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Example Application 1

Slope Stability

for a

Cohesive and Frictional Soil

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Soil Properties for Slope

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Modeling Procedure

Step 1 Create the slope model grid, set boundary conditions, assign material

model and specify properties.

Step 2 Analyze the stability of the slope for different strength properties.

Step 3 Analyze the stability of the slope if a groundwater phreatic surface is

specified in the slope.

Step 4 Analyze the stability of the slope if a groundwater flow calculation is specified

first to establish the phreatic surface, and then the stability of the slope is

calculated.

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The [adjust total stress] configuration option is used for this exercise because pore pressures will be changed instantaneously when the phreatic

surface is added. [Include advanced constitutive models] is checked to allow changing material properties.

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A project title is assigned, and a project file slope.prj is created and stored in a working directory.

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Step 1-1 Enter the [Build]/[Geometry]/[Slope] tool and set the slope geometry parameters.

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Step 1-2 Press [OK] and then press [Edit] in the [Virtal] tools.

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Step 1-3 In the [Edit] tool, select [Boundary] edit stage and press [Automatic boundary cond.] to apply roller boundaries on the sides and fixed

boundary on the base.

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Step 1-4 Select [Mesh] edit stage and turn off [Use automated zoning]. Manually change the zoning to produce 20 zones in the x-direction and 10

zones in the y-direction.

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Step 1-5 Select the [Materials] edit stage and then [Create] to open the Define Material dialog. Select the [Mohr-Coulomb] model and enter the

properties: density=1500, bulk modulus=1e8, shear modulus=0.3e8, cohesion=1e10, tensile strength=1e10 and friction=20. The material has the

group name soil. Press [OK] to add soil to the material list.

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Step 1-6 Press [SetAll] to assign the material soil to all zones in the model. Press [OK] to exit the [Edit] tool.

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Step 1-7 Press [Execute] to create the FLAC commands for this model. Assign gravity loading using the [Settings]/[Gravity] tool.

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Step 2-1 Motion in the grid can be monitored by tracking the displacements of gridpoints. Enter the [Utility]/[History] tool and select[ydisp]

gridpoint history and clicking the mouse on a gridpoint in the slope. Gridpoint i=10, j=10 is selected in the plot above. The y-displacement of this

gridpoint will be monitored during the calculation.

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Step 2-2 Select [Run]/[Solve] and press [OK] to calculate the initial equilibrium state. The material does not failure because strength properties

are set high. The unbalanced history is plotted versus step using the [Plot}/{Quick] tool.

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Step 2-3 Press [Plot]/[History] and select the y-displacement history to plot a history of y-displacement at gridpoint (10,10) versus step. Save the

state as sl1.sav.

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Step 2-4 Enter [In Situ/[Initial] and press Clear?[Displmt & velocity] to rest displacements and velocities to zero.

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Step 2-5 Enter [Material]/[ChageProp], press [SelAll] and change cohesion to 0.0 in all zones.

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Step 2-6 Press [Settings]/[Mech] and select [Large strain] to run the calculation in large-strain mode.

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Step 2-7 Press [Run]/[Cycle] and run the calculation200 steps. Use [Plot]/[Model] to select displacement vectors and x-velocity contours. The

extent of failure is indicated on the plot.

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Step 2-8 Continue the calculation for an additional 800 steps. The grid distortion in large-strain mode is now evident. Save the state as sl2.sav.

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Step 2-9 Return to state sl1.sav and press[Follow] to create a separate branch. Repeat stage sl2.sav commands, but this time change the

cohesion to 1e4 and tensile strength to 0.0. The slope is stable with this strength. Save the state as sl3.sav.

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Step 3-1 The location of the water table is set in the [Utility]/[Table] tool. Click on [Create] to create table 1. Then, press [Edit] to open the Edit

table points dialog. Enter three points at (0,5), (6.11,5) and (20,9). Press [OK] and [Execute] to send the TABLE command to FLAC.

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Step 3-2 Enter the [Settings]/[GW] tool. Specify water density = 1000, and set water table number = 1. Press [Execute].

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Step 3-3 Saturated material density below the water table is set manually when in non-GW mode. The FISH function wet_density.fis is called

into FLAC in the [FISH editor] pane. Both [Call file] and [Execute] function are selected. The function is executed to change the density of all zones

below the water table to 1800. The plot shows both the water table and density contours.

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Step 3-4 The weight of the water at the toe of the slope is added as a pressure boundary condition using the [In Situ]/[Apply] tool. Select

[pressure] stress keyword, and drag the mouse from i=7,j=6 to i=1, j=4. The Apply value dialog opens. Enter the starting value of 0.0 and the y-

variation of 2e4.

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Step 3-5. The phreatic surface is now added. Save this state as sl4.sav.

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Step 3-6 Run the model for 6000 mechanical steps using the [Run]/[Solve] tool. The failed slope is indicated by the displacement vectors plot.

Save the state as sl5.sav.

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Step 4-1 Double-click on the new state to start a new model in the project tree. Select [File]/[Model options] and include [GWFlow] to active the

groundwater flow configuration option.

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Step 4-2 Repeat Steps 1-1 to 1-5 to recreate the slope model. Note that a project branch, branch B, is created in the project tree. The commands

are the same as for sl1.sav except that CONFIG gw ats is now given at the start.

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Step 4-3 Assign porosity=0.3 and permeability=1e-10 to all zones using the [Material]/[GWProp] tool.

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Step 4-4 Assign water bulk modulus=1e4 and water density=1000 in the [Settings]/[GW] tool.

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Step 4-5 Set the pore pressure boundary conditions in the [In Situ]/[Apply] tool. Select [Groundwater]/[pp] and drag the mouse along the right

boundary from i=21,j=9 to i=21,j=1. Press [Assign] to open the Apply value dialog. Set the starting pp value = 0.0 and the y-variation to 9e4. Press

[OK] to create the APPLY command.

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Step 4-6 Repeat the procedure to create the pore pressure boundary condition on the left boundary. The starting point is at i=6, j=6 and the

ending point is at i=1, j=1. The starting pp value=0.0 and they-variation = 5e4. Press [OK] and the [Execute] to send the commands to FLAC.

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Step 4-7 Assign gravity using the [Settings]/[Gavity] tool.

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Step 4-8 The steady fluid flow state can be checked using the Qratio.fis FISH function. Open the function in the [FISH editor] tool. Call the

function into FLAC.

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Step 4-9 The FISH function is executed in the [Utility]/[History] tool. Select [Fish->History] and create three FISH histories, first qratio, then inflow

and outflow.

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Step 4-10 Also select gwtime to monitor flow time during the calculation. Press [Execute] to send the commands to FLAC.

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Step 4-11 This is an uncoupled calculation. First a flow only run is performed. Turn off the mechanical calculation in the [Settings]/[Mech] tool.

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Step 4-12 Select the [Run]/[Solve] tool to run the flow only calculation.

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Step 4-13 When the run stops, plot the water table, pore pressure contours and flow vectors Save the state as slgw1.sav. Branch names can be

changed by right-clicking on the name.

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Step 4-14 Check that steady state flow is reached by plotting inflow and outflow histories. Flows match at steady state.

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Step 4-15 Turn on the mechanical calculation in the [Settings]/[Mech] tool and turn off the groundwater flow calculation and set water bulk

modulus=0.0 in the [Settings]/[GW] tool.

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Step 4-16 The weight of the water at the toe of the slope is added as a pressure boundary condition using the [In Situ]/[Apply] tool. Select

[pressure] stress keyword, and drag the mouse from i=7,j=6 to i=1, j=4. The Apply value dialog opens. Enter the starting value of 0.0 and the y-

variation of 2e4.

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Step 4-17 Record a history of y-displacement in the [Utility]/[History] tool.

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Step 4-18 Perform the mechanical only calculation using the [Run]/[Solve] tool.

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Step 4-19 Equilibrium is checked with the y-displacement history and unbalanced force history. The state is saved as slgw2.sav.

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Step 4-20 The cohesion is set to 1e4 and tensile strength to 0.0 in the [[Material]/[ChangeProp] tool.

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Step 4-21 Displacements and velocities are reset in the [In Situ]/[Initial] tool.

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Step 4-22 The mechanical calculation is continued in large-strain mode using the [Settings]/[Mech] tool.

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Step 4-23 An additional 1000 steps are performed using the [Run]/[Cycle] tool.

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Step 4-24 Slope failure is indicated from the plot showing displacement vectors. The state is saved as slgw3.sav.

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Step 4-25 Slope failure is also indicated by the y-displacement history plot.