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1、.Objectives1. Determine the embankment and foundation acceleration response and deformation for a design basis earthquake without liquefaction present in the foundation.2. Determine the embankment and foundation acceleration response and deformation for a design basis earthquake where a liquefied la

2、yer is present in the foundation soil.3. Determine the extent of ground improvement required to restrict the deformation measured at the embankment toe and crest to 0.7 m for the case where part of the liquefied layer has been remediated using stone columns.Development of Design Ground Motion for FL

3、AC modeling1. The design spectrum for the bedrock at the base of the soil column is shown in Figure 1 below. Use the red line (median line) to define the design spectrum for bedrock. The spectrum is the target spectrum for the input motion used at the base of the DEEPSOIL model, as discussed later.2

4、. Prior to running the DEEPSOIL analysis, spectrally match the Taft record (taftmod.acc) to the bedrock design target spectrum using Seisomatch and baseline correct the matched record using Seismosignal. (For your analysis, use only the first 20 seconds of the input motion.)3. Use the equivalent lin

5、ear method in DEEPSOIL and the layering shown in Figure 2 to perform a 1-D response analysis to determine the input motion at the base of the FLAC model. a. Assign the spectrally-matched time history to layer 20 as the input rock motion for the DEEPSOIL analysis.b. Use the layers 6 through 19 in Fig

6、ure 2 to represent the soil column properties that extend with depth below the base the FLAC model.c. Use the properties of layer 1 through 5 from FLAC Model 7.pdf in the DEEPSOIL analysis for the corresponding layersd. For the DEEPSOIL analysis, assume that all layers (1-19) are sand and that the S

7、eed and Idriss upper bound curves represent the shear modulus degradation and damping behavior of these sandy soils.e. Assume that layer 20 represents bedrock in the DEEPSOIL model with a velocity of 600 m/s and 2 percent damping.f. For the subsequent FLAC modeling, use the motion in layer 5 from th

8、e DEEPSOIL analysis to assign to the base of the FLAC model.4. Required Informationa. Plot of the unaltered TAFT acceleration time historyb. Comparison plot of the target acceleration response spectrum versus the response spectrum of the spectrally-matched time history.c. Plot of the input time hist

9、ories for the DEEPSOIL analysis showing the inputted acceleration, velocity and displacement.d. DEEPSOIL profile and propertiese. Plot of acceleration time history in layer 5f. Comparison of acceleration response spectrum (base input) vs. layer 5FLAC Properties, Geometry and Static Calculations1. Th

10、e elastic soil properties, drained friction angles, and model geometry given in FLAC model 7.pdf apply to foundation and embankment soil for the case where a liquefied zone is not present in the model. a. Assume that Poissons ratio is 0.25 in all materials that do not liquefy.b. Use hysteretic dampi

11、ng for all layers in the model.2. Required informationa. Plot of model geometry with boundary conditionsb. Table of model elastic and Mohr-Coulomb properties for each layerc. Plot of density for each layerd. Contour plot of total vertical stresse. Contour plot of effective vertical stressf. Contour

12、plot of pore water pressure g. Contour plot of shear modulush. Contour plot of bulk modulusi. FLAC code for the static analysisFLAC Dynamic Calculations (No-liquefaction)1. For objective 1, perform a FLAC dynamic analysis where a liquefiable layer is not present in the model using the motion in laye

13、r 5 from the DEEPSOIL analysis.2. The soil properties for this case will be the same as the static case except that hysteretic damping will be added for the dynamic analyses.3. Analyze the response and deformation of the embankment and foundation and provide the following information.4. Required inf

14、ormationa. Contour plot of hysteretic properties (c0 and c1)b. History plot of X-acceleration and base of FLAC model (node 12,1)c. History plot of X-acceleration at base of embankment (node 12,6)d. History plot of X-acceleration at crest of embankment (node 9,11)e. History plot of X-displacement at

15、the toe of the embankment (node 9,6)f. History plot of X-displacement at the crest of the embankment (node 9,11)g. Vector displacement plot of nodes with contour plot of X-displacement on same ploth. Hysteresis loop plot for zone 9,4i. Hysteresis loop plot for zone 16,4 FLAC Liquefaction Calculation

16、s1. Use the FLAC model to calculate the cyclic stress ratio induced by the earthquake (CSREQ) at the toe of the embankment (i.e., zone i=9 j=4).a. This can be done by making a plot of the shear stress as a function of dynamic time. From this plot, find the peak shear stress, tmax, then multiply this

17、 by 0.65 to convert it to an equivalent shear stress and divide this value by the effective vertical stress in the potentially liquefiable zone from the static analysis.b. (Note also the CSREQ is calculated without including the effects of liquefaction in the FLAC model. Thus, you must run the FLAC

18、model without liquefaction present to estimate CRSEQ. c. The necessary routine to calculate CRSEQ can be added to the FLAC code given in FLAC model 7.pdfdef strain1 deltay = 2; 2 m vertical spacing between nodes strain1 = (xdisp(9,5) - xdisp(9,4)/deltay strain2 = (xdisp(16,5) - xdisp(16,4)/deltay if

19、 dytime < 0.01 inishear = sxy(9,4) ; initial static shear stress inieffvert = syy(9,4)+pp(9,4) ; ini. eff. vert. stress (compression is neg.) endif CSREQ = 0.65*(sxy(9,4)-inishear)/inieffvertend2. In addition, use the FLAC model to calculate the factor of safety against liquefaction as a function

20、 of dytime using the instructions below.a. Note that CSREQ and FS are calculated without liquefaction present in the model. You can ensure that liquefaction will not occur by setting the variables in the FLAC code from FLAC Model 7 to the following values.startliq = 21; start time for liquefaction l

21、iqtime = 21; when liquefaction is at 100 percentb. The factor of safety against liquefaction is calculated from:FS = CSRL/CSREQc. CSRL represents the soils resistance to liquefaction is a function of density as measured by the SPT N160 value. For a N160 of 10 in the liquefied zone, CSRL is determine

22、d from Fig. 3 and is 0.11. This value does not change during earthquake cycling.d. The FLAC code developed above can be modified to calculate the factor of safety: def strain1 deltay = 2; 2 m vertical spacing between nodes strain1 = (xdisp(9,5) - xdisp(9,4)/deltay strain2 = (xdisp(16,5) - xdisp(16,4

23、)/deltay if dytime < 0.01 inishear = sxy(9,4) ; initial static shear stress inieffvert = syy(9,4)+pp(9,4) ; ini. eff. vert. stress (compression is neg.) endif CSRL = 0.11; for N160 = 10; M7.5 earthquake CSREQ = 0.65*(sxy(9,4)-inishear)/inieffvert if CSREQ = 0 ; doesn't allow FS to be undefine

24、d CSREQ = 0.01 endif if CSREQ < 0 ; changes neg. values to positive CSREQ = CSREQ*(-1) endif if CSREQ > 0 CSREQ = CSREQ endif FS = CSRL/CSREQ if FS > 2 ; place a cap on FS for plotting. FS = 2 endifend3. Required Informationa. CRS vs dytime plotb. FS vs dytime plotModeling the Effects of Li

25、quefaction1. For calculating the liquefaction deformation for objective 2, assume that the liquefied zone is 2-m thick and starts at 2 m below the ground surface and is continuous (i.e., liquefied zone = 4th layer from bottom of the FLAC model).2. The liquefied sand is clean (i.e., no fines), mean g

26、rain size D50 of 0.5 mm and the water-table is the same as given in FLAC Model 7.pdf. Assume that the SPT N160 value in the liquefied zone is 10.3. Use the FS versus dytime plot to determine when liquefaction is 100 percent completed in the liquefied zone (i.e., liqtime). Use the same plot to determ

27、ine when liquefaction is starting (i.e., startliq) 4. Use the information given in the class notes to determine the residual friction angle and residual shear modulus of the soil when liquefaction is 100 percent completed.5. For liquefaction in the foundation soil, make the following changes to the

28、model.a. The initial shear modulus prior to liquefaction of the liquefiable zone is 20 MPa with a Poisson ratio of 0.25. This value should degrade to an appropriate residual value, as determined from the Sr/Gr plots in course notes and the G/Gmax curve for sand (Seed and Idriss, upper bound). b. Ass

29、ume the bulk modulus in the potentially liquefied zone changes from its initial value to the bulk modulus of water when liquefaction is fully achieved.c. Assume the friction angle of the liquefiable zone changes from an initial value of 30 degrees to an appropriate residual value when liquefaction i

30、s fully achieved.d. Hysteretic damping should not be applied to the liquefied zone.6. Required Informationa. Contour plot of hysteretic properties (c0 and c1)b. History plot of X-acceleration and base of FLAC model (node 12,1)c. History plot of X-acceleration at base of embankment (node 12,6)d. Hist

31、ory plot of X-acceleration at crest of embankment (node 9,11)e. History plot of X-displacement at the toe of the embankment (node 9,6)f. History plot of X-displacement at the crest of the embankment (node 9,11)g. Vector displacement plot of nodes with contour plot of X-displacement on same ploth. Hy

32、steresis loop plot for zone 9,4i. Hysteresis loop plot for zone 16,4 Modeling Ground Improvement Properties1. For Objective 3, you are to include ground improvement in the FLAC model in the liquefied zone to reduce the displacement of the toe and crest of the embankment to 0.5 m.2. The area replacem

33、ent ratio for the ground improvement can be obtained from the course notes. Fig. 5.24 is appropriate for estimating the required area replacement ratio.3. The required composite friction angle for the remediated zone is calculated from:fcomp = tan -1 mc Ra tan fC + mm (1-Ra) tan fMa. Assume that the

34、 foundation sand matrix soil has a drained friction angle, fM, of 30 degrees. b. Assume that the stone column has a drained friction angle, fC, of 45 degrees.c. For calculating the post-remediation deformation of the embankment, assume that in the remediated zone, the composite friction angle and co

35、mposite shear modulus do not degrade with earthquake cycling.4. The required composite shear modulus for the remediated zone is calculated from:Gcomp = (GC * AC + GM*AM)/Aa. Assume that the foundation sand matrix soil in the liquefied zone (layer 4) has a shear modulus, GM, of 20 MPa. The shear modulus for column, GC, used in analyzing the stone column remediation is 200 MPa. b. For calculating the post-remediation deformation of t