 14.3.For this exercise, the cohesion property is set to zero.

The Plaxis Hardening Soil properties (adapted from Table 10.12 of the Plaxis Material Modelsmanual, 2002) are listed in Table 14.4. Note in Table 14.4, that the cohesion property is set to zero,and the power m to one, for this exercise.

The formulation of the Cysoil model has components in common with the Plaxis Hardening Soilmodel. See Section 2.4.9 in Theory and Background for a description of the Cysoil model. Aconnection, as shown in Table 14.5, is proposed between hardening Cysoil properties and PlaxisHardening Soil properties. Note, however, that among other things, differences exist in the hard-ening and dilatancy laws. (See the Plaxis Material Models manual for a description.) Thus, themodel responses should not be expected to be identical.

Table 14.3 Mohr-Coulomb drained properties for sand and clay layers*

Sand layer Clay layer

Dry density (kg/m3) 1700 1600Young’s modulus (MPa) 40.0 10.0Poisson’s ratio 0.3 0.35Cohesion (Pa) 0 0Friction angle (degrees) 32 25Dilation angle (degrees) 2 0Porosity 0.3 0.3

* adapted from Table 4.1 of the Plaxis Tutorial manual (2002)

FLAC Version 6.0


Table 14.4 Plaxis Hardening Soil properties*

Hardening-Soil Property Sand layer Clay layer

Dry density (kg/m3) 1700 1600pref (MPa) 0.1 0.1Erefur (MPa) 90 24

Erefoed (MPa) 30 4

Poisson’s ratio, νur 0.2 0.2Cohesion 0 0Friction angle (degrees) 32 25Dilation angle (degrees) 2 0Power, m 1 1Knc

0 0.5 0.5Failure ratio, Rf 0.9 0.9

* adapted from Table 10.12 of the Plaxis Material Models manual (2002)

Table 14.5 Relation between Cysoil and Plaxis Hardening Soil properties

Plaxis Hardening-Soil Hardening Cysoil

Eref

50 –

Erefur Geref = E

refur

2(1+νur )Erefoed Kiso

ref = Erefoed

– R = Erefur

3(1−2νur )Eref

oed

− 1

Cohesion, C zero

Friction angle, φ φf

Dilation angle, ψ ψf

Poisson’s ratio, νur νur

Power, m idem

Knc0 (using cap) K0

Tensile strength zero

Failure ratio, Rf idem

FLAC Version 6.0


The following procedure is used to develop properties for the Cysoil model in this example. TheCysoil model can represent the nonlinear stress/strain response for loading and unloading that ischaracteristic of soils. In this example, the model is supplemented by a friction/strain-hardeningtable and a cap-hardening table to produce a hardening Cysoil stress/strain function comparable tothe Hardening Soil model of Plaxis.

1. Table 14.5 is used to derive the hardening Cysoil properties shown in Table 14.6. TheFISH function ‘SETUP.FIS” listed in Section 14.6.1 performs the derivation of Cysoilproperties from the Hardening Soil properties. Note that the cap-yield surface parameter,α, is set to one.*

The soils are assumed to be normally consolidated. Accordingly, initial (mobilized)friction is calculated from the known K0 using the equation

sin φm = 1 −K0

1 +K0(14.1)

Table 14.6 Hardening Cysoil properties

Sand layer Clay layer

Dry density, ρ (kg/m3) 1700 1600Cap-yield surface parameter, α 1.0 1.0Ultimate friction angle, φf (degrees) 32 25Ultimate dilation angle, ψf (degrees) 2 0Multiplier, R 1.667 3.333Geref (MPa) 37.5 10.0Kisoref (MPa) 30.0 4.0

Reference pressure, pref (MPa) 0.1 0.1Poisson’s ratio, νur 0.2 0.2Cohesion, C 0 0Power, m 1 1Knc

0 0.5 0.5Initial mobilized friction angle, φm (degrees) 19.47 19.47Failure ratio, Rf 0.9 0.9

2. The Cysoil properties,Ke andGe, are stress-dependent, and these properties are specifiedafter the initial pre-excavation stress state is established. The “ININV.FIS” FISH function(see Section 3 in the FISH volume) is used to initialize pore pressures and stressesautomatically from the known K0, and for the initial water level at the ground surface.

* The value of α = 1 was found to provide the best fit when the Cysoil model was compared to theHardening Soil model in a benchmark exercise (see Section 18).

FLAC Version 6.0


Initial (current) shear and bulk modulus distributions are then assigned, according toEqs. (2.261) and (2.244) in Theory and Background, from the initial effective stressesand layer properties. The FISH functionini stiff, listed in Section 14.6.2, calculatesthe initial distributions of Ge and Ke in the model. Note that the maximum shear andbulk moduli, G and K , are also calculated in this FISH function, and are arbitrarily setto 20 times Ge and Ke, respectively.

3. The friction hardening table is now generated for the sand and the clay using Eq. (2.264)in Theory and Background. The FISH function “FRIC TABLE.FIS,” listed in Sec-tion 14.6.3, creates the friction hardening tables: table 1 is the friction hardening tablefor sand, and table 2 is the hardening table for clay.

4. An initial plastic strain consistent with the initial friction, φm, is calculated. Eq. (2.264)in Theory and Background is used to calculate the initial plastic strain for both sandand clay. The FISH function “GAMMAP.FIS,” listed in Section 14.6.4, performs thiscalculation to set the Cysoil property es plastic.

5. The Cysoil property pc is also stress-dependent. It is assumed that the clay and sandare normally consolidated on the cap. The initial effective stress is used to calculate theinitial values for p′ and q, and the initial value for pc is then derived from the cap yieldfunction, Eq. (2.249) in Theory and Background. The cap pressure is calculated inFISH function “INI CAP.FIS,” listed in Section 14.6.5.

6. A cap table is calculated for the clay and sand using Eq. (2.257) in Theory and Back-ground. This is performed in FISH function “CAP TABLE.FIS,” listed in Section 14.6.6.The function assumes a maximum effective pressure (estimated to be 10 MPa) for thesimulation. This ensures that the appropriate range of pressure values is covered by thecap pressure table. Table 3 is the cap table for sand, and table 4 is the cap table for clay.

7. The value of plastic volumetric strain, consistent with the initial value of pc, is calculatedin FISH function “ EVP0.FIS,” listed in Section 14.6.7, using Eq. (2.257) in Theory andBackground.

8. Constant dilation properties are specified for clay and sand.

FLAC Version 6.0


14.2 Modeling Procedure

A recommended procedure to simulate this type of problem with FLAC is illustrated by performingthe analysis in six steps:

Step 1: Generate the model grid, and assign material models, material properties andboundary conditions to represent the physical system.

Step 2: Determine the initial in-situ stress state of the ground prior to construction.

Step 3: Determine the initial in-situ stress state of the ground with the diaphragm wallinstalled.

Step 4: Lower the water level within the region to be excavated to a depth of 20 mbelow the ground surface.

Step 5: Excavate to a depth of 2 m.

Step 6: Install the horizontal struts at the top of the wall, and then excavate to a depthof 10 m.

The model is created using the GIIC, FLAC ’s graphical interface. Upon entering the GIIC, thegroundwater flow option, the adjust total stress option*, structural elements and advanced consti-tutive models are activated from the Model Options dialog. The SI system of units is also selectedfor this example. The dialog is shown in Figure 14.2.

We set up a project file to save the model state at various stages of the simulation. We click on ?

in the Project File (*.prj) dialog to select a directory in which to save the project file. We assigna title to our project and save the project as “EXCAVATE.PRJ.” (Note that the “.PRJ” extensionis assigned automatically.) This project file contains the project tree, and allows direct access toall the save (“.SAV”) files that we will create for the different stages of the analysis. We can stopworking on the project at any stage, save it and re-open it at a later time simply by opening theproject file (from the File / Open Project menu item); the entire project and associated save fileswill be accessible in the GIIC.

A record of the FLAC commands used to create this model can also be saved separately usingthe File / Export Record menu item. A listing of the record created for this model is given inSection 14.5.

* The automatic adjustment of total stresses for external pore-pressure change is selected because wewill use this facility for the dewatering stage. See Section 1.9.7 in Fluid-Mechanical Interaction.

FLAC Version 6.0


Figure 14.2 Model options selected for braced excavation example

14.2.1 Model Generation

We begin the analysis by building the model grid using the Build tool in the one-step (simplegrid) generation mode. The braced excavation is a common form of retaining structure used ingeotechnical engineering. We can find this type of geometry in the grid library available from theBuild / Generate / Library tool. We click on the “Retaining wall, 2 interfaces” library item to access thisgrid type. The grid library dialog for this tool is shown in Figure 14.3.

We click OK to begin manipulating this grid to fit our problem geometry. Note that it is onlynecessary to consider half of the problem region shown in Figure 14.1 because of the symmetricgeometry. The grid corners are selected to correspond to the right half of the excavation, withthe axes origin at the centerline of the excavation. The automatic zoning option is selected, and45 zones are specified in the horizontal direction in the Zoning Options dialog. This producesa uniform mesh density with a zone size of 1 m. By using this library item, the wall is createdautomatically as a set of beam elements, connected to the grid on both sides by interfaces. Notethat the boundary conditions (roller boundaries on the sides and pinned boundary at the bottom)can also be selected in this tool by checking the Automatic boundary cond.? box. The FLAC commandsare automatically generated to create this grid when the Execute button is pressed. The grid createdfor the braced excavation example is shown in Figure 14.4. The figure also shows the location ofthe wall beams, and identifies the two interfaces by ID numbers 1 and 2.

FLAC Version 6.0


Figure 14.3 Grid library tool for retaining wall grid

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Figure 14.4 Grid created for braced excavation

FLAC Version 6.0


We can now assign material properties for the diaphram wall and the soil/wall interface. We needto specify the material properties for the diaphragm wall because the initial model grid includesthe structural elements representing the wall. We click on the Structure / SEProp tool, and then clickon one of the beam elements to open the Beam Element Properties dialog. The dialog is dividedinto two panes, as shown in Figures 14.5 and Figure 14.6. We enter the area, Young’s modulusand moment of inertia from Table 14.1. (The area is 1.26 m2 because the two-dimensional modelassumes a 1 m dimension out of the analysis plane.) We do not assign the density of the wall at thisstage because we will first calculate the equilibrium stress state before the wall is constructed; thisis done by neglecting the weight of the wall.

Figure 14.5 Beam properties assigned for the diaphragm wall– mechanical properties

Figure 14.6 Beam properties assigned for the diaphragm wall– geometric properties

FLAC Version 6.0


The soil/wall interface properties are prescribed using the Alter / Interface tool. We click on theProperty radio button in this pane and then click on the circled number at one end of the interfacehighlighted in the model plot. An Interface Properties dialog will appear, as shown in Figure 14.7.We select the Unbonded button and then enter the interface properties.

Figure 14.7 Interface material properties dialog

It is usually reasonable to select the interface normal- and shear-stiffness properties such that thestiffness is approximately ten times the equivalent stiffness of the stiffest neighboring zone. Bydoing this, the deformability at the interface will have minimal influence on both the compliance ofthe total model and the calculation speed. The equivalent stiffness of a zone normal to the interfaceis

max

[(K + 4

3G)

�zmin

](14.2)

where:K & G are the bulk and shear moduli, respectively; and�zmin is the smallest width of an adjoining zone in the normal direction.

The max [ ] notation indicates that the maximum value over all zones adjacent to the interface isto be used (e.g., there may be several materials adjoining the interface).

In this example, the smallest grid width adjacent to the interface is 1 m, and the maximum equivalentstiffness is approximately 55 MPa. Therefore, we select a representative value of 550 MPa/m forthe normal and shear stiffnesses.

The groundwater properties porosity and permeability are assigned in the Material / GWProp tool. Weclick on the SetAll button to open the Model Groundwater properties dialog to enter these properties.

FLAC Version 6.0


Note that the “permeability” required by FLAC is actually the mobility coefficient (i.e., the coefficientof the pore pressure term in Darcy’s law – see Section 1.7.1 in Fluid-Mechanical Interaction).When we click OK , these properties are assigned to all zones in the model.

We specify gravity using the Settings / Gravity tool. We select a gravitational magnitude of 10.0 m/sec2

to simplify this example. We also assign the water density at this point using the Settings / GW tool.We set the water density to 1000 kg/m3.

We save the model state at this stage by clicking on the Save button at the bottom of the Recordpane. We name the saved state “EXC GRID.SAV”; a new “branch” with this name appears in theproject tree shown in the Record pane. See Figure 14.8. Note that the commands associated withthis branch have now been grayed out. If we find we have made a mistake or wish to modify thesecommands, we can press the Edit button at the bottom of this pane. We can then edit the commandsin this pane and re-execute them in FLAC by pressing the Rebuild button at the bottom of the pane.The state must be saved again if modifications are made.

Figure 14.8 Project tree at completion of step 1

FLAC Version 6.0


14.2.2 Soil Material Model Assignment

Two parallel branches are created in the project to evaluate the behavior of the soils. In the firstbranch, the clay and sand are defined as Mohr-Coulomb materials; in the second, the soils aredefined as Cysoil materials.

We create the first branch by continuing from save state “EXC GRID.SAV.” We can enter Mohr-Coulomb properties either by using the Material / Assign tool or the Material / Model tool. For this example,we use the Material / Model tool because the Cysoil model properties can only be entered with this tool.We select the Mohr-Coulomb material model from the models list, assign a group name “sand mc,”select the rectangular range and drag the mouse over the bottom half of the model grid. The Mohr-Coulomb properties dialog opens, as shown in Figure 14.9. We enter the properties for sand fromTable 14.3. We repeat this procedure for the clay properties with the group name “clay mc,” andthen press Execute to send these commands to FLAC.

Figure 14.9 Mohr-Coulomb properties dialog with sand properties

Before saving the state with Mohr-Coulomb materials, the static equilibrium is specified for theinitial pre-excavation stress state with the water table at the ground surface. The pore pressure andtotal (and effective) stress distributions must be compatible at the initial state. This is accomplishedby using the FISH function “ININV.FIS” provided in the FISH library. (See Section 3 in the FISHvolume.) We call in this FISH function from the FISH library by clicking on the Utility / FishLib tool.We click on the Library/Groundwater/ininv menu item in the FISH/Library dialog, and press OK .This opens the FISH Call Input dialog, as shown in Figure 14.10. We enter the phreatic surfaceheight (wth = 40) and the Ko ratios (k0x = 0.5 and k0z = 0.5) in the dialog, and press OK . The FISHfunction will then be called into FLAC and executed. The pore pressure distribution and total stressadjustment are calculated automatically. After the pore pressure distribution is calculated, we usethe In Situ / Fix tool to fix the pore pressures along the top and side boundaries, and saturation alongthe top boundary, to satisfy the flow conditions. The initial pore pressure distribution is shown inFigure 14.11.

FLAC Version 6.0


Figure 14.10 FISH library function “ININV.FIS” – input dialog

FLAC (Version 6.00)

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1.000

2.000

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Figure 14.11 Initial pore pressure distribution – Mohr-Coulomb material

The state of the model with Mohr-Coulomb material, and at the initial stress state prior to construc-tion, is saved as “EXC MC01.SAV.”

In order to create the second branch with Cysoil properties, we double-click the left mouse buttonon the branch named “EXC GRID.SAV” in order to move back to the state before the materialmodel is assigned. Now we re-enter the Material / Model tool. This time we select the Cysoil materialand follow the same procedure previously used to enter properties for the Mohr-Coulomb model,

FLAC Version 6.0


but now for a “sand cy” group and a “clay cy” group. The Model cysoil properties dialog opens,as shown in Figure 14.12.

The Cysoil properties given in Table 14.6 are input in this dialog. Note that when this dialog isexecuted, the second branch is automatically created in the project tree.

In addition to the Cysoil properties shown in Figure 14.12, it is also necessary to specify thestress-dependent properties and hardening table functions. These are applied as FISH functions,as described in Section 14.1.1. The “SETUP.FIS” FISH function is executed first to derive Cysoil-related properties based on Hardening Soil properties. This function can be opened and executedfrom the FISH editor, which is accessed from the Fish tab in the Resource pane. Figure 14.13displays the FISH editor with “SETUP.FIS” loaded for execution.

The initial in-situ stress state is determined using “ININV.FIS” in the same way as for the Mohr-Coulomb material described above. The stress-dependent properties and hardening table functionscan now be prescribed using the remaining FISH functions, “INI STIFF.FIS,” “FRIC TABLE.FIS,”“GAMMAP.FIS,” “INI CAP.FIS,” “CAP TABLE.FIS” and “ EVP0.FIS.” These are loaded andexecuted in the same manner as “SETUP.FIS.”

The model with Cysoil material and the initial stress state specified is saved as “EXC01CY.SAV.”Figure 14.14 shows the project tree at this stage.

Figure 14.12 Cysoil properties dialog with sand properties

FLAC Version 6.0


Figure 14.13 “SETUP.FIS” function loaded into FISH editor

Figure 14.14 Project tree at completion of step 2 showing the Mohr-Coulombmaterial branch and Cysoil material branch

FLAC Version 6.0


14.2.3 Install Diaphragm Wall

The next stage of the analysis is the installation of the diaphragm wall. This is simulated by addingthe weight of the wall in the model. We begin at “EXC01MC.SAV” for the Mohr-Coulomb material,and include the weight of the wall by specifying a mass density for the beam elements. We use theStructure / SEProp tool to enter the density in the Beam Elements Properties dialog. We also turn offthe flow mode and ensure that the water bulk modulus is zero because we do not wish to generatepore pressures during this stage. We press Run / Solve again to find the equilibrium state with thewall weight included. We save this state as “EXC02MC.SAV.” Figure 14.15 shows the total verticalstress distribution at this stage.

The same procedure is repeated for the Cysoil material beginning at “EXC01CY.SAV.” The totalvertical stress distribution at equilibrium for this stage is shown in Figure 14.16. There is a slightdifference in stress distribution around the wall in the Cysoil material compared to the wall in Mohr-Coulomb material. This can be attributed to the difference between the stress-dependent stiffnessproperties of the Cysoil material and the constant, uniform stiffness properties of the interfacesadjacent to the wall. Although the difference is minor, a stress-dependent variation of interfacestiffnesses could be applied using FISH in order to provide a closer representation. The equilibriumstate for Cysoil material with the wall in place is saved as “EXC02CY.SAV.”

14.2.4 Dewater to a Depth of 20 m

For the dewatering stage, we assume, for simplicity, that the water level is dropped instantaneouslywithin the excavation region.* We start from “EXC02MC.SAV” and set the saturation and porepressure to zero using the In Situ / Initial tool. We click on the GP Info/Groundwater/saturationmenu item and drag the mouse over the gridpoints within the dewatered region (0 ≤ x ≤ 10,20 ≤ y ≤ 40). The affected gridpoints will be highlighted. We click on Assign to open the dialogto specify a zero saturation value for these gridpoints. We click OK to create this command, thenclick on the GP Info/Groundwater/pp menu item and press Assign . A dialog will open to assign azero pore pressure to the same region. Figure 14.17 shows the In Situ / Initial tool with the affectedregion selected from 0 ≤ x ≤ 10, 20 ≤ y ≤ 40.

The saturation and pore pressure are also fixed at zero in the dewatered region. This is accomplishedwith the In Situ / Fix tool. The mouse is dragged over the affected gridpoints, with the fixed saturationmode selected, and then with the fixed pore-pressure mode selected. Figure 14.18 shows the toolwith the affected region highlighted.

The total stress is adjusted automatically when we impose this change in the pore pressures. Thisis a result of selecting the Adjust Tot. Stress box in the Model Options dialog. We can check thatthis adjustment to total stress has been made by plotting effective stresses before and after thesecommands are issued: the effective stresses are unchanged in the model when the instantaneouspore-pressure change is imposed.

* For a more realistic solution, FLAC can calculate the gradual lowering of the phreatic surface andchange of the stress state, due to pumping.

FLAC Version 6.0


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Figure 14.15 Total vertical stress contours for initial saturated statewith weight of wall included – Mohr-Coulomb material

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Figure 14.16 Total vertical stress contours for initial saturated statewith weight of wall included – Cysoil material

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Figure 14.17 In Situ/Initial tool with saturation and pore pressure set to zero indewatered region

Figure 14.18 In Situ/Fix tool with saturation and pore pressure fixed in dewa-tered region

FLAC Version 6.0


We can now solve for the coupled response that results from the dewatering. In the Settings / GW

tool, we set groundwater flow on, and set the water bulk modulus to 10,000 Pa. We need tospecify the water bulk modulus for this calculation, so we specify this low value in order to speedconvergence to steady-state flow. We can do this because we are not interested in the transientbehavior. (Note that there is a lower limit for the water bulk modulus to satisfy numerical stability– see Section 1.4.2.1 in Fluid-Mechanical Interaction.) This is an unsaturated flow analysis, sowe can also use the fast-unsaturated flow scheme to speed the calculation to steady state. (SeeSection 1.4.1 in Fluid-Mechanical Interaction.) We check the <funsat>Fast unsaturated flow calculation?

box to turn on this scheme.

We free the saturation condition for gridpoints along the top boundary outside the excavation. Theregion near the ground surface can now become unsaturated if the water level drops. We also freethe fixed pore-pressure condition along the left boundary below the excavation so that pore pressurescan change during dewatering. We initialize the displacements in the model to zero so that we canmonitor the displacement change that occurs due only to the dewatering. Press the Displmt & Velocity

button in the In Situ / Initial tool to initialize displacements and velocities. Then click on Run/Solve tosolve for the equilibrium state with dewatering.

The steady-state pore pressure distribution after dewatering is shown in Figure 14.19. Figure 14.20plots the displacement vectors at equilibrium. This indicates the amount of settlement inducedby the dewatering: approximately 8 cm. We save the model state as “EXC03MC.SAV” for theMohr-Coulomb material.

We repeat this dewatering procedure for the Cysoil material. The final pore pressure distribution isnearly identical to that for the Mohr-Coulomb material, as shown in Figure 14.19. The displacementsinduced by dewatering, however, are greater (approximately 25 cm), as shown in Figure 14.21. Themodel with Cysoil material is saved at this stage as “EXC03CY.SAV.”

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27-Mar-08 8:36 step 7971Flow Time 1.1033E+09 -4.167E+00 <x< 4.917E+01 -6.667E+00 <y< 4.667E+01

Pore pressure contours 0.00E+00 5.00E+04 1.00E+05 1.50E+05 2.00E+05 2.50E+05 3.00E+05 3.50E+05 4.00E+05


0 1E 1 0.000

1.000

2.000

3.000

4.000

(*10^1)

0.500 1.500 2.500 3.500 4.500(*10^1)

JOB TITLE : .


Figure 14.19 Pore pressure distribution following dewatering– Mohr-Coulomb material

FLAC (Version 6.00)

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Displacement vectorsscaled to max = 2.000E-01max vector = 8.143E-02

0 5E -1

Boundary plot

0 1E 1

0.000

1.000

2.000

3.000

4.000

(*10^1)

0.500 1.500 2.500 3.500 4.500(*10^1)

JOB TITLE : .


Figure 14.20 Displacements induced by dewatering– Mohr-Coulomb material

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0 5E -1

Boundary plot

0 1E 1

0.000

1.000

2.000

3.000

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(*10^1)

0.500 1.500 2.500 3.500 4.500(*10^1)

JOB TITLE : .


Figure 14.21 Displacements induced by dewatering– Cysoil material

14.2.5 Excavate to 2 m Depth

We are now ready to begin the excavation. We start from “EXC03MC.SAV,” set flow off, andset the water bulk modulus to zero for this mechanical-only calculation. We again initialize thedisplacements, using the Displmt & Velocity button, in order to evaluate the deformation induced by theexcavation.

We use the MaterialAssign tool to perform the excavation. We excavate by assigning the null modelto the material to be removed. We click on the zones in the region 0 ≤ x ≤ 10, 38 ≤ y ≤ 40.These zones are then removed from the model plot, and the corresponding MODEL null commandsare created for sending to FLAC. See Figure 14.22.

We press Run/Solve to calculate the equilibrium state with this first excavation. This is the long-termresponse (with water bulk modulus set to zero). We save this state as “EXC04MC.SAV.”

The displacements induced by this excavation are illustrated in Figure 14.23. A maximum heaveof roughly 4.3 cm occurs at the bottom of the excavation. We can also calculate the response ofthe wall. For example, the moment distribution in the wall after the first excavation is shown inFigure 14.25. Note that various results for the wall response (e.g., wall displacements, axial forces,shear forces) can be plotted using the Plot items dialog in the Plot/Model tool.

FLAC Version 6.0


This step is now repeated with Cysoil material starting from “EXC03CY.SAV.” The displacementsinduced by this excavation stage are plotted in Figure 14.24, and indicate a maximum heave ofroughly 1.8 cm. The moment distribution for this case is plotted in Figure 14.26; the maximumvalue is approximately 1.3 times that for the wall in Mohr-Coulomb material.

Figure 14.22 Excavated zones in the MaterialAssign tool

FLAC Version 6.0


FLAC (Version 6.00)

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0 1E -1

Y-displacement contours 1.00E-02 2.00E-02 3.00E-02 4.00E-02

Contour interval= 1.00E-02(zero contour omitted)Boundary plot

0 1E 1 0.000

1.000

2.000

3.000

4.000

(*10^1)

0.500 1.500 2.500 3.500 4.500(*10^1)

JOB TITLE : .


Figure 14.23 Displacements induced by excavation to 2 m depth –Mohr-Coulomb material

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0 1E -1

Y-displacement contours -1.00E-02 -5.00E-03 5.00E-03 1.00E-02 1.50E-02

Contour interval= 5.00E-03(zero contour omitted)Boundary plot

0 1E 1

0.000

1.000

2.000

3.000

4.000

(*10^1)

0.500 1.500 2.500 3.500 4.500(*10^1)

JOB TITLE : .


Figure 14.24 Displacements induced by excavation to 2 m depth – Cysoil ma-terial

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Boundary plot

0 1E 1

Beam Plot

Moment onStructure Max. Value# 1 (Beam ) 3.850E+05Beam Plot

0.000

1.000

2.000

3.000

4.000

(*10^1)

0.500 1.500 2.500 3.500 4.500(*10^1)

JOB TITLE : .


Figure 14.25 Moment distribution in wall after excavation to 2 m depth – Mohr-Coulomb material

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Boundary plot

0 1E 1

Beam Plot

Moment onStructure Max. Value# 1 (Beam ) -5.185E+05Beam Plot

0.000

1.000

2.000

3.000

4.000

(*10^1)

0.500 1.500 2.500 3.500 4.500(*10^1)

JOB TITLE : .


Figure 14.26 Moment distribution in wall after excavation to 2 m depth – Cysoilmaterial

FLAC Version 6.0


14.2.6 Install Strut and Excavate to 10 m Depth

For the final excavation step, we install a horizontal strut at the top of the wall and then excavate toa 10 m depth. We use the StructureBeam tool to install the strut. We press the Add radio button in theModes menu, then move the mouse on the model view to one end position of the strut, and hold theleft button and move the mouse to the other end position. A line indicating the location of the strutwill be drawn. We can position the strut more precisely by right-clicking the mouse over each endlocation. A dialog opens and we enter the endpoint coordinates. Note that the left node is free. Weposition the right node at the same location as the top node of the wall, and consequently, the rightnode is slaved to the existing node of the wall.* Figure 14.27 shows the position of the strut in theStructureBeam tool.

Figure 14.27 Positioning the horizontal strut using the StructureBeam tool

The strut is not rigidly connected to the wall in this exercise. We define a pin connection (whichpermits free rotation at the strut/wall connection) by selecting the Pin radio button in the Modes listand clicking the mouse over the connecting node. An arrow is drawn at the node, denoting this asa pin connection (see Figure 14.28).

* When the mouse is positioned to create a new node at the same location as an existing node, the newnode is automatically slaved to the existing node. If two separate (non-slaved) nodes are requiredat the same position, first offset the mouse slightly to create the new node, and then reposition thenew node at the same location as the existing node, using the Move mode.

FLAC Version 6.0


Figure 14.28 Selecting a pin connection in the StructureBeam tool

We also prescribe a different material property number to the strut in the Beam tool so that we canassign the strut properties. We click on the PropID radio button in the Modes list, and the identificationnumber B1 appears over the beam elements in the model plot. We click on the strut element, and adialog opens to allow us to rename the property ID to B2.

We now press Execute to send these commands to FLAC to create the strut, pin the strut to the wall,and assign the property number. Two nodes (32 and 33) are created, connected as a single beamelement, and assigned property number 1002. A pin connection is defined between node 33 andwall node 2.

We enter the Structure / Node tool to assign fixity conditions for the strut. Node 1531 is located alongthe centerline of the excavation. We click on this node to open a Node: 32 dialog, as shown inFigure 14.29. We fix this node from movement in the x-direction, and from rotating (which areappropriate conditions for a node located along a line of symmetry), by clicking on the X-velocity

and Rotation check boxes in the dialog. We click OK and then Execute to send the node conditioncommands to FLAC.

FLAC Version 6.0


Figure 14.29 Node 32 dialog in the StructureNode tool

We assign the strut properties using the Structure/SEProp tool. We click on the strut element in thistool and open the Beam Element Properties dialog (as we did previously for the wall properties) toenter the strut properties as listed in Table 14.2.

We are now ready to perform the second excavation step. We use the MaterialAssign tool and change thezones within the range 0 ≤ x ≤ 10, 30 ≤ y ≤ 38 to null material. We press Run / Solve to calculatethe equilibrium state with this second excavation. We save this state as “EXC05MC.SAV.”

The total displacements induced by the excavation to the 10 m depth is illustrated in Figure 14.30;the moment distribution in the wall and axial force in the strut are shown in Figure 14.32.

This stage is repeated for Cysoil material. The total displacements are plotted in Figure 14.31for comparison to the Mohr-Coulomb material. The maximum displacement at the bottom of theexcavation is less than half that for the Mohr-Coulomb material. Also, the extent of the excavation-induced displacement is more confined than that for the Mohr-Coulomb material; compare they-displacement contour plot in Figure 14.31 to that in Figure 14.30.

The wall moments and strut load for Cysoil material are plotted in Figure 14.33. The values areroughly the same as those for Mohr-Coulomb material.

The surface settlement behind the wall for the Cysoil material is roughly the same as that for theMohr-Coulomb material. This can be seen in the surface settlement profiles plotted in Figure 14.34.

FLAC Version 6.0


FLAC (Version 6.00)

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0 5E -1

Y-displacement contours -6.00E-02 -3.00E-02 3.00E-02 6.00E-02 9.00E-02 1.20E-01 1.50E-01 1.80E-01

Contour interval= 3.00E-02(zero contour omitted)

0.000

1.000

2.000

3.000

4.000

(*10^1)

0.500 1.500 2.500 3.500 4.500(*10^1)

JOB TITLE : .


Figure 14.30 Displacements induced by excavation to 10 m depth – Mohr-Coulomb material

FLAC (Version 6.00)

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0 5E -1

Y-displacement contours -9.00E-02 -6.00E-02 -3.00E-02 3.00E-02 6.00E-02

Contour interval= 3.00E-02(zero contour omitted)

0.000

1.000

2.000

3.000

4.000

(*10^1)

0.500 1.500 2.500 3.500 4.500(*10^1)

JOB TITLE : .


Figure 14.31 Displacements induced by excavation to 10 m depth – Cysoil ma-terial

FLAC Version 6.0


FLAC (Version 6.00)

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Boundary plot

0 1E 1

Beam Plot


Axial Force onStructure Max. Value# 2 (Beam ) 1.028E+06

0.000

1.000

2.000

3.000

4.000

(*10^1)

0.500 1.500 2.500 3.500 4.500(*10^1)

JOB TITLE : .


Figure 14.32 Moment distribution in wall and axial force in strut after exca-vation to 10 m depth – Mohr-Coulomb material

FLAC (Version 6.00)

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Boundary plot

0 1E 1

Beam Plot


Axial Force onStructure Max. Value# 2 (Beam ) 9.757E+05

0.000

1.000

2.000

3.000

4.000

(*10^1)

0.500 1.500 2.500 3.500 4.500(*10^1)

JOB TITLE : .


Figure 14.33 Moment distribution in wall and axial force in strut after exca-vation to 10 m depth – Cysoil material

FLAC Version 6.0


FLAC (Version 6.00)

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27-Mar-08 8:24 step 0 Table PlotCysoil

Mohr-Coulomb

15 20 25 30 35 40 45

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

(10 )-01

JOB TITLE : .


Figure 14.34 Surface settlement profiles

14.3 Observations

This example illustrates the effect of the material model on soil deformational response for unloadingproblems such as the construction on a braced excavation. The heave that occurs at the bottomof the excavation is considerably greater for the construction in Mohr-Coulomb material than it isfor Cysoil material. This is primarily attributed to the stress-dependent elastic moduli and stifferunloading response of the Cysoil material. This is evident from the comparison of the displacementcontour plots in Figure 14.30 for the Mohr-Coulomb material, and Figure 14.31 for the Cysoilmaterial.

This model example was derived for comparison to the excavation example with Mohr-Coulombmaterial and Hardening Soil material given in the Plaxis Material Models Manual (2002). Aqualitative agreement with those results is shown here. Also, see Section 18 for a comparisonbetween the Cysoil model and the Hardening Soil model in a field benchmark study.

14.4 References

Plaxis BV. PLAXIS Version 8, Material Models Manual. R.B.J. Brinkgreve (ed.). Delft: Plaxis,2002.

Plaxis BV. PLAXIS Version 8, Tutorial Manual. R.B.J. Brinkgreve (ed.). Delft: Plaxis, 2002.

FLAC Version 6.0


14.5 Data File “EXCAVATE.DAT”

;Project Record Tree export;Title:Braced Excavation

;*** BRANCH: TWO TESTS ****new;... STATE: EXC GRID ....config gwflow atsgrid 46,40gen 0.0,0.0 0.0,10.0 10.0,10.0 10.0,0.0 i=1,11 j=1,11gen 10.0,0.0 10.0,10.0 45.0,10.0 45.0,0.0 i=12,47 j=1,11gen 0.0,10.0 0.0,40.0 10.0,40.0 10.0,10.0 i=1,11 j=11,41gen 10.0,10.0 10.0,40.0 45.0,40.0 45.0,10.0 i=12,47 j=11,41model el i=1,10 j=1,10model el i=12,46 j=1,10model el i=1,10 j=11,40model el i=12,46 j=11,40; Attach gridsattach aside from 11,1 to 11,11 bside from 12,1 to 12,11; Beam-interfacesstruct node 1 (10.0,10.0)struct node 2 (10.0,40.0)struct beam begin node 1 end node 2 prop 1001 seg 30interface 1 aside from 11,11 to 11,41 bside from node 1 to node 2interface 2 aside from 12,11 to 12,41 bside from node 2 to node 1struct prop 1001; Fixed boundary conditionsfix x i=1 j=1,11fix x y i=1,11 j=1fix x i=47 j=1,11fix x y i=12,47 j=1fix x i=1 j=11,41fix x i=47 j=11,41struct prop 1001 e 5.95E9 area 1.26 I 0.167interface 1 unglued kn=5.5E8 ks=5.5E8 cohesion=2500.0 dilation=0.0 &friction=12.5 tbond=0.0 bslip=Off

interface 2 unglued kn=5.5E8 ks=5.5E8 cohesion=2500.0 dilation=0.0 &friction=12.5 tbond=0.0 bslip=Off

prop por=0.3 perm=1.0E-10 notnullset gravity=10.0water density=1000.0save exc grid.sav

;*** BRANCH: MOHR-COULOMB ****;... STATE: EXC01MC ....

FLAC Version 6.0


;group ’sand mc’ notnull j 1 20model mohr group ’sand mc’prop density=1700.0 bulk=3.33333E7 shear=1.53846E7 cohesion=1000.0 &tension=0.0 friction=32.0 dilation=2.0 group ’sand mc’group ’clay mc’ notnull j 21 40model mohr group ’clay mc’prop density=1600.0 bulk=1.11111E7 shear=3703700.0 cohesion=5000.0 &tension=0.0 friction=25.0 dilation=0.0 group ’clay mc’set echo offcall Ininv.fisset wth=40 k0x=.5 k0z=.5ininvfix pp i 1fix pp i 47fix pp j 41fix saturation j 41save exc01mc.sav;... STATE: EXC02MC ....;initial xdisp 0 ydisp 0initial xvel 0 yvel 0struct prop 1001 density 2000.0set flow=offwater bulk=0.0hist 999 unbalsolvesave exc02mc.sav;... STATE: EXC03MC ....;initial xdisp 0 ydisp 0initial xvel 0 yvel 0initial saturation 0.0 i 1 11 j 21 41initial pp 0.0 i 1 11 j 21 41fix saturation i 1 11 j 21 41fix pp i 1 11 j 21 41free pp i 1 j 1 20free pp i 13 47 j 41set flow=onwater bulk=10000.0set funsat=onhistory 1 gpp i=4, j=17history 2 gpp i=17, j=17history 3 gpp i=28, j=37history 4 gwtimesolve

FLAC Version 6.0


save exc03mc.sav;... STATE: EXC04MC ....;set flow=offwater bulk=0.0initial xdisp 0 ydisp 0initial xvel 0 yvel 0model null i 1 10 j 39 40group ’null’ i 1 10 j 39 40group delete ’null’solvesave exc04mc.sav;... STATE: EXC05MC ....;model null i 1 10 j 31 38group ’null’ i 1 10 j 31 38group delete ’null’struct node 32 0.0,40.0struct node 33 10.0,40.0 pin slave x y 2struct beam begin node 32 end node 33 seg 1 prop 1001struct node 32 fix x rstruct prop 1002 density 3000.0 spacing 2.0 e 4E9 area 1.0 I 0.083struct chprop 1002 range 31 31solvesave exc05mc.sav;... STATE: EXC05MCTABLE ....set echo offcall settle.fisset id table=11settlementsave exc05mctable.sav

;*** BRANCH: CYSOIL ****restore exc grid.sav;... STATE: EXC01CY ....group ’sand cy’ notnull j 1 20model cysoil group ’sand cy’prop density=1700.0 bulk=3.333E7 shear=1.5385E7 dilation=2.0 frict=32.0 &alpha=1.0 multiplier=1.667 ftable=1 cptable=3 group ’sand cy’group ’clay cy’ notnull j 21 40model cysoil group ’clay cy’prop density=1700.0 bulk=1.111E7 shear=3703703.0 dilation=0.0 frict=25.0 &alpha=1.0 multiplier=3.333 ftable=2 cptable=4 group ’clay cy’call setup.fissetupset echo off

FLAC Version 6.0


call Ininv.fisset wth=40 k0x=.5 k0z=.5ininvcall ini stiff.fisini stiffcall fric table.fisset nt=1 num=200 gr=gr sand beta=beta sand fri=fri sandfric tablecall fric table.fisset nt=2 num=200 gr=gr clay beta=beta clay fri=fri clayfric tablecall gammap.fisset gr=gr sand beta=beta sand fri=fri sandgammapprop es plastic = gammap notnull group ’sand cy’set gr=gr clay beta=beta clay fri=fri claygammapprop es plastic = gammap notnull group ’clay cy’call evp0.fisevp0call cap table.fisset nt=3 num=250 em=m sand ki=ki sand mul=mul sandcap tableset nt=4 num=250 em=m clay ki=ki clay mul=mul claycap tablefix pp i 1fix pp i 47fix pp j 41fix saturation j 41save exc01cy.sav;... STATE: EXC02CY ....;initial xdisp 0 ydisp 0initial xvel 0 yvel 0struct prop 1001 density 2000.0set flow=offwater bulk=0.0hist 999 unbalsolvesave exc02cy.sav;... STATE: EXC03CY ....;initial xdisp 0 ydisp 0initial xvel 0 yvel 0initial saturation 0.0 i 1 11 j 21 41initial pp 0.0 i 1 11 j 21 41

FLAC Version 6.0


fix saturation i 1 11 j 21 41fix pp i 1 11 j 21 41free pp i 1 j 1 20free pp i 13 47 j 41set flow=onwater bulk=10000.0set funsat=onhistory 1 gpp i=4, j=17history 2 gpp i=17, j=17history 3 gpp i=28, j=37history 4 gwtimesolvesave exc03cy.sav;... STATE: EX04CY ....;set flow=offwater bulk=0.0initial xdisp 0 ydisp 0initial xvel 0 yvel 0model null i 1 10 j 39 40group ’null’ i 1 10 j 39 40group delete ’null’solvesave ex04cy.sav;... STATE: EXC05CY ....;model null i 1 10 j 31 38group ’null’ i 1 10 j 31 38group delete ’null’struct node 32 0.0,40.0struct node 33 10.0,40.0 pin slave x y 2struct beam begin node 32 end node 33 seg 1 prop 1001struct node 32 fix x rstruct prop 1002 density 3000.0 spacing 2.0 e 4E9 area 1.0 I 0.083struct chprop 1002 range 31 31solvesave exc05cy.sav;... STATE: EXC05CYTABLE ....set echo offcall settle.fisset id table=10settlementsave exc05cytable.sav

;*** BRANCH: COMPARE RESULTS ****new

FLAC Version 6.0


;... STATE: EXC COMPARE ....config gwflow atscall table10cy.datcall table11mc.datsave exc compare.sav

;*** plot commands ****;plot name: Unbalanced forceplot hold history 999;plot name: ppplot hold pp fill bound;plot name: syyplot hold syy fill bound;plot name: dispplot hold displacement max 0.2 ydisp fill zero bound;plot name: pp histplot hold history 1 line 2 line 3 line vs 4;plot name: esyyplot hold esyy fill;plot name: momplot hold bound struct beam moment 1 fill white struct beam axial 2 fill &gray

;plot name: settlementlabel table 10Cysoillabel table 11Mohr-Coulombplot hold table 10 line 11 line alias ’surface settlement’

FLAC Version 6.0


14.6 FISH Functions

14.6.1 “SETUP.FIS”

;Name: setup.fis;Purpose: derive cysoil properties from hardening soil propertiesdef setup

eur clay = 24e6eur sand = 90e6eoed clay = 4e6eoed sand = 30e6nu = 0.2fri clay = 25.fri sand = 32.m clay = 1.0m sand = 1.0beta clay = 1.0beta sand = 1.0rf = 0.9pa = 100e3k0 = 0.5al = 1.0pmax = 1e7 ; maximum effective pressure for cap tables

; --- derived quantities ---mul clay = eur clay/(3.*(1.-2.* nu)*eoed clay)mul sand = eur sand/(3.*(1.-2.* nu)*eoed sand)gr clay = eur clay/(2.*(1.+ nu))gr sand = eur sand/(2.*(1.+ nu))coek = 2.*(1.+ nu)/(3.*(1.-2.* nu))ki clay = eoed clay ;/(3.*(1.-2.* nu))ki sand = eoed sand ;/(3.*(1.-2.* nu))m clay = min(m clay,0.9)m sand = min(m sand,0.9)sinphi = (1.- k0)/(1.+ k0)phi0 = 180.0*atan(sqrt(sinphiˆ2/(1-sinphiˆ2)))/pibeta = beta claygr = gr claynum = 200fri = fri claynt = 1em = m clayki = ki claymul = mul clay

end

FLAC Version 6.0


14.6.2 “INI STIFF.FIS”

;Name: ini stiff.fis;Purpose: Initialize bulk and shear moduli for cysoil modeldef ini stiff

loop ii (1,izones)if ii # 11 then

; --- sand ---loop jj (1,20)

esyy = syy(ii,jj)+pp(ii,jj)esxx = sxx(ii,jj)+pp(ii,jj)qval = -( esyy- esxx)/ alpval = -( esyy+2.* esxx)/3.val = sqrt(qval*qval+pval*pval)/ paz prop(ii,jj,’shear current’)=gr sand*valz prop(ii,jj,’bulk current’)= coek*gr sand*valz prop(ii,jj,’shear’)=gr sand*val*20.z prop(ii,jj,’bulk’)= coek*gr sand*val*20.

end loop; --- clay ---

loop jj (21,40)esyy = syy(ii,jj)+pp(ii,jj)esxx = sxx(ii,jj)+pp(ii,jj)qval = -( esyy- esxx)/ alpval = -( esyy+2.* esxx)/3.val =sqrt(qval*qval+pval*pval)/ paz prop(ii,jj,’shear current’)=gr clay*valz prop(ii,jj,’bulk current’)= coek*gr clay*valz prop(ii,jj,’shear’)=gr clay*val*20.z prop(ii,jj,’bulk’)= coek*gr clay*val*20.

end loopend if

end loopend

FLAC Version 6.0


14.6.3 “FRIC TABLE.FIS”

;Name: fric table.fis;Purpose: generate friction table for cysoil model;Input: nt/integer/1/Friction table number;Input: num/integer/200/number of entries in Friction tabledef fric table

Gi = beta*( gr/ pa)loop ii (1, num+1)

phic = ( fri/float( num))*float(ii-1)sval = sin( phic*degrad)coe = sin( fri*degrad)/ rfxval = ( coe/(1.-sval/ coe)- coe)/ Giytable( nt,ii) = phicxtable( nt,ii) = xval

end loopytable( nt, num+2) = phicxtable( nt, num+2) = 0.2

end

FLAC Version 6.0


14.6.4 “GAMMAP.FIS”

;Name:gammap;Input: gr/string/gr sand/Gref;Input: beta/string/beta sand/Beta;Input: fri/string/fri sand/friction;Purpose: initialize es plastic from frictiondef gammapGi = beta*( gr/ pa)sval = sin( phi0*degrad)coe = sin( fri*degrad)/ Rfgammap = ( coe/(1.-sval/ coe)- coe)/ Giend

FLAC Version 6.0


14.6.5 “INI CAP.FIS”

;Name: ini cap.fis;Purpose: initialize cap pressure from normal consolidationdef ini caploop ii (1,izones)

if ii # 11 then; --- sand ---

loop jj (1,20)mul = mul sandesyy = syy(ii,jj)+pp(ii,jj)esxx = sxx(ii,jj)+pp(ii,jj)qval = -( esyy- esxx)/ alpval = -( esyy+2.* esxx)/3.pcval=sqrt(qval*qval+pval*pval)z prop(ii,jj,’cap pressure’)=pcval


loop jj (21,40)mul = mul clayesyy = syy(ii,jj)+pp(ii,jj)esxx = sxx(ii,jj)+pp(ii,jj)qval = -( esyy- esxx)/ alpval = -( esyy+2.* esxx)/3.pcval=sqrt(qval*qval+pval*pval)z prop(ii,jj,’cap pressure’)=pcval

end loopend if

end loopend

FLAC Version 6.0


14.6.6 “CAP TABLE.FIS”

;Name: cap table.fis;Purpose: generate cap table for cysoil model;Input: nt/integer/1/Cap table number;Input: num/integer/200/number of entries in Cap tabledef cap table; (cap m); (make sure the whole range of pressures is covered)

coe = 1.- emevpmax=(( pmax/ pa)ˆcoe)*( mul/(1.+ mul))* pa/(coe* ki)

;de = evpmax/float( num)ratr = (1.+ mul)/ mulxtable( nt,1) = 0.0ytable( nt,1) = 0.0mex = 1./(1.- em)coep = pa*((1.- em)*ratr* ki/ pa)ˆ2 mexloop ii (2, num)xval = de*float(ii-1)ytable( nt,ii) = coep*(xvalˆ2 mex)xtable( nt,ii) = xval

end loopend

FLAC Version 6.0


14.6.7 “ EVP0.FIS”

;Name: evp0;Purpose: initialize ev plastic from initial cap pressuredef evp0loop ii (1,izones)

if ii # 11 then; --- sand ---

loop jj (1,20)mul = mul sandpcval=z prop(ii,jj,’cap pressure’)coe = 1.-m sandevp=((pcval/ pa)ˆcoe)*( mul/(1.+ mul))* pa/(coe*ki sand)z prop(ii,jj,’ev plastic’) = evp


loop jj (21,40)mul = mul claypcval=z prop(ii,jj,’cap pressure’)coe = 1.-m clayevp=((pcval/ pa)ˆcoe)*( mul/(1.+ mul))* pa/(coe*ki clay)z prop(ii,jj,’ev plastic’) = evp

end loopend if

end loopend

FLAC Version 6.0

example applications : 14 : dewatered construction of a...

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