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179 APPENDIX D-1 Sample Element Tests â Treasure Island Site Stress-Controlled Cyclic Direct Simple Shear Test on Medium Dense and Dense Sand General To conduct an element test, at a minimum, the following is required: (i) site characterization, including results of in-situ testing that can be correlated to a set of the initial Constitutive Model (CM) parameters; (ii) results of drained testing processed in the form of modulus reduction and damping curves; (iii) results of undrained testing presented in the form of stress- strain loops and excess pore water pressure (PWP) time history. In engineering practice, all of this information is rarely available. In this appendix, results of element testing based upon limited information about the site conditions and undrained soil response are presented. The soil specimen is representative of medium dense to dense silty sand. The specimen was consolidated to a relatively high mean effective stress and sheared under constant shear stress in a Cyclic Direct Simple Shear (CyDSS) device. The corresponding results of drained testing (required to develop the modulus reduction and damping curves), were not available. However, published information, obtained by testing of soil from the same geologic unit was available. The available information served as a basis for element testing with two CM-s (UCSDSAND3 and PM4SAND). For the element test with UCSDSAND3, two approaches were followed: (i) fit the results of CyDSS test using a generic set of material parameters (select five parameters based upon the results of in-situ testing and keep remaining 17 parameters as âdefaultâ values); and (ii) follow the same approach but modify several default parameters until the âbestâ match between model and the CyDSS test results is achieved. The element test with PM4SAND is based upon the first approach. The final CM parameter sets developed herein were used to evaluate the Treasure Island Case history which is presented in Appendix E-4. Site Characterization â Medium Dense Sand Layer (NIS Sand) The site, referred to herein as the NIS site, is in the San Francisco Bay (SFB) area, just north of San Jose, California, and about 50 km southeast of the Treasure Island site. The NIS site geology is typical of the SFB geology and is therefore, similar to its Treasure Island site counterpart. It consists of, from top to bottom: (i) fill and young alluvium; (ii) Young Bay Mud, YBM; (iii) Medium Dense Sand, MDS; and (iii) Old Bay Mud, OBM. The dynamic properties of the YBM and OBM have been developed in the past and are readily available. The dynamic
180 properties of the MDS, including results of CyDSS are not readily available. This is mostly due to the difficulty in sampling below groundwater elevation at depths exceeding 10 m. The MDS at the NIS is characterized in Figure D-1 and Table D-1. The grain size distribution curve is shown in Figure D-1. Comparison with the boundaries of most liquefiable soils identified by Tsuchida (1970) indicates that this silty sand is potentially liquefiable. Other relevant information about his material, including select results of the Cone Penetration Test sounding and measurement of shear wave velocity by means of ReMi, are provided in Table D- 1. Figure D-1. Grain Size Distribution of the MDS at the NIS Site Compared to Boundaries of Most Liquefiable Soils. Table D-1. Measured Properties of the Silty Sand (2.1 m thick Layer; Sample depth = 17.7 m). Parameter / Property Range Average Corrected Cone Resistance 2.6 - 43.4 MPa 21.5 MPa Sleeve Friction Resistance 84.7 - 811.0 kPa 397.7 kPa Shear Wave Velocity 394 â 406 m/s 400 m/s Density of the MDS layer varies significantly (see broad range in cone tip and sleeve friction resistance). An estimate of Standardized SPT blow count (N60) from average cone tip resistance of 21.5 MPa would be correlated to N60 = 48 which would classify this sand as âdenseâ material. Similarly, one would classify this material as âstiff to very dense soilâ based upon an average shear wave velocity of 400 m/s. However, one may argue that, if soil classification based upon average values from Table D-1 is correct, it would not be possible to push a thin-walled Pitcher
181 sampler into this material. Given that it was possible to push a thin-walled Pitcher sampler into this material, a possibility that this material behaves as an MDS was not initially dismissed. It is also possible that the results of shear wave velocity measured by ReMi are overestimated. Resolution of ReMi decreases with depth and so does the accuracy of measurements with this method. Modulus Reduction and Damping Modulus reduction and damping curves are generated by processing results of drained testing in a specific way. Typically, two different test types are required â the Resonant Column (RC) testing to evaluate curves in the small-strain range (10-4% to 10-2%) and (drained) CyDSS or Cyclic Triaxial (CyTX) testing to evaluate these properties beyond 10-2%. The sampling, testing, and data interpretation process is burdensome and is therefore rarely performed on a project- specific basis, and almost never for all layers in the soil profile. Figure D-2 shows modulus reduction and damping curves developed during the Treasure Island site characterization program that followed the 1989 M 6.9 Loma Prieta Earthquake. They are representative of the MDS layer at an approximate depth of 36 m b.g.s. [Approximate mid-height of a 13-m thick MDS layer with shear wave velocity ranging from 234 to 366 m/s (Gibbs, et al. 1992)]. Testing was performed by Hwang and Stokoe (1993) in an RC device on âintactâ specimens of the MDS. (a) (b) Figure D-2. Modulus Reduction and Damping Curves â Medium Dense Silty Sand at the Treasure Island Site by Hwang and Stokoe (1993). Undrained Testing â Stress Controlled âIntactâ specimen of silty sand, extracted by means of Pitcher sampler from a 2.1-m thick layer of silty sand, was available for testing. The approximate sampling depth was 17.7 m below the ground surface. The specimen was tested at the University of California, Berkeley (UCB)
182 Geotechnical Laboratory as a part of a commercial project. The UCB unidirectional CyDSS was used for testing. The testing device is schematically depicted in Figure D-3. Figure D-3. Schematics of UCB Unidirectional CyDSS and Arrangement of Vertical LVDTs (Modified after Cappellaro et al., 2021) The test was a constant volume, stress control test. Dimensions of the specimen and main parameters of the CyDSS test are tabulated in Table D-2. Relevant information (testing matrix) is also provided in Table D-2. Table D-2. Specimen Dimensions and Key Parameters of the CV CyDSS Test on Silty Sand Specimen Diameter 61.2 mm Specimen Height 17.4 mm Initial Vertical Pressure 234.2 kPa Cyclic Shear Ratio 0.207 Uniform Shear Stress Amplitude 48.5 kPa Period of Loading 5.0 s Number of Shearing Cycles 55 Max. Shear Strain 9% CV = Constant Volume (Test); CyDSS = Cyclic Direct Simple Shear (Test) Test CyDSS test results are presented in the form of stress-strain loops in Figures D-4a. The same results are presented in the form of normalized excess PWP buildup in Figures D-4b, where normalization is with the initial vertical effective stress, and in Figure D-4c where the normalization is with the initial mean effective stress assuming Ko = 0.5. Depending upon the normalization stress, the normalized excess PWP is denoted as ru or ru*. As shown in Figure D- 4, cycling was stopped after 55 cycles when the maximum shear strain passed 9%. Significant PWP buildup occurred after 25 cycles (50% of ru; over 100% ru*). The specimen likely liquefied at some point toward the end of the test, likely around 45 cycles.
183 (a) (b) Figure D-4. Results of CyDSS Testing of Dense Silty Sand: (a) Stress-Strain Response; (b) Normalized Excess PWP Response. Element Tests â General Documentation for most CMs includes table of generic material parameters (usually two generic parameter tables, one for stress-controlled testing and an another one for strain- controlled testing), and a spreadsheet-type tool (or tools). Spreadsheet-type tools are also available for comparison of measured and calculated histories, including stress-strain plots and histories of PWP response. Examples of such tools include Khosravifar et al. (2018) and Boulanger et al. (2022) (Python script accessible at PM4SAND c a l i b r a t i o n ) Tabulated values of CM parameters are available for loose sand, MDS, dense sand, and very dense sand (UCSDSAND3), and equations based on relative density and suggested values (PM4SAND). Element Test â UCSDSAND3 The first step of element testing, including of the element testing with UCSDSAND3, is fitting of the modulus reduction and damping curves. When using UCSDSAND3, this is done with the Khosravifar et al. (2018) model. This is a simple CM based upon hyperbolic equation that is modified for closer fit of the modulus reduction and damping curves. Model parameters include Gmax, γmax,r, d, Pr, Φ, and S0. They are listed in Table D-3 and are explained in the cited reference. The Khosravifar et al. (2018) model was coded in a spreadsheet which was used, in an iterative manner, to fit the Hwang and Stokoe (1993) modulus reduction and damping curves reproduced in Figure D-2. The final result of the iterative process is shown in Figure D-5. Note: Khosravifar et al. (2018) do not provide equation for damping.
184 (a) (b) Figure D-5. Element Test with UCSDSAND3 â Matching of Hwang and Stokoe (1993) Generic Curves with the Khosravifar et al. (2018) Model Fitting of the stress-strain and excess PWP curves was performed by calculating the response of a 9-noded quadrilateral plane-strain element1. The fitting (i.e., fitting by means of numerical modeling) was performed in two steps. In the first step, the vertical pressure is gradually applied to the element, while it is allowed to deform in the direction of loading (vertical), and the lateral deformation is constrained. In the second step, the lateral constraints of the top and middle of the element are removed, and shear stress with specific magnitude and frequency is applied to the top of the element. The lateral degree of freedom of nodes at the top and middle of the element is constrained to similar in each layer. In addition, the PWP is allowed to dissipate from the top surface of the element. The UCSDSAND3 documentation by Khosravifar et al. (2018) offers a choice of four generic material sets (sets for âloose sand,â âMDS,â âdense sand,â and âvery dense sandâ). Given the assessed properties of the NIS sand, which range between MDS and dense sand (DS), element test was performed for both. The results are compared to the CyDSS test results in Figure D-6. A closer agreement has been achieved with a generic set of parameters for DS. This includes a match over an extended number of cycles. A calculated shear strain of 9% was reached after 15 cycles for MDS and after 25 cycles for DS. 1 The nodes at the four corners of this element have three degrees of freedom (DOF): two DOF for solid displacements and one degree of freedom for the pore fluid pressure. The other five nodes have two DOF for solid displacement.
185 Figure D-6. Comparison of Measured and Calculated ru for the TI Sand. MDS, DS, and VDS = Generic Sets of Parameters for â Medium Dense,â â Dense,â and â Very Denseâ Sand. The element test continued with the DS generic set of parameters. Following several iterations, an improved agreement between measured and calculated was achieved. The process was monitored in terms of shear strain history, pore pressure history, and shear stress- strain response. The final results are presented in Figures D-7 (excess PWP response) and D-8 (sequential stress-strain response). The corresponding input parameters are presented in Table D-3. Agreement between measured and calculated excess PWP shown in Figure D-6 is not âperfectâ regardless if MDS or DS set of parameters is used. Better agreement can be achieved by modifying other model parameters, as shown in Figures D-7 (excess PWP response) and D-8 (sequential stress-strain response). Table D-3. Input Parameters of the UCSDSAND3 Model Model Parameters(1), (2) Value Model Parameters(1), (2) Value Density, ðð (ðð ) 2,030 Small-strain shear modulus at reference pressure, ðºðºðððððð,ðð( ðð ) 20 Bulk modulus at a reference pressure, ðµðµðð( ðð ) 43.3 Pressure dependence coefficient, ðð 0.0001 (0.5) Maximum shear strain at a reference pressure, ð¾ð¾ðððððð,ðð (%) 10 Model friction angle, (degree) 38 (40) Model cohesion, 0 (ðððð ) 0.01 (1.73) Reference mean effective pressure, ððððâ² (ðððð ) 50 (101) Phase transformation angle, ðððð(ððegree) 24 (30.8) Contraction coefficient, ðððð 0.005 Contraction coefficient, ðððð 1 Contraction coefficient, ðððð 0.6 Contraction coefficient, ðððð 4.6 Contraction coefficient, ðððð -1 Dilation coefficient, ðððð 0.45 Dilation coefficient, ðððð 3 Dilation coefficient, ðððð -0.4 Liquefaction parameter 1 1 Liquefaction parameter 2 0 Number of yield surface, ðð 20 Atmospheric pressure, ðððð (ðððð ) 100 Permeability (m/s) 1e-8 (1) The input parameters were selected based on the generic set of parameters recommended for âDense Sandâ by Khosravifar et al. (2018). Several of the parameters were modified to improve the match between the CM and measurement results. Therefore, two values of the parameters are presented herein. The values in the parentheses are for the generic âdense sand.â The values
186 above values in parentheses represent modification of the generic parameters at the end of iterative process; (2) More information about the input parameters is provided in Khosravifar et al. (2018). Figure D-7. Element Test with UCSDSAND3 â Comparison of Measured and Calculated Normalized Excess PWP Response. (a) (b) (c) (d)
187 (e) (f) Figure D-8. Element Test with UCSDSAND3 â Comparison of Measured and Calculated. Element Test â PM4SAND The element test with PM4SAND, including parameter fitting, was performed in OPENSEES. These parameters were further transferred into FLAC/FISH script (âexample driver #3â) that is provided by the PM4SAND developers and is downloadable from the University of California, Davis website at https://pm4sand.engr.ucdavis.edu/pm4sand-files). The results of this iterative process are shown in Figure D-9. The fitting parameters are listed in Table D-4. (a) (b) Figure D-9. Element Test with PM4SAND â Comparison of Hwang and Stokoe (1993) and Calculated Curves. Fitting of the stress-strain and excess PWP curves was a performed by calculating the response of FLACâs 4-node âsspquadupâ plane-strain element. The nodes at the four corners of the element have three DOFs: two DOFs for solid displacements and one DOF for the pore fluid pressure. The default values and equations suggested by Boulanger and Ziotopoulou (2017) were used for the initial element test. They were further adjusted changed through a
188 successive trial-and-error process to achieve closer match between measured and calculated. The initial and final input parameters are presented in Table D-4. Table D-4. Input Parameters of the PM4SAND Model Model Parameter(1) Value Model Parameter(1) Value Apparent relative density, ð·ð·ðð (%) 67 The variable controls the rate of strain accumulation in undrained cyclic loading, ðððð(-) 1.80 (Internal) Shear modulus coefficient, ðºðº0 (-) 154 Friction angle, ððððððâ² (°) 38 (33) Contraction rate parameter, âðððð(-) 0.35 Poissonâs ratio, ðð0(-) 0.3 Atmospheric pressure, ððð´ð´ (kPa) 101.3 The variable controls the small-strain modulus degradation as cumulative plastic deviator strain, ð¶ð¶ðºðºðºðº(-) 0.14 (2.0) A variable that adjusts the ratio of plastic modulus to the elastic modulus, âðð (-) 0.46 (Internal) The variable controls the rotated dilatancy surface and is applied to reduce the rate under which dilatancy is increasing, ð¶ð¶ðºðºð·ð· (-) 10 (Internal) Minimum void ratio, ðððððððð (-) 0.5 The variable controls the effect that sustained static shear stress have on plastic modulus, ð¶ð¶ðððððð 20.16 (Internal) Maximum void ratio, ðððððððð (-) 0.8 The value of 10 is for quarzitic sand per the recommendations of Bolton (1986), ðð (-) 10.0 The variable that controls dilatancy and the peak effective friction angle, ðððð (-) 0.75 (0.5) The variable which was developed to lower the critical state line to better approximate typical results for direct, simple shear loading, ð ð (-) 1.5 The variable that controls the stress ratio at which contraction transitions to dilation, ðððð (-) 0.1 The variable controls reasonable modeling and numerical stability, ðð (-) 0.01 The variable that controls the dilatancy relationship at the time of initialization, ð´ð´ðððð (-) 1.425 (Internal) The variable controls the minimum value the reduction factor of the elastic moduli can attain during reconsolidation, ð¹ð¹ð ð ðððð,ðððððð 0.17 (0.04) The variable that controls relation the relative density and cyclic strength, ðððððððð (-) 0.7 (Internal) The variable defines the mean effective stress up to which reconsolidation strains are enhanced, ððâ²ð ð ðððð,ðð (kPa) -20.26 The variable controls strain levels at which fabric effects become important, ððð§ð§ (-) 250 - - Note: The values in the parentheses are default parameters; âInternalâ in parentheses denotes a default parameter which is calculated by the CM internally with reference to one or more other input parameters. The values above values in parentheses represent modification of the generic parameters at the end of iterative process Comparison between measured and calculated excess PWP response is presented in Figure D-10.
189 Figure D-10. Element Test with PM4SAND â Comparison of Measured and Calculated Normalized Excess PWP Response. Measured and calculated stress-strain response is compared, for 10-cycle intervals, in Figure D-11. (a) (b) (c) (d)
190 (e) (f) Figure D-11. Element Test with PM4SAND â Comparison of Measured and Calculated. References Boulanger, R.W., Ziotopoulou, K and Oathes, T. (2022), âScripts that produce multiple PM4Sand drivers for different loading paths, batch files for running them in FLAC, and post-processing codes for plotting,â University of California, Davis, Davis, California. Cappellaro, C., Cubrinovski, M., Bray, J.D., Chiaro, G., Riemer, M.F. and Stringer, M.E. (2021), âLiquefaction resistance of Christchurch sandy soils from direct simple shear tests,â S oi l D y n am i cs an d E arthq uak e E n g i n eeri n g , Vol. 141, 10.1016/j.soildyn.2020.106489 Gibbs, J. F., Fumal, T. E., Boore, D. M., and Joyner, W. B. (1992), âSeismic Velocities and Geologic Logs from Borehole Measurements at Seven Strong-Motion Stations that Recorded the 1989 Loma Prieta Earthquake , â Report N o. 92-287, US Geological Survey, Menlo Park, California. Hwang, S. K., and Stokoe, K. H. (1993), âDynamic Properties of Undisturbed Soil Specimens from Treasure Island, California,â G eotechn i cal E n g i n eeri n g Report N o. G R93 -4 , Geotechnical Engineering Center, Civil Engineering Department, University of Texas at Austin, Austin, Texas. Khosravifar, A., Elgamal, A., Lu, J., and Li, J. (2018). âA 3D model for earthquake-induced liquefaction triggering and post-liquefaction response.â S oi l D y n am i cs an d E arthq uak e E n g i n eeri n g , Vol. 110, pp. 43â52. Tsuchida (1970), "Prediction and Countermeasure against the Liquefaction in Sand Deposits," Abstract, S em i n ar i n the P ort an d H arb or Research I n sti tute, p. 3.1 - 3.33 (In Japanese).