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191 APPENDIX D-2 Element Tests â WLA Site Strain- and Stress-Controlled Undrained Cyclic Direct Simple Shear Tests Matched with UCSDSAND3 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. Following completion of this study, Wildlife Liquefaction Array (WLA) site is one of few sites, including soil liquefaction case history sites, where much, if not all the required information, is available. This required information is presented in a series of Appendices of this study. Information relevant for element testing of the WLA Site Silty Sand (âcriticalâ Layer) is presented in an abbreviated form below. Site Characterization â WLA âUnit Bâ (Silty Sand) The WLA is in a relatively recent (approximately 115-year-old) flood plain. The soil profile at the site consists of an approximately 2.6 to 2.7 m thick layer of clay of variable plasticity (CL to CH) underlain by a liquefiable silty sand layer (SM). Thickness of the silty sand layer, referred to in Appendix B-1 and herein as âUnit B,â ranges from approximately 3.9 m to 4.3 m. Below the silty sand layer is an approximately 5.4 to 5.5 m thick layer of lean clay (CL) underlain by a âdeepâ layer of silt (approximately 90 m or more in thickness). Information that follows refers to the âUnit Bâ (silty sand). âUnit Bâ at the WLA site is characterized in Figures D-1 and D-2 and in Table D-1. The grain size distribution curve, reproduced from Appendix B-1 and representative of the âintactâ sample, is shown in Figure D-1. Comparison with boundaries of most liquefiable soils identified by Tsuchida (1970) is provided for reference, only. Other relevant information about this material, including select Standard Penetration Test (SPT) results and its interpretation in terms of relative density, Dr, is shown in Figure D-2.
192 Figure D-1. Grain Size Distribution of the WLA Site Silty Sand (Test on â Intactâ Sample after Cyclic Direct Simple Shear (CyDSS) Test) Compared to the Boundaries of Most Liquefiable Soils. (a) (b) Figure D-2. Interpreted Results of In-Situ Testing and Location of Specimen for CyDSS Test. SPT = Standard Penetration Test; (N1)60 = Standardized and Normalized SPT Blow Count.
193 Representative Dr = 69%, evaluated from Standardized and Normalized SPT Blow Count (N1)60 = 23 based upon the Idriss and Boulanger (2008) correlation, is listed in Table D-1 along with a range of shear wave velocity measurements. Table D-1. Summary and Interpretation of SPT and sCPT Soundings in the â Critical Layerâ Parameter / Property Range Average Standardized Normalized SPT Blow Count (N1)60 4 â 26 (39) 23 Shear Wave Velocity, Vs 74 â 219 m/s 147 m/s Relative Density, Dr 29 - 75 69 (Boundary of Medium Dense to Dense Sand) Note: The âCriticalâ layer (âUnit Bâ) is approximately 4.0- m thick saturated silty sand layer that extends from a depth of about 2.6 to 6.5 m b.g.s. (Figure D-2). Range of Dr was estimated based on the results of SPT sounding ((N1)60 = 22 (see Figure D-2) using the Idriss and Boulanger (2008) correlation. Two extreme blow counts of (N1)60 = 39 (see Figure D-2) were not included in averaging. Modulus Reduction and Damping Modulus reduction and damping curves for the WLA site liquefiable âUnit Bâ (Silty Sand) were developed for the purposes of this study using the results of advanced laboratory testing, in- situ testing, and back-analysis of strong motion records at the site. Detailed information is presented in Appendix B-1. Curves used in this study are shown with a thick red line in Figure D-3. (a) (b) Figure D-3. Interpreted Modulus Reduction and Damping Curves for the WLA Site Silty Sand (Developed as a part of this Study; see Figure 6-2 of Matasovic et al., 2023 for Legend).
194 Undrained Testing â Strain-Controlled The CyDSS testing was performed on âIntactâ samples of silty sand. Typically, because âintactâ sample is destroyed by testing, multiple samples are required (one per strain level). Because number of available âintactâ samples of silty sand was small (two samples), staged testing was performed. The staging was successive, as schematically illustrated in Figure D-4(a). The corresponding excess cyclic PWP response is shown in Figure D-4(b). (a) (b) Figure D-4. Strain-Controlled CyDSS Test on â Intactâ Sample of WLA Site Silty Sand: (a) Applied Shear Strain History; and (b) Excess PWP Response (Normalized PWP Ratio, ru Plot). Undrained Testing â Stress-Controlled The stress-controlled testing was performed on the second âintactâ sample of silty sand recovered from the same Shelby tube sample that was tested in a strain-controlled manner. Test Cyclic Shear Stress Ratio, CSR was 0.2. The test was stopped when the second-cycle shear strain approached device limits, i.e., exceeded 3.75%. The test results are shown in Figure D-5.
195 (a) (b) Figure D-5. Stress-Controlled CyDSS Test on â Intactâ Sample of WLA Site Silty Sand: (a) Applied Shear Stress Time History; and (b) Excess PWP Response (Time History of Normalized PWP Ratio, ru). Figure D-5 reveals that the tested sample liquefied in the first stress cycle. An additional âintactâ sample was not available to repeat this CyDSS test at a lower CSR and delay soil liquefaction to subsequent cycles. Element Test â UCSDSAND3 CM Sub-Model The first step of element testing, including of the element testing with UCSDSAND3, is fitting of the modulus reduction and damping curves. When using the UCSDSAND3, this is done with the Khosravifar et al. (2018) sub-model. This is a relatively simple part of the main CM (i.e., of UCSDSAND3) that is based upon modified hyperbolic model. The modification adds curve fitting parameters that allow for a closer fit of the modulus reduction curves (Note: The Khosravifar sub-model does not have a provision for fitting of damping.) Parameters of the Khosravifar et al. (2018) sub-model include Gmax, γmax,r, d, Pr, Φ, and S0. They are listed in Table D-2 and are explained in the cited reference. The Khosravifar et al. (2018) sub-model was coded in a spreadsheet which was used, in an iterative manner, for fitting of target modulus reduction curves. The target curves were developed for the WLA Site Silty Sand as a part of this study and are shown in Figure D-3. The final result of the iterative process is shown in Figure D-6.
196 (a) (b) Figure D-6. Element Test with UCSDSAND3 â Matching of the WLA Site Silty Sand Curves with the Khosravifar et al. (2018) CM Sub-Model. Element Test â UCSDSAND3 Main Model (Strain-Controlled) The UCSDSAND3 documentation (Khosravifar et al., 2018) offers a choice of four generic material (parameter) sets: (i) âvery loose and loose sandâ (0 < Dr 40%);â (ii) âmedium dense sandâ (40 < Dr 60%);â (iii) âdense sandâ (60 < Dr 80%); and (iv) âvery dense sandâ (80 < Dr 100%). Processed information, as presented in Appendix B-1 and reproduced in Table D-1 herein, indicates that silty sand of the âCriticalâ layer is âmedium denseâ (average (N1)60 = 22; average Dr = 69%). Therefore, the UCSDSAND3 model parameters were selected accordingly. These model parameters are reproduced from Khosravifar et al. (2018) in Table D-2 (in âgreenâ). Table D-2. WLA Silty Sand - Input Parameters of the UCSDSAND3 Model (Strain-Controlled) Model Parameter Value Model Parameter Value Density, ðð (ðð ) 2,018(2,030) Small-strain shear modulus at reference pressure, ðºðºðððððð,ðð( ðð ) 88.3 (17.5) Bulk modulus at a reference pressure, ðµðµðð( ðð ) 235.8 (45.6) Pressure dependence coefficient, ðð 0.5 (0.001) Maximum shear strain at a reference pressure, ð¾ð¾ðððððð,ðð (%) 10 (10) Model friction angle, (degree) 34 (30) Model cohesion, 0 (ðððð ) 1.73 (0.01) Reference mean effective pressure, ðððð� (ðððð ) 101 (38) Phase transformation angle, ðððð(ððegree) 28.9 (25.0) Contraction coefficient, ðððð 0.0071 (0.008) Contraction coefficient, ðððð 1.6 (3.0) Contraction coefficient, ðððð 0.54 (0.4) Contraction coefficient, ðððð 5.92 (9.0) Contraction coefficient, ðððð -0.7 (0.0) Dilation coefficient, ðððð 0.405 (0.5) Dilation coefficient, ðððð 3.0 (3.0)
197 Dilation coefficient, ðððð -0.37 (-0.3) Liquefaction parameter 1 1.0 (1.0) Liquefaction parameter 2 0.0(0.0) Number of yield surface, ðð 20 (20) Atmospheric pressure, ðððð (ðððð ) 100 (100) Permeability (cm/s) 10-6 (10-6) Note: The values shown in this Table in âgreenâ are representative of a generic set of parameters. The values presented in âblueâ and listed in parentheses correspond to the âbest fitâ parameters developed herein. Figure D-7 shows comparison of measured and calculated histories of shear strain (measured and calculated coincide; calculated shown on top), shear stress, and excess PWP histories. The calculations are performed with a set of generic parameters listed in Table D-2. (a) (b)
198 (c) Figure D-7. WLA Site Silty Sand (CyDSS Test on â Intactâ Specimen). Comparison of Measured and Calculated: (a) Shear Strain History (Staged Loading); (b) Shear Stress Response; and (c) Excess PWP. NCM = Not Calibrated Model. Figure D-7 reveals a significant mismatch between recorded and calculated shear stress response. The calculated excess PWP builds faster than in the experiment but, at the end, correctly matches experimentally-observed soil liquefaction (ru ⥠0.95). Better match between recorded and calculated can be obrtained by model calibration. This is an iterative proces in which model parameters are adjusted until satisfactory fit is obtained. The results of the first 15 iterations on material parameters are presented in Figure D-8. The corresponding (i.e., âadjustedâ) set of CM parameters is presented in âblueâ (parentheses) in Table D-2. (a)
199 (b) (c) Figure D-8. WLA Site Silty Sand. Comparison of Measured and Calculated: (a) Shear Strain History (Staged Loading); (b) Calculated Shear Stress Response; and (c) Calculated Excess PWP Response. CM = Calibrated Model. Figure D-8 shows comparison of measured and calculated histories of shear strain (measured and calculated coincide; calculated values are shown on top), shear stress, and excess PWP histories. The comparison is representative of 15 iterations on material parameters. Even after 15 iterations, there is a significant discrepancy between measured and calculated shear stress response. The agreement between measured and calculated is very good for shear strains of 0.01% and 0.0316% that are representative of small-strain response. Agreement at larger strains could be achieved in successive iterations. The match between measured and calculated excess PWP response is âvery good,â however. Figure D-9 shows comparison of measured and calculated stress-strain response as an evolution of cyclic loops.
200 (a) (b) (c) (d) (e) (f) Figure D-9. WLA Site - Comparison of Measured and Calculated Stress-Strain Response in a Staged CyDSS Strain-Controlled Test on â Intactâ Specimen of Silty Sand. Consistent with information shown in Figure D-9(b), the discrepancy between measured and calculated shear stress response is significant at shear strains of 0.316% and 1.0%. The discrepancy affects damping which is proportional to the area of loops. Calculated response is âoverdamped.â
201 Figure D-10 compares recorded stress-strain response to results of calculations (element test). Figure D-10(a) is a comparison for generic material (model) parameter set (Not Calibrated Model; NCM). Figure D-10(b) is a comparison for calibrated material (model) parameter set (Calibrated Model; CM) (15 iterations). Figure D-10 reveals that notably better match can be achieved if model parameters are calibrated (i.e., if element test is performed). (a) (b) Figure D-10. WLA Site Silty Sand, Strain-Controlled Test. Comparison of Measured and Calculated Stress-Strain Loops: (a) NCM; (b) Calibrated Model (CM). The representation of element test results as a stress-strain response can be deceiving, however. This is because this type of presentation may hide relatively good match in low strain range. Therefore, in addition to this type of presentation, presentation of element test in a form of histories shown in Figures D-7 and D-8 is recommended. Element Test â UCSDSAND3 Main Model (Stress-Controlled) Parameters of the UCSDSAND3 cab also be developed based upon the results of stress- controlled testing. Khosravifar et al. (2018) offer a choice of four generic material (parameter) sets: (i) âvery loose and loose sandâ (0 < Dr 40%);â (ii) âmedium dense sandâ (40 < Dr 60%);â (iii) âdense sandâ (60 < Dr 80%); and (iv) âvery dense sandâ (80 < Dr 100%). Processed information, as presented in Appendix B-1 and reproduced in Table D-1 herein, indicates that silty sand of the âCriticalâ layer is âmedium denseâ (average Dr = 52). Therefore, the UCSDSAND3 model parameters were selected accordingly. These model parameters are reproduced from Khosravifar et al. (2018) in Table D-2 (in âgreenâ).
202 Table D-3. WLA Silty Sand - Input Parameters of the UCSDSAND3 Model (Stress-Controlled) Model Parameter(1), (2) Value Model Parameter(1), (2) Value Density, ðð (ðððð ðð3â ) 2,018 (2,030) Small-strain shear modulus at reference pressure, ðºðºðððððð,ðð(ðððððð) 88.3 (17.5) Bulk modulus at a reference pressure, ðµðµðð(ðððððð) 235.86 (45.6) Pressure dependence coefficient, ðð 0.5 (0.001) Maximum shear strain at a reference pressure, ð¾ð¾ðððððð,ðð (%) 10 (10.0) Model friction angle, ðð (degree) 34.15 (30.0) Model cohesion, ðð0 (ðððððð) 1.73 (0.01) Reference mean effective pressure, ðððð� (ðððððð) 101 (38.0) Phase transformation angle, ðððððð(ððegree) 28.9 (27.0) Contraction coefficient, ðððð 0.0071 (0.04) Contraction coefficient, ðððð 1.6 (4.0) Contraction coefficient, ðððð 0.54 (0.3) Contraction coefficient, ðððð 5.92 (12.5) Contraction coefficient, ðððð -0.7 (1.0) Dilation coefficient, ðððð 0.405 (0.5) Dilation coefficient, ðððð 3.0 (3.0) Dilation coefficient, ðððð -0.37 (-0.3) Liquefaction parameter 1 1.0 (1.0) Liquefaction parameter 2 0.0 (0.0) Number of yield surface, ðððððð 20 (20) Atmospheric pressure, ðððð (ðððððð) 100 (100) Permeability (cm/s) 10-6 (10-6) Note: The values shown in this Table in âgreenâ are representative of a generic set of parameters. The values presented in âblueâ and listed in parentheses correspond to the âbest fitâ parameters developed herein. Figure D-11 shows comparison of measured and calculated histories of shear strain (measured and calculated coincide; calculated shown on top), shear stress, and excess PWP histories. The calculations are performed with a set of generic parameters listed in Table D-3.
203 (a) (b) (c) Figure D-11. Comparison of Measured and Calculated: (a) Applied Shear Stress History; (b) Calculated Shear Strain Response (UCSDSAND3); and (c) Excess PWP. NCM = Not Calibrated Model. Figure D-11 reveals no match between recorded and calculated shear strain response. The calculated excess PWP reaches ru 0.3 while experimental data reval soil liquefaction in the second cycle. Better match between recorded and calculated can be obrtained by model calibration. This is an iterative proces in which model parameters are adjusted until satisfactory fit is obtained. The results of the first five iterations on material parameters are presented in Figure D-12. The corresponding (i.e., âadjusedâ) set of CM parameters is presented in âblueâ (parentheses) in Table D-3.
204 (a) (b) (c) Figure D-12. Comparison of Measured and Calculated: (a) Applied Shear Stress History; (b) Calculated Shear Strain Response (UCSDSAND3); and (c) Excess PWP. CM = Calibrated Model. Figure D-12 shows very good agreement between measured and calculated response (measured and calculated coincide; calculated values are shown on top). Good agreement between measured and calculated is also evident in Figure D-13 which shows progress of element testing with applied cycles of shear stress. There is no âoverdampingâ and the representation of element test results as a stress-strain response is appropriate in this case.
205 (a) (b) (c) Figure D-13. WLA Site - Comparison of Measured and Calculated Stress-Strain Response in a CyDSS Stress-Controlled Test on â Intactâ Specimen of Silty Sand. Figure D-14 compares recorded stress-strain response to results of calculations (element test). Figure D-14(a) is a comparison for generic material (model) parameter set (NCM). Figure D- 14(b) is a comparison for calibrated material (model) parameter set (Calibrated Model; CM) (5 iterations). Figure D-14 reveals that significantly better match can be achieved if model parameters are calibrated (i.e., if element test is performed).
206 (a) (b) Figure D-14. WLA Site Silty Sand, Stress-Controlled Test. Comparison of Measured and Calculated Stress-Strain Loops: (a) NCM; (b) Calibrated Model (CM). References Idriss, I. M. and Boulanger, R. W. (2008), âSoil Liquefaction during Earthquakes,â M on og raph M N O -1 2, Earthquake Engineering Research Institute, Oakland, CA, 261 pp. 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 , Elsevier, Vol. 110, pp. 43â52. Matasovic, N., Witthoeft, A., Borghei, A, and Elgamal, A. (2023), âGuidance on Seismic Site Response Analysis with Pore Water Pressure Generation,â F i n al Report, Prepared for NCHRP Project 12-114 and submitted to Transportation Research Board of the National Academies of Sciences, Engineering and Medicine by Geo-Logic Associates, Inc., Costa Mesa, California. Tsuchida (1970), "Prediction and Countermeasure against the Liquefaction in Sand Deposits,â A b stract of the S em i n ar i n the P ort an d H arb or Research I n sti tute, pp. 3.1 - 3.33 (In Japanese).