CVEEN 7330

CVEEN 7330

FLAC Modeling Exercise 2Table of Contents

1Table of Contents

2Objectives:

2FLAC Input:

3Shake Inputs:

4Required Outputs from FLAC:

4Required Output from Shake:

4Required Calculations and Discussion:

5FLAC Hints:

6Seismosignal Hints:

6FLAC Solution:

12SHAKE Solution:

16Required Calculations and Discussion:

16Source Code

Objectives:

This model compares the dynamic results from FLAC with those of SHAKE. FLAC is a 2D nonlinear dynamic code. SHAKE is a 1D equivalent code. Thus, we will compare the results of these two methods for a simple ground response problem with a homogenous soil profile.

FLAC Input:

Use and an example file: C:\Program Files\Itasca\flac500\Options\3-Dynamic\ op_03_12.prj

Geometry:

20 m high model by 1 m width.

Boundary Conditions:

Fix all elements in the y direction

Model Type:

Elastic

Material Properties:

density = 2000 kg/m3

shear modulus = 0.97e8 N/m2 = 97 MPa

bulk modulus = 2e8 N/m2 = 200 Mpa

Input Acceleration Time History:

Taft Record from EduShake (unscaled)

Shake Inputs:

Geometry:

20 m deep model with 1 m thick layers.Material Properties:

density = 2000 kg/m3

shear modulus = 0.97e8 N/m2 = 97 Mpa

Infinite half space (layer 21)

Linear modulus and damping curves

Den = 19.6 kN/m3

Damping = 1.0 percent

Input Acceleration Time History:

Taft Record from EduShake (unscaled)

Strain ratio = 0.65

Cutoff frequency = 15 Hz

Required Outputs from FLAC:

1. Acceleration time history at base of model

2. Acceleration time history at middle of model

3. Acceleration time history at top of model

4. Shear stress versus shear strain time history for middle of model

5. Shear stress versus shear stain time history for bottom of model

6. Response spectrum (5 percent damp) as a function of period for surface acceleration time history (use Seismosignal and the digital results from no. 3 above). The response spectrum has most of its amplitude in the period range from 0 to 1 second, so in Seismosignal make a plot of the response spectrum for this range, (i.e., max. period equal to 1 second).

7. FISH Source code for FLAC model.

Required Output from Shake:

1. Acceleration time history at top of model (layer 1

2. Acceleration time history at middle of model (layer 10)

3. Shear stress versus shear strain time history for middle of model (layer 20)

4. Shear stress versus shear stain time history for bottom of model (layer 10)

5. Response spectrum (5 percent damp) as a function of period for surface acceleration time history (use Seismosignal and the digital results from no. 1 above). Make this plot like that of No. 6 from the FLAC output, so the two plots can be compared.

Required Calculations and Discussion:

1. Calculate the fundamental period of the 20 m thick soil column using Eq. (7.16) in Kramer.

2. Compare the maximum shear strain develop in the middle and bottom of the layers for the FLAC and SHAKE results. Discuss how well the maximum shear strains compare for both layers for both models.

3. Make a composite plot of the surface response spectra for both FLAC and SHAKE. Discuss how well the response spectra compare.

FLAC Hints:

1. See file :\Program Files\Itasca\flac500\Options\3-Dynamic\ op_03_12.prj for clues on how to generate stress vs. strain time histories and acceleration time histories.

2. Use must use an elastic model with hysteretic damping in FLAC to compare with SHAKE. This is done with the following commands:

model elas

ini dy_damp hyst default 3.325 0.823

(The default hyst damping model in FLAC produces shear modulus and damping curves that are most similar to Sand (Seed and Idriss, 1970) for the modulus curves and Sand (Seed and Idriss Lower Bound) for the damping curves. These curves are provided in Edushake.

3. To read in the Taft acceleration time history, your FLAC code should have

his read 100 taft.acc

apply xacc 9.81 his 100

apply yacc 0 j = 1

(Note that the 9.81 multiplier is applied to the Taft record to convert the record from acceleration (g) to acceleration (m/s). You must use units that are consistent with the FLAC analysis (m, s, N, Pa, etc.)

(Note that apply yacc 0 j = 1 prevents rocking of the model along the grid point j = 1.)

4. Use Seismosignal to produce the acceleration response spectra from surface time histories output by FLAC and SHAKE.

5. To output a surface time history from FLAC, your FLAC commands should have:

set dydt = 0.0008

(This command must be before the solve command and is required to produce an equal time step.)

his write 8 vs 1; top acc. history to table

set hisfile out-flac-0001.his

(The first command in this sequence writes history 8 (acceleration at top of model) vs. history 1 (dynamic time step) to create an acceleration time history.)

(The second command writes the results to a file called out-flac-0001.his, which you can access using Seismosignal to produce an acceleration response spectrum).

Seismosignal Hints:

1. When you read the FLAC surface time history file into Seismosignal, be careful to input the time step correctly. In FLAC, you set the time step dy/dt equal to 0.0008 and this time step was used for the calculations. However, when FLAC output this time history (see file out-flac-0001.his), the program has changed the time step to 0.008. Be careful to use the 0.008 value in Seismosignal when reading the file; otherwise you time series and response spectrum will not be correct.

FLAC Solution:

Figure 1. Acceleration time history at base of FLAC model

Figure 2 Acceleration time history at middle of FLAC model

Figure 3 Acceleration time history at top of FLAC model

Figure 4 Shear stress vs shear strain middle of model

Figure 5 Shear stress vs shear strain bottom of model

Figure 6 Response spectrum for surface from FLAC using Seismosignal.

SHAKE Solution:

Figure 7 Acceleration time history at top of SHAKE model

Figure 8 Accleration time history at middle of SHAKE model (layer 10)

Figure 9 Time history of shear strain at middle of SHAKE model (layer 10)

Figure 10 Time history of shear strain at bottom of SHAKE model (layer 20)

Figure 11 Response spectrum for surface from SHAKE using Seismosignal

Figure 12 Comparison of surface response spectra from FLAC (red) and SHAKE (blue) for a homogeneous soil profile.

Required Calculations and Discussion:

1. T0 = 4H/Vs = 4(20m)/220m/s = 0.36 s

2. The maximum shear strains from the plots are as follows:

FLAC (middle) = 10 x 10-4 = 0.001 = 0.1 percent

FLAC (bottom) = 25 x 10-4 = 0.0025 = 0.25 percent

SHAKE (middle) = 0.1 percent

SHAKE (bottom) = 0.27 percent

The shear strains calculated by both models compare well.

3. The response spectra from both models compare reasonably well. The amplitudes of the spectra are very similar. The SHAKE spectrum is shifted slightly to the right (to longer period) when compared with the FLAC spectrum.

Source Code

conf dyn ext 5

grid 1 20

model elastic

prop dens 2000 shear 0.97e8 bulk 2e8

fix y

his read 100 taft.acc

apply xacc 9.81 his 100 yvel 0 j=1

;apply yacc 0.0 j=1; this prevents rocking along gridpoint j = 1

def strain1

strain1 = xdisp(1,2) - xdisp(1,1)

strain10 = xdisp(1,11) - xdisp(1,10)

end

set dydt = 0.0008

his 1 dytime

his 2 sxy i 1 j 1

his 3 strain1

his 4 sxy i 1 j 10

his 5 strain10

his 6 xacc i=1 j=1

his 7 xacc i 1 j 11

his 8 xacc i 1 j 21

ini dy_damp hyst default -3.325 0.823

set dytime = 12

solve dytime 74

his write 8 vs 1; top acc. history

set hisfile inp-flac-0001.his