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Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation (2024)

Chapter: APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake

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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
×
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
×
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
×
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
×
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
×
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
×
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
×
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
×
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Suggested Citation:"APPENDIX E-3 Wildlife Liquefaction Array Site: Site Response in the 2012 M 4.9 Hovley Earthquake." National Academies of Sciences, Engineering, and Medicine. 2024. Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation. Washington, DC: The National Academies Press. doi: 10.17226/27537.
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247 APPENDIX E-3 Wildlife Liquefaction Array Site Site Response in the 2012 M 4.9 Hovley Earthquake General This Appendix presents results of numerical modeling of the response of the Wildlife Liquefaction Array (WLA) site in the 2012 M 4.9 Hovley earthquake. The WLA site is representative of a deep soil profile site. The analysis documented herein differs from its counterparts presented in Appendix E-1 and E-2 as follows: (i) input motion [including the Strong Motion (SM), record and a depth at which it was applied in the analysis]; (ii) thickness of the soil profile; and (iii) relative density of the soil that account for the impact of the 1987 M 6.6. Superstition Hills earthquake that liquefied the site. The analysis documented herein was performed in general accordance with the “Guidance for Effective-Stress Site Response Analysis” outlined in Section 8.2 of the main report. Detailed site characterization is provided in Appendix B-1. Model Selection Table E-1 lists the software and constitutive models used to calculate response of the WLA site in the 2012 M 4.9 Hovley earthquake. Detailed information about the selected software is provided in Section 4.2 of the main report. Detailed information about the selected constitutive models (CMs) is provided in Section 4.3 of the main report. Table E-1. Selected Software and CMs SHAKE2000 D-MOD2000 FLAC PLAXIS OpenSeesPL S-I MKZ LE-MC PM4SAND UBCSAND UCSDSAND3 HSsmall PM4SAND UBCSAND U-CLAY2 and U-CLAY1 UCSDSAND3 PM4SAND PM4SILT CM = Constitutive Model; LE-MC = Linear Elastic-Mohr Coulomb; HSsmall = Hardening Soil (with small-strain stiffness); S-I = Seed - Idriss Equivalent-Linear model. See Appendix A-2 for references and detailed information about CMs used herein. Software listed in this table was run either its native 1D mode (SHAKE2000 and D-MOD2000) or in a simulated 1D mode (FLAC, PLAXIS, and OpenSeesPL).

248 2012 M 4.9 Hovley Earthquake and Ground Motions Relevant information about the 2012 M 4.9 Hovley earthquake and ground motions induced at the site are presented in Table E-2. Table E-2. Key Parameters of Input Motion. Earthquake Date and Time M R PGA (E-W) ruIn-Hole (30 m b.g.s.) Surface Hovley August 27, 2012 04:41 GMT 4.9 8 km 0.252 g 0.303 g ≥ 0 . 6 5 M = Moment Magnitude; R = Approximate site-to-source distance; PGA = Peak Ground Acceleration; E-W = East- West; ru = pore water pressure ratio (peak pore water pressure normalized with the initial vertical effective stress). Ground motions, as recorded in the 2012 M 4.9 Hovley earthquake, are shown in Figure E-1. The corresponding acceleration response spectra are shown in Figure E-2. (a) ground surface (b) 30 m below ground surface Figure E-1. Acceleration Histories Recorded in the 2012 M 4.9 Hovley Earthquake: (a) Ground Surface; (b) 30 m Downhole.

249 Figure E-2. Acceleration Response Spectra in the 2012 M 4.9 Hovley Earthquake: (a) Ground Surface; (b) 30 m Downhole. Figure E-3 presents the normalized pore water pressure (PWP) response of the WLA site silty sand layer ("Unit B”) in the 2012 M 4.9 Hovley earthquake. The normalization is with the initial vertical effective stress, and these normalized values are referred to as the PWP ratio (ru). Figure E-3. Normalized Excess PWP Recorded at the WLA Site in the 2012 M 4.9 Hovley Earthquake.

250 Site Exploration and Characterization Relevant information about the re-instrumented WLA site, including site location and layout, and results of site characterization efforts, is provided in the site characterization report that is enclosed as Appendix B-1. Select information is reproduced from Appendix B-1 in Figure E-4. Layers as input in the SRA Model are shown with “gray” lines. (a) Shear Wave Velocity (b) Relative Density (c) Plastic Index Figure E-4. Site Response Model of the Re-Instrumented WLA Site (Layers as Input in the SRA Model are Shown with “ Gray” Lines) Compared to Geotechnical Model of the WLA Site. Further processing of information shown in Figure E-4 is shown in Figure E-5. The shear wave velocity profile shown in Figure E-4(a) was “smoothed” and as such input into the SRA Model. The “smoothed” shear wave velocity profile is indicated by the “magenta” line in Figure E-5.

251 (a) (b) Figure E-5. WLA Site – Interpreted Soil Profile with Location of SM Instruments. Shear Wave Velocity Profiles are documented in Appendix B-1. Advanced Laboratory Testing and Interpretation of the Results Table E-3 summarizes information on the available results of advanced laboratory testing. Detailed information about this testing is provided in Appendix B-1. Table E-3 – Summary of Advanced Laboratory Testing Soil RC and TS CyDSS Note Clay Y N - Silty Sand Y Y (Stress and Strain-Controlled) “Critical” Layer See Appendix C-2 for test results Lean Clay G N Stress-Dependent EPRI (1993) Curve Silt G N Stress-Dependent EPRI (1993) Curve CyDSS test results are available only for silty sand (Stress- and Strain-Controlled). These test results are presented in Appendix C-2. RC = Resonant Column; TS = Torsional Shear; CyDSS = Cyclic Direct Simple Shear; Y = Available and used Herein; N = Not available; G = Generic.

252 Element Testing Table E-4 lists the results of element tests performed and documented in this study, including in Appendix D-2. The CM sub-model testing, i.e., fitting of the modulus reduction and damping curves is documented in Appendix E-1. Given that stress-dependent EPRI (1993) curves were used for Lean Clay and Silt, results from prior CM sub-model testing were available. Program (i.e., SRA software) names are obscured are obscured for administrative reasons. Table E-4 – Summary of Element Testing (Refer to Appendix E-1) Soil SHAKE2000 D-MOD2000 FLAC PLAXIS OpenSeesPL Clay N/A MKZ - - U-CLAY2 Silty Sand N/A MKZ LE-MC HSsmall UCSDSAND3 Lean Clay N/A MKZ - - U-CLAY-1 Silt N/A MKZ - - U-CLAY-1 N/A = Not Applicable (Direct Input of Modulus Reduction and Damping Curves). Select results of the CM sub-model testing are presented in Figures E-6 and E-7. Additional information is presented in Appendices E-1 and D-3. (a) WLA Lean Clay (6.5 m to 15 m) (b) WLA Silt (15 m to 31 m) Figure E-6. CM Sub-Model Testing with the MKZ Model (Program 2). Modulus Reduction and Damping Curves were Developed and/or Assigned as a Part of Site Exploration Effort.

253 (a) WLA Clay (0 - 2.6 m) (b) WLA Silty Sand (2.6 m to 6.5) (c) WLA Lean Clay (6.5 m to 15 m) (d) WLA Silt (15 m to 30 m) Figure E-7. CM Sub-Model Testing with the UCSDSAND3 Model (Program 4). Modulus Reduction and Damping Curves were Developed and/or Assigned as a Part of Site Exploration Effort (Appendix B-1). SRA Model Development The site response analysis model of the WLA site is presented in Figure E-5. It includes idealized soil stratification, groundwater elevation, and an interpreted shear wave velocity profile (“smoothed” in e in Figure E-5(b)). Input motion was applied as a “within” motion in SHAKE2000 and OpenSeesPL analyses. In D-MOD2000, the transmitting base option was used. In FLAC, the applied acceleration history option was used. The basic material properties, i.e., material properties that are not software-specific are provided for each layer in the Attachment. System Testing Figure E-8 documents the process of system testing (i.e., model testing at the soil profile level) for Program 2 and Program 4 (program names are obscured are obscured for administrative reasons). Upon completion of the system testing, for both programs, the Rayleigh damping

254 model parameters assessed were fine-tuned in an iterative process. The fine-tuning was performed with the Hovley in-hole record scaled to Peak Ground Acceleration (PGA) of 0.05 g. The results of the fine-tuning, i.e., Rayleigh damping model parameter (n) and the target viscous damping (D) correspond to spectra indicated in “black” in Figure E-8. Note that the n = 5 and D = 0.5% pair provides the best match for both programs and all three CMs considered. (a) Program 2 (MKZ) (b) Program 4 (UCSDSAND3) (c) Program 4 (PM4SAND) Figure E-8. System Testing with Program 2 (MKZ) and Program 4 (UCSDSAND3 and PM4SAND).

255 Results - Ground Surface Response The Total Stress Analysis (TSA) was performed first to establish a Total Stress (TS) nonlinear reference model. Results of the TSA with select software are presented in Figure E-9. The recorded ground surface response is shown for reference. (a) Program 1 (S-I) (b) Program 2 (MKZ) (c) Program 3 (LE-MC) (d) Program 5 (HSsmall) Figure E-9. Results of TSA – Recorded and Calculated Ground Surface Response with Select Software and CMs. The Effective Stress Analysis (ESA) was performed without and with excess PWP dissipation. The results of ESA with excess PWP dissipation allowed are presented in Figure E-10. The recorded input motion and recorded ground surface response are shown for reference.

256 (a) Program 2 (MKZ) (b) Program 3 (PM4SAND) (c) Program 3 (UBCSAND) (d) Program 3 (UCSDSAND3) (e) Program 5 (PM4SAND) (f) Program 5 (UBCSAND)

257 (g) Program 4 (UCSDSAND3) (h) Program 4 (PM4SAND) Figure E-10. Results of ESA – Recorded and Calculated Ground Surface Response with Select Software and CMs. Results - Response within Soil Profile Figure E-11 shows selected results of the TSA in a profile view. Input PGA (recorded at approximately 30 m b.g.s.) and PGA recorded within the profile are shown for reference along with inferred peak stress and strain response. This inferred peak stress and strain response is reproduced from the main report as Figure E-15(i). The calculated and inferred shear stress are normalized with the initial vertical effective stress. (a) Peak Ground Acceleration (b) Normalized Peak Shear Stress

258 (c) Peak Shear Strain Figure E-11. Results of TSA - Recorded and Calculated Response. Figure E-12 shows selected results of TSA presented in the form of stress-strain loops calculated in the middle of the submerged portion of the “critical” layer. (a) Program 2 (MKZ) (b) Program 5 (HSSmall) Figure E-12. Results of TSA - Calculated Stress-Strain Response at 6 m b.g.s. Figure E-13 shows selected results of the ESA in a profile view (results with excess PWP dissipation allowed). Input PGA (recorded at approximately 30 m b.g.s.) and PGA recorded within the profile are shown for reference along with inferred peak stress and strain response. This inferred peak stress and strain response is reproduced from the main report as Figure E- 15(i). An excess PWP response is presented herein in the form of normalized PWP ratio (ru). Both ru and calculated and inferred shear stress are normalized with the initial vertical effective stress.

259 (a) Peak Ground Acceleration (b) Normalized Peak Shear Stress (c) Peak Shear Strain (d) Normalized Excess PWP Figure E-13. Results of ESA - Recorded and Calculated Response. Figure E-14 shows select results of ESA as history of ru buildup. The recorded acceleration history is shown for reference.

260 (a) (b) Figure E-14. Effective Stress Response of “ Critical” Layer: (a) Calculated Normalized Excess PWP at 3.5 m b.g.s.; (b) Input Motion (Shown for Reference). Figure E-15 shows selected results of ESA presented in the form of stress-strain loops calculated in the middle of the submerged portion of the “critical” layer. Figure E-15(i) shows stress-strain loop as inferred from the interpretation of Newton’s second law, closely spaced SM records, and unit weight of soil between the SM instruments (i.e., a proxy for mass density).

261 (a) Program 2 (MKZ) (b) Program 3 (PM4SAND) (c) Program 3 (UBCSAND) (d) Program 3 (UCSDSAND3) (e) Program 5 (PM4SAND) (f) Program 5 (UBCSAND) (g) Program 4 (UCSDSAND3) (h) Program 4 (PM4SAND) (i) Inferred from SM Records Figure E-15. Results of ESA - Calculated Stress-Strain Response at 6 m b.g.s. Reference EPRI (1993), “Guidelines for Site Specific Ground Motions,” T echn i cal Report T R-1 0 2293 , Electric Power Research Institute, Palo Alto, California, Vols. 1-5.

262 APPENDIX E-3 Attachment Site Response Model of the Re-Instrumented WLA Site Layer No. Soil Type Thickness (m) Depth* (m) Vs (m/s) ksat (m/s) γ (kN/m3) 1 WSA 0.73 0.37 73 3.05E-06 17.0 2 WSA 0.77 1.12 85 3.05E-06 17.0 3 WSA 0.63 1.82 94 3.05E-06 18.9 4 WSA 0.85 2.56 107 3.05E-04 18.9 5 WSB 0.98 3.47 119 3.05E-04 19.4 6 WSB 1.37 4.65 137 3.05E-04 19.4 7 WSB 1.46 6.07 158 3.05E-04 19.4 8 Sand, D: 6-15 m (EPRI 1993) 1.43 7.51 168 3.05E-06 19.4 9 Sand, D: 6-15 m (EPRI 1993) 1.83 9.14 183 3.05E-06 19.4 10 Sand, D: 6-15 m (EPRI 1993) 1.83 10.97 195 3.05E-06 19.4 11 Sand, D: 6-15 m (EPRI 1993) 2.13 12.95 209 3.05E-06 19.4 12 Sand, D: 6-15 m (EPRI 1993) 2.13 15.09 216 3.05E-06 19.4 13 Sand, D: 16-37 m (EPRI 1993) 2.13 17.22 226 3.05E-06 19.4 14 Sand, D: 16-37 m (EPRI 1993) 2.13 19.35 232 3.05E-06 19.4 15 Sand, D: 16-37 m (EPRI 1993) 2.13 21.49 235 3.05E-06 19.4 16 Sand, D: 16-37 m (EPRI 1993) 2.13 23.62 239 3.05E-06 19.4 17 Sand, D: 16-37 m (EPRI 1993) 1.22 25.30 241 3.05E-06 19.4 18 Sand, D: 16-37 m (EPRI 1993) 1.52 26.67 244 3.05E-06 19.4 19 Sand, D: 16-37 m (EPRI 1993) 1.52 28.19 247 3.05E-06 19.4 20 Sand, D: 16-37 m (EPRI 1993) 2.44 30.17 250 3.05E-06 19.4 Dw (m) H (m) (Vs)avg (m/s) Ts (s) fs (Hz) 1.50 31.39 200.1 0.628 1.59 (1) Depth* = depth of middle of the layer; Vs = soil shear wave velocity; k = saturated hydraulic conductivity; γ = saturated or wet unit weight of soil; Dw = depth of groundwater table; H = total thickness of soil profile; (Vs)avg = weighted average shear wave velocity; T = 1st mode period; fs = 1st mode frequency.

263 Parameters and Coefficients of the MKZ Model (Program 2) Layer No. MKZ - Nonlinear Stress-Strain MKZ - PWP Dissipation γr (-) β s K2 m n 1 0.00100 1.70 0.67 - - - 2 0.00100 1.70 0.67 - - - 3 0.00100 1.70 0.67 0.0025 0.43 0.62 4 0.00100 1.70 0.67 0.0025 0.43 0.62 5 0.00100 1.50 0.68 0.0025 0.43 0.62 6 0.00100 1.50 0.68 0.0025 0.43 0.62 7 0.00100 1.50 0.68 0.0025 0.43 0.62 8 0.00032 0.65 0.90 0.0025 0.43 0.62 9 0.00032 0.65 0.90 0.0025 0.43 0.62 10 0.00032 0.65 0.90 0.0025 0.43 0.62 11 0.00032 0.65 0.90 0.0025 0.43 0.62 12 0.00032 0.65 0.90 0.0025 0.43 0.62 13 0.00032 0.45 0.90 0.0025 0.43 0.62 14 0.00032 0.45 0.90 0.0025 0.43 0.62 15 0.00032 0.45 0.90 0.0025 0.43 0.62 16 0.00032 0.45 0.90 0.0025 0.43 0.62 17 0.00032 0.45 0.90 0.0025 0.43 0.62 18 0.00032 0.45 0.90 0.0025 0.43 0.62 19 0.00032 0.45 0.90 0.0025 0.43 0.62 20 0.00032 0.45 0.90 0.0025 0.43 0.62 Layer No. MKZ - PWP Generation ν f P F S γtv (%) 1 - - - - - - 2 - - - - - - 3 3.5 2 1.04 2.6 1.7 0.02 4 3.5 2 1.04 2.6 1.7 0.02 5 5 2 1.04 2.6 1.7 0.02 6 5 2 1.04 2.6 1.7 0.02 7 5 2 1.04 2.6 1.7 0.02 8 3.5 2 1.04 2.6 1.7 0.02 9 3.5 2 1.04 2.6 1.7 0.02 10 3.5 2 1.04 2.6 1.7 0.02 11 3.5 2 1.04 2.6 1.7 0.02 12 3.5 2 1.04 2.6 1.7 0.02 13 3.5 2 1.04 2.6 1.7 0.02 14 3.5 2 1.04 2.6 1.7 0.02 15 3.5 2 1.04 2.6 1.7 0.02 16 3.5 2 1.04 2.6 1.7 0.02 17 3.5 2 1.04 2.6 1.7 0.02 18 3.5 2 1.04 2.6 1.7 0.02 19 3.5 2 1.04 2.6 1.7 0.02 20 3.5 2 1.04 2.6 1.7 0.02 Rayleigh Damping (2) 𝛂𝛂𝐫𝐫 𝛃𝛃𝐫𝐫 0.0834 1.67e-4 Rayleigh damping coefficients, 𝛂𝛂𝐫𝐫, and 𝛃𝛃𝐫𝐫, are calculated by using the period of the soil layer as 0.628 s, the viscous damping, 𝛏𝛏, as %0.5, and the 𝒏𝒏 value as 5.

264 Parameters and Coefficients of the UCSDSAND3 Model (OpenSees) Layer No. CM Parameters of modulus reduction curve 𝒅𝒅 𝑷𝑷𝒓𝒓′(kPa) 𝝋𝝋 (°) 𝒔𝒔𝟎𝟎 (kPa) 𝜸𝜸𝒎𝒎𝒎𝒎𝒎𝒎,𝒓𝒓(%) 𝑵𝑵𝒀𝒀𝒀𝒀 1 U-Clay 1 0.0 100 0 4 10 20 2 U-Clay 1 0.0 100 0 5 10 20 3 U-Clay 1 0.0 100 0 8 10 20 4 U-Sand3 0.0 35 0 10.5 10 20 5 U-Sand3 0.0 40 30 1.5 10 20 6 U-Sand3 0.0 60 30 1.5 10 20 7 U-Sand3 0.0 80 30 4 10 20 8 U-Clay 1 0.0 100 0 35 10 20 9 U-Clay 1 0.0 100 0 35 10 20 10 U-Clay 1 0.0 100 0 35 10 20 11 U-Clay 1 0.0 100 0 35 10 20 12 U-Clay 1 0.0 100 0 35 10 20 13 U-Clay 1 0.0 100 0 70 10 20 14 U-Clay 1 0.0 100 0 70 10 20 15 U-Clay 1 0.0 100 0 70 10 20 16 U-Clay 1 0.0 100 0 70 10 20 17 U-Clay 1 0.0 100 0 70 10 20 18 U-Clay 1 0.0 100 0 70 10 20 19 U-Clay 1 0.0 100 0 70 10 20 20 U-Clay 1 0.0 100 0 70 10 20 Layer No. Parameters for generation of PWP Soil Stiffness 𝝋𝝋𝑷𝑷𝑷𝑷 (°) 𝒄𝒄𝒎𝒎 𝒄𝒄𝒃𝒃 𝒄𝒄𝒄𝒄 𝒄𝒄𝒅𝒅 𝒄𝒄𝒆𝒆 𝝂𝝂 𝑩𝑩𝒓𝒓 (MPa) 𝑮𝑮𝒎𝒎𝒎𝒎𝒎𝒎 (MPa) 1 - - - - - - 0.40 43.3 9.3 2 - - - - - - 0.40 58.9 12.6 3 - - - - - - 0.40 80.3 17.2 4 - - - - - - 0.30 47.5 21.9 5 20.10 0.03 5.00 0.20 16.00 2.00 0.30 60.4 27.9 6 20.10 0.03 5.00 0.20 16.00 2.00 0.30 80.5 37.1 7 20.10 0.03 5.00 0.20 16.00 2.00 0.40 231.4 49.6 8 - - - - - - 0.40 258.9 55.5 9 - - - - - - 0.40 308.1 66.0 10 - - - - - - 0.40 350.6 75.1 11 - - - - - - 0.40 401.6 86.1 12 - - - - - - 0.40 431.5 92.5 13 - - - - - - 0.40 468.7 100.4 14 - - - - - - 0.40 494.4 105.9 15 - - - - - - 0.40 507.5 108.7 16 - - - - - - 0.40 527.4 113.0 17 - - - - - - 0.40 534.2 114.5 18 - - - - - - 0.40 547.8 117.4 19 - - - - - - 0.40 561.6 120.3 20 - - - - - - 0.40 575.5 123.3 Layer No. 𝒌𝒌𝒔𝒔𝒎𝒎𝒔𝒔 (m/s) 𝑩𝑩𝒇𝒇(GPa) 𝑩𝑩𝒆𝒆(GPa) 𝝆𝝆 (Mg/m 3) Parameters for soil dilation 𝒅𝒅𝒎𝒎 𝒅𝒅𝒃𝒃 𝒅𝒅𝒄𝒄 1 1.00.E-04 2.20 4.40 1.73 - - -

265 2 1.00.E-04 2.20 4.40 1.73 - - - 3 1.00.E-04 2.20 4.40 1.93 - - - 4 1.00.E-03 2.20 4.40 1.93 - - - 5 1.00.E-04 2.20 4.40 1.97 0.15 3 -0.2 6 1.00.E-04 2.20 4.40 1.97 0.15 3 -0.2 7 1.00.E-04 2.20 4.40 1.97 0.15 3 -0.2 8 1.00.E-05 2.20 4.40 1.97 - - - 9 1.00.E-05 2.20 4.40 1.97 - - - 10 1.00.E-05 2.20 4.40 1.97 - - - 11 1.00.E-05 2.20 4.40 1.97 - - - 12 1.00.E-05 2.20 4.40 1.97 - - - 13 1.00.E-05 2.20 4.40 1.97 - - - 14 1.00.E-05 2.20 4.40 1.97 - - - 15 1.00.E-05 2.20 4.40 1.97 - - - 16 1.00.E-05 2.20 4.40 1.97 - - - 17 1.00.E-05 2.20 4.40 1.97 - - - 18 1.00.E-05 2.20 4.40 1.97 - - - 19 1.00.E-05 2.20 4.40 1.97 - - - 20 1.00.E-05 2.20 4.40 1.97 - - - 𝑑𝑑 = pressure dependent coefficient; 𝑃𝑃𝑟𝑟′ = reference mean effective pressure; 𝜑𝜑 = model friction angle; 𝑠𝑠0 = model cohesion; 𝛾𝛾𝑚𝑚𝑚𝑚𝑚𝑚,𝑟𝑟 = maximum shear strain at reference pressure; 𝑁𝑁𝑌𝑌𝑌𝑌 = number of yield surface; 𝜑𝜑𝑃𝑃𝑃𝑃 = phase transformation angle; 𝑐𝑐𝑚𝑚, 𝑐𝑐𝑏𝑏, 𝑐𝑐𝑐𝑐, 𝑐𝑐𝑑𝑑, 𝑐𝑐𝑒𝑒 = contraction parameters; 𝜈𝜈 = Poisson’s ratio; 𝐵𝐵𝑟𝑟 = bulk modulus; 𝐺𝐺𝑚𝑚𝑚𝑚𝑚𝑚 = small-strain shear modulus; 𝑘𝑘𝑠𝑠𝑚𝑚𝑠𝑠 = soil permeability; 𝐵𝐵𝑓𝑓 = bulk modulus of water; 𝐵𝐵𝑒𝑒 = combined bulk modulus; 𝜌𝜌 = soil density; 𝑑𝑑𝑚𝑚, 𝑑𝑑𝑏𝑏, 𝑑𝑑𝑐𝑐 = soil dilation parameters. Rayleigh damping parameters: 𝜶𝜶𝒓𝒓 = 0.08 and 𝜷𝜷𝒓𝒓 = 0.00017.

266 Parameters and Coefficients of the PM4SAND Model (Program 4) Layer No. CM 𝝆𝝆 (Mg/m3) Primary parameter Fluid properties 𝒀𝒀𝒖𝒖(𝒌𝒌𝑷𝑷𝒎𝒎) 𝑮𝑮𝟎𝟎 𝒉𝒉𝒑𝒑𝒑𝒑 𝒌𝒌𝒔𝒔𝒎𝒎𝒔𝒔 (cm/s) 𝝆𝝆𝒘𝒘 (Mg/m3) 𝑩𝑩𝒆𝒆(GPa) 1 PM4SILT 1.73 36.3 450 1.20 1.00E-04 1.00 2.20 2 PM4SILT 1.73 36.3 358 1.20 1.00E-04 1.00 2.20 3 PM4SILT 1.93 25.1 420 1.20 1.00E-04 1.00 2.20 4 PM4SILT 1.93 25.1 454 1.20 1.00E-04 1.00 2.20 5 PM4SAND 1.97 N/A 509 0.44 1.00E-04 1.00 2.20 6 PM4SAND 1.97 N/A N/A 0.44 1.00E-04 1.00 2.20 7 PM4SAND 1.97 N/A N/A 0.44 1.00E-04 1.00 2.20 8 PM4SILT 1.97 30.6 622 1.20 1.00E-05 1.00 2.20 9 PM4SILT 1.97 30.6 647 1.20 1.00E-05 1.00 2.20 10 PM4SILT 1.97 30.6 657 1.20 1.00E-05 1.00 2.20 11 PM4SILT 1.97 30.6 672 1.20 1.00E-05 1.00 2.20 12 PM4SILT 1.97 30.6 654 1.20 1.00E-05 1.00 2.20 13 PM4SILT 1.97 30.6 651 1.20 1.00E-05 1.00 2.20 14 PM4SILT 1.97 30.6 635 1.20 1.00E-05 1.00 2.20 15 PM4SILT 1.97 30.6 608 1.20 1.00E-05 1.00 2.20 16 PM4SILT 1.97 30.6 592 1.20 1.00E-05 1.00 2.20 17 PM4SILT 1.97 30.6 579 1.20 1.00E-05 1.00 2.20 18 PM4SILT 1.97 30.6 570 1.20 1.00E-05 1.00 2.20 19 PM4SILT 1.97 30.6 562 1.20 1.00E-05 1.00 2.20 20 PM4SILT 1.97 30.6 543 1.20 1.00E-05 1.00 2.20 𝜌𝜌 = soil density; 𝑆𝑆𝑢𝑢 = undrained shear strength; 𝐺𝐺0 = shear modulus coefficient; ℎ𝑝𝑝𝑝𝑝 = contraction rate parameter; 𝑘𝑘𝑠𝑠𝑚𝑚𝑠𝑠 = permeability; 𝜌𝜌𝑤𝑤 = water density; 𝐵𝐵𝑒𝑒 = soil and water combined bulk modulus. Rayleigh damping parameters: 𝜶𝜶𝒓𝒓 = 0.04 and 𝜷𝜷𝒓𝒓 = 0.0004.

Next: APPENDIX E-4 Owi Island Site Case Study: Site Response in the 1985 M 6.2 Chiba-Ibaragi Earthquake »
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 Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation
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There are many seismic site response analysis programs that operate in either the time domain or the frequency domain. These programs are available as public domain software, as commercial products, and/or through direct contact with the authors.

NCHRP Web-Only Document 383: Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation, from TRB's National Cooperative Highway Research Program, is supplemental to NCHRP Research Report 1092: Seismic Site Response Analysis with Pore Water Pressure Generation: Guidelines.

Supplemental to the document is an Implementation Plan.

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