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Example Application of a Seismic

Analysis 1.6

Seismic Analysis of an

Embankment Dam

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Coordinates used to create the model geometry

(350, 550)

(717.2, 680) (800, 680)

(1470, 550) (0, 550) (1800, 550)

(1800, 400) (0, 400)

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The modeling procedure is divided into eight steps:

1. Determine representative static and dynamic material characteristics of the soils, and estimate

representative material properties. This includes an estimate for material damping parameters to represent

the inelastic cyclic behavior of the materials.

2. Calculate the deconvoluted dynamic loading for the base of the model, derived from the target seismic

record for the site, and evaluate the seismic motion characteristics.

3. Adjust input motion for accurate wave propagation, and create an appropriate model grid.

4. Calculate the static equilibrium state for the site, including the steady-state groundwater conditions with

the reservoir at full pool.

5. Apply the dynamic loading conditions.

6. Perform preliminary undamped simulations to check model conditions and estimate the dominant

frequencies of the site resonance and the maximum cyclic shear strains for the given site conditions.

7. Run a series of simulations with actual strength properties and representative damping—assuming the

soils do not liquefy— in order to evaluate the model response.

8. Perform the seismic calculation assuming the soils can liquefy.

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Material Properties for foundation and embankment soils

The foundation and embankment soils are modeled as elastic-perfectly plastic Mohr-Coulomb

materials. Drained properties are required because this is an effective-stress analysis.

Foundation Embankment

Soil 1 Soil 2 Soil 1 Soil 2

Unit weight (pcf) 125 125 113 120

Young’s modulus (ksf) 12,757 12,757 6,838 6,838

Poisson’s ratio 0.3 0.3 0.3 0.3

Bulk modulus (ksf) 10,631 10,631 5,698 5,698

Shear modulus (ksf) 4,906 4,906 2,630 2,630

Cohesion (psf) 83.5 160 120 120

Friction angle (degrees) 40 40 35 35

Dilation angle (degrees) 0 0 0 0

Porosity 0.3 0.3 0.3 0.3

Hydraulic conductivity (ft/sec) 3.3x10-6 3.3x10-7 3.3x10-6 3.3x10-8

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Modulus reduction curve for clayey soils (from SHAKE-91 data) FLAC default hysteretic damping

with L1=-3.156 abd L2=1.904

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Damping ratio curve for clayey soils (from SHAKE-91 data) FLAC default hysteretic damping with

L1=-3.156 and L2=1.904

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Step 1-1 Preprocess ground motion- In the first project file, in the [Model Options] dialog select the [Dynamic] configuration option. We will use

this project file to preprocess our acceleration file. Save the file as “INPUT.PRJ”.

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Step 1-2 Under the [Utility] Tab, select the [Seismic] tool. This will open the Dynamic Input Wizard.

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Step 1-3 Navigate to the history file “ACC_DECONV.HIS”, specify that it is an acceleration history and the units are in (ft/s2).

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Step 1-4 Frequency components above five Hz are removed using the filter. The input records are updated after the green “start” button is

pressed.

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Step 1-5 The displacement drift is removed via a low-frequency sinusoid function. The final diplacement drift is found to be approximately 0.3ft.

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Step 1-6 By pressing the green circular “start” button, the drift is removed and the final displacement is corrected to zero.

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Step 1-7 Export the processed data in a velocity table and name the file “INPUT.TAB”.

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Step 1-8 The processed data is read into FLAC using the [Utility]/[Table] tool.

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Step 1-9 The table is assign an ID of 104.

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Step 1-10 A plot of the processed data is created using the [Plot]/[Table] tool.

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Step 1-11 The table is converted to a datafile and saved.

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Step 2-1 Model Geometry- In the second project file, the [Dynamic] and [GWFlow] configuration options in the Model Options dialog are selected.

We will use this project file to build and solve our model. Save the file as “EARTHDAM.PRJ”.

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Step 2-2 The model geometry will be constructed in the geometry builder.

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Step 2-3 The model boundary will be created using the box tool.

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Step 2-4 The Build button is pressed to extract one quad block.

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Step 2-5 The boundaries will be altered under the [Edit] stage.

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Step 2-6 The block is split in four locations using the [Blocks]/[Split blocks] tool.

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Step 2-7 The vertex locations are adjusted to correspond with the dam geometry using the [Blocks]/[Move points] tool.

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Step 2-8 The final dam geometry.

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Step 2-9 Automatic boundary conditions are set under the boundary edit stage.

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Step 2-10 The mesh is densified under the edit mesh stage. Automatic zoning is turned off and the number of zones is adjusted for each edge.

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Step 2-11 Once the model is built, press OK.

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Step 2-12 Select execute to send the commands to FLAC.

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Step 2-13 The [Alter]/[Shape] tool is used to define the stratigraphy.

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Step 2-14 Material properties are assigned using the [Material]/[Assign] tool.

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Step 2-15 Groundwater properties are assigned using the [Assign]/[GWProp].

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Step 2-16 The model is saved as “EDAM1.SAV”.

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Step 3-1 Static calculations- The embankment soils are removed using the [Material]/[Cut&Fill] tool.

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Step 3-2 Groundwater flow is turned off and the water density is set using the [Settings]/[GW] tool.

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Step 3-3 The FISH function “ININV.FIS” is called using the FISH Library. This function initializes stress distribution for groundwater problems.

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Step 3-4 Permeability and water table height are defined in the FISH input parameters.

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Step 3-5 [Run]/[Solve] is selected and “execute” is pressed to bring the model to equilibrium.

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Step 3-6 The model is saved as “EDAM2.SAV”.

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Step 3-7 Pore pressure distribution in foundation soils.

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Step 3-8 At the beginning of the next stage, materials are added to the model in stages to simulate the construction process.

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Step 3-9 The model is solved again using the [Run]/[Solve] tool.

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Step 3-10 This stage is saved as “EDAM3.SAV”.

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Step 3-11 Displacements induced by embankment construction in one step.

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Step 3-12 The pressure distribution is applied along the upstream slope to represent the weight of the reservoir water. A mechanical pressure is

assigned in the [In Situ]/[Apply] tool. The pressure ranges from zero at elevation 670 ft to 7496.2 psf at elevation 550 ft.

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Step 3-13 Pore pressure is applied to the left boundary of the model, corresponding to the reservoir elevation at 670 ft using the [Insitu]/[Apply]

tool.

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Step 3-14 Using the [Insitu]/[Fix] tool, pore pressure is fixed along the along the downstream slope to allow flow across this surface.

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Step 3-15 Porosity and permeability are assigned for the embankment materials using the [Material]/[GWProp] tool.

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Step 3-16 Four histories are assigned: three pore pressure histories and one history for groundwater time.

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Step 3-17 The state is saved as “EDAM4.SAV”.

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Step 3-18 Groundwater calculations are turned on using the [Settings]/[GW] tool.

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Step 3-19 The water bulk modulus is set to 4.1 × 103 psf. The low value of water modulus will speed the calculation to steady-state flow.

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Step 3-20 The fast-flow scheme SET fastwb on is used to speed the calculation to steady state.

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Step 3-21 The model is solved by clicking [Run]/[Solve]. The uncoupled method is checked along with the phreatic surface option.

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Step 3-22 The stage is saved as “EDAM5.SAV”.

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Step 3-23 Pore pressure histories.

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Step 3-24 Pore-pressure distribution at steady state flow for reservoir raised to 670 ft.

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Step 3-25 Total vertical-stress distribution at steady state flow for reservoir raised to 670 ft.

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Step 3-26 Factor of safety is calculated using the [Run]/[SolveFOS] tool. The resulting FOS plot is created using the [Plot]/[FoS] tool.

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Step 4-1 Dynamic calculation with elastic material and no damping- A new branch is created after “EDAM5.SAV”.

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Step 4-2 Water bulk modulus is set to 4.1E6 lb/ft2.

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Step 4-3 Dynamic calculations are turned on using the [Settings]/[Dyna] tool.

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Step 4-4 Large strain calculations are turned on using the [Settings]/[Mechanical] tool.

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Step 4-5 Processed data stored in Table 104 is loaded into the model using the [Utility]/[Call] tool.

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Step 4-6 Navigate to “TABLE104.DAT”.

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Step 4-7 Clear displacements and velocities using the [In Situ]/[Initial] tool. In this way, only seismic induced motions and deformations are shown in the model results.

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Step 4-8 Echo commands from call files and FISH to console is turned off using the [Settings]/[Misc] tool.

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Step 4-9 Several more FISH functions are called using the [Utility]/[Call] tool, starting with “STRAIN_HIST.FIS”.

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Step 4-10 “RELDISPX.FIS”, “INIPP.FIS” and “EXCPP.FIS” are all called and executed. These functions are implemented to monitor the shear strain

and excess pore pressure at selected locations.

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Step 4-11 Acceleration and velocity histories are recorded at several gridpoints throughout the model.

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Step 4-12 History step size is set to 100 using the [Utility]/[History] tool.

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Step 4-13 The solve limit is set to 1E7 steps.

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Step 4-14 The FISH function “MON_EX.FIS” is called and executed using the [Utility]/[Call] tool. “MON_EX.FIS” monitors shear strains throughout

the model and stores the maximum shear strain calculated during dynamic loading.

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Step 4-15 This stage is saved as “EDAM6E.SAV”.

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Step 4-16 Elastic material properties are assigned using the [Material]/[ChangeProp] tool. Cohesion and tension are changed to 1E10 lb/ft2.

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Step 4-17 Free field boundaries are applied using the [In Situ]/[Apply] tool.

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Step 4-18 An sxy boundary condition of -9358 lbf/ft2 is applied to the bottom of the model. A velocity record is applied by checking the [table] radio

button and selecting Table 104 as the multiplier.

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Step 4-19 A compliant boundary condition is assumed for the base. Therefore, it is necessary to apply a quiet boundary along the bottom of the

model to minimize the effect of reflected waves at the bottom. Quiet boundary conditions are assigned in both the x- and y-directions.

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Step 4-20 The state is saved as “EDAM7E.SAV”.

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Step 4-21 Dynamic calculations are turned on and the dynamic time limit is set to 40 before the model is solved. Then the state is saved as

“EDAM8E.SAV”.

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Step 4-22 X acceleration versus dynamic time is written to Table 14 using the [Utility]/[History] tool.

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Step 4-23 “FFT_TABLES.FIS” is loaded into FLAC using the [Utility]/[Call] tool. The parameters fft_inp1 and fft_inp2 are set to 14 and 24,

respectively.

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Step 4-24 “FFT.FIS” is loaded into FLAC using the [Utility]/[Call] tool. This routine performs a fast fourier transformation on the information stored

in FFT_IN and returns power spectrum in FFT_OUT.

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Step 4-25 “ACC_DECONV.HIS” and “ACC_TARGET.HIS” are loaded into FLAC as histories 33 and 34, respectively, using the [Utility]/[History] tool.

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Step 4-26 Histories 33 and 34 are written to tables using the [Utility]/[History] tool.

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Step 4-27 This stage is saved as “EDAM9E.SAV”.

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Step 4-28 Comparison of input velocity to x-velocity monitored at model base, applied shear stress.

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Step 4-29 Comparison of velocity histories at the base and top of model.

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Step 5-1 Mohr-Coulomb material with hysteretic damping- The commands from “EDAM6E.SAV” are copied in the next stage “EDAM6MH.SAV”.

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Step 5-2 In the second stage, hysteretic damping is applied using the [In Situ]/[Initial] tool.

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Step 5-3 Hysteretic damping does not completely damp high-frequency components, so a small amount of stiffness-proportional rayleigh damping

is also applied using the [In Situ]/[Initial] tool.

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Step 5-4 Free-field conditions are applied on the side boundaries. An sxy stress history and quiet boundaries are applied at the base, in the same

way as for the undamped simulation. This stage is saved as “EDAM7MH.SAV”.

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Step 5-5 The dynamic calculation is turned on and the dynamic time limit is set to 40 before the model is solved. Then the state is saved as

“EDAM8MH.SAV”.

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Step 5-6 X-displacement contours at 40 seconds.

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Step 5-7 Shear-strain increment contours at 40 seconds

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Step 5-8 Shear stress versus shear strain in embankment soil 2 at zone (77, 20).

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Step 6-1 Mohr-Coulomb material with rayleigh damping- The commands from “EDAM6E.SAV” are copied into “EDAM6MR.SAV”.

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Step 6-2 The FISH function “GREDUCE.FIS” is executed to reduce the elastic moduli by a factor of 0.8.

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Step 6-3 Rayleigh damping is set to 6.3% with a center frequency of 1.0 Hz.

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Step 6-4 Free-field conditions are applied on the side boundaries. An sxy stress history and quiet boundaries are applied at the base, in the same

way as for the undamped simulation. This stage is saved as “EDAM7MR.SAV”.

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Step 6-5 Dynamic calculations are turned on and the dynamic time limit is set to 40 before the model is solved. Then the state is saved as

“EDAM8MR.SAV”.

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Step 6-6 x-displacement contours at 40 seconds.

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Step 6-7 Shear-strain increment contours at 40 seconds.

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Step 6-8 Shear stress versus shear strain in embankment soil 2 at zone (77, 20).

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Step 7-1 Finn material with hysteretic damping- Embankment soils are changed to liquefiable materials. Finn/Byrne material properties are

assigned for all the regions in the model using the [Material]/[Model] tool then the solve command is issued.

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Step 7-2 The same commands are pasted into the rercord pane as the previous 6th stage.

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Step 7-3 Latency is reduced to 50 for the earthdam using the [Material]/[ChangeProp] tool.

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Step 7-3 This stage is saved as “EDAM6FH.SAV”.

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Step 7-4 The hysteretic damping parameters are set in the next stage.

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Step 7-5 Hysteretic damping does not completely damp high-frequency components, so a small amount of stiffness-proportional rayleigh damping

is also applied using the [Insitu]/[Initial] tool.

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Step 7-6 The free-field is applied on the side boundaries. An sxy stress history and quiet boundaries are applied at the base, in the same way as the

previous branches.

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Step 7-7 Pore pressure is saved to extra grid variable 2 using the “SAVEPP.FIS” function.

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Step 7-8 The FISH function “GETEXCESSPP.FIS” is called using the FISH editor and is used to calculate the excess pore pressure for each zone in

order to evaluate the potential for liquefaction. Then this state is saved as “EDAM7FH.SAV”.

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Step 7-9 The dynamic time limit is set to 40 and the model is solved.This stage is saved as “EDAM8FH.SAV”.

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Step 7-10 X-displacement contours at 40 seconds.

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Step 7-11 Shear strain increment contours at 40 seconds.

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Step 7-12 Relative displacements at gridpoint (62,29) along upstream slope.

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Step 7-13 Excess pore-pressure ratio contours (values greater than 0.99).

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Step 8-1 Finn material with rayleigh damping- Copy and paste the commands from “EDAM6FH.SAV” into the new branch “EDAM6FR.SAV”.

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Step 8-2 Copy and paste the commands from “EDAM7MR.SAV” to “EDAM7FR.SAV”. The FISH functions “SAVEPP.FIS” and “GETEXCESSPP.FIS” are

called and executed before the state is saved as “EDAM7FR.SAV”.

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Step 8-3 The dynamic time limit is set to 40 and the model is solved. This state is saved as “EDMA8FR.SAV”.

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Step 8-4 X-displacement contours at 40 seconds.

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Step 8-5 Shear strain increment contours at 40 seconds.

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Step 8-6 Excess pore-pressure ratio contours (values greater than 0.99).