National Academies Press: OpenBook

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

Chapter: APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 Earthquake

« Previous: APPENDIX E-6 Treasure Island Site: Site Response in the 1989 M 6.9 Loma Prieta Earthquake
Page 328
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 328
Page 329
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 329
Page 330
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 330
Page 331
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 331
Page 332
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 332
Page 333
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 333
Page 334
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 334
Page 335
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 335
Page 336
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 336
Page 337
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 337
Page 338
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 338
Page 339
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 339
Page 340
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 340
Page 341
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 341
Page 342
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 342
Page 343
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 343
Page 344
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 344
Page 345
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 345
Page 346
Suggested Citation:"APPENDIX E-7 Centrifuge ExperimentResponse of Laminar Box that Simulates WLA Site in M 7.1 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.
×
Page 346

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

328 APPENDIX E-7 Centrifuge Experiment Response of Laminar Box that Simulates WLA Site in M 7.1 Earthquake General The centrifuge experiment designed to fill-in a “void” within the suite of case histories available. In particular, it was designed to simulate response at a relatively shallow liquefiable site shaken by a very strong ground motion. The simulated shallow liquefiable site is a “replica” of the top 7 m of the Wildlife Liquefaction Array (WLA) site, but with shear wave velocity representative of remolded clay and silty sand. The input motion is a motion from the 1949 M 7.1 Western Washington earthquake scaled up to 0.57 g [0.57 g is the upper bound of motion that could be reproduced by a hydraulic actuator at the University of New Hampshire (UNH) centrifuge facility]. As designed and targeted, silty sand liquefied in the centrifuge experiment at a depth of 4.2 m. The excess Pore Water Pressure (PWP) ratio was ru ≥ 0.95. Relevant information about recorded ground motion is provided in Appendix C-1 along with the information on how this motion was modified and about motion that was achieved at the base of the UNH laminar box. Model Selection Table E-1 lists the software and constitutive models used to calculate response of the UNH laminar box in the 1949 M 7.1 Western Washington 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 UCSDSAND3 UCSDCLAY PM4SAND PM4SILT S-I = Seed-Idriss equivalent-linear model; LE-MC = Linear Elastic-Mohr Coulomb (also Total Stress Analysis); HSsmall = Hardening Soil (with small-strain stiffness). See Appendix A-2 for references and detailed information about CMs used herein.

329 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). Input Motion Relevant information about the input motion is presented in graphic and tabulated form below. Table E-2. Key Parameters of Input Motion. Earthquake Date M R Station PGA (EW) Western Washington Earthquake (AKA Olympia Earthquake) April 13, 1949 7.1 68 km Olympia WHTL (Ground Surface) Recorded at Station In Centrifuge Experiment 0.349 g 0.57 g M = Moment Magnitude; R = Approximate site-to-source distance; PGA = Peak Ground Acceleration; EW = East- West (Component): N86E; AKA = also known as. WHTL = Washington Highway Testing Laboratory Ground motions, as recorded in the centrifuge experiment, are shown in Figure E-1(a) – E-1(d). Input motion (i.e., motion at the base of the laminar box) is shown in Figure E-1(e). (a) (b) (c)

330 (d) (e) Figure E-1. Acceleration Histories Recorded in the Centrifuge Experiment. The Olympia WHTL (EW) Motion (Input) was Scaled up to 0.57 g. Acceleration response spectra of the input motion and recorded ground surface response are shown in Figure E-2. Figure E-2. Centrifuge Experiment – Input Motion and Recorded Surface Response. Material Characterization Soil for the experiment (clay and silty sand) was recovered from the WLA. Basic characterization of this soil, including index properties and grain size distribution curves, is provided in Appendix B-1.

331 The WLA clay and silty sand was remolded and placed in the UNH laminar box using the procedures presented in Appendix C-1. The results of advanced testing of remolded samples of these soils, as presented in Appendix C-3, were not usable. Therefore, the results of drained testing from previous studies and the results of undrained CyDSS of testing of intact samples of WLA silty sand were used instead. These results are presented in Appendices B-1 (drained testing) and C-2 (undrained CyDSS testing) 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 C-2. Table E-3 – Summary of Advanced Laboratory Testing Soil RC and TS CyDSS Note Clay Y - - Silty Sand Y Y (Stress and Strain-Controlled) “Critical” Layer See Appendix C-2 for test results (1) 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. RC = Resonant Column; TS = Torsional Shear; CyDSS = Cyclic Direct Simple Shear; Y = Available and used herein. Element Testing Table E-4 lists the results of element tests performed and documented in this study. The element testing of the results of undrained stress-controlled CyDSS testing of medium dense sand is provided in Appendix D-1. The CM sub-model testing, i.e., fitting of the modulus reduction and damping curves is documented herein. Program (i.e., SRA software) names into which CMs are embedded are obscured are obscured for administrative reasons. Table E-4 – Summary of Element Testing Material (Test Type) SHAKE2000 D-MOD2000 FLAC PLAXIS OpenSeesPL Clay N/A MKZ LE-MC HSsmall UCSDCLAY PM4SILT Silty Sand N/A MKZ LE-MC HSsmall UCSDSAND3 PM4SAND N/A = Not Applicable (Direct Input of Modulus Reduction and Damping Curves). Selected results of the CM sub-model testing are presented in Figures E-3 and E-4. Additional information is presented in Appendices D-2 and D-3.

332 (a) Clay (b) Silty Sand Figure E-3. CM Sub-Model Testing with the MKZ Model (Program 2). (a) Clay (b) Silty Sand Figure E-4. CM Sub-Model Testing with the UCSDSAND3 Model (Program 4). The element testing of the results of undrained stress-controlled and strain-controlled CyDSS testing of intact specimen of silty sand is provided in Appendix D-2. Sample element test with UCSDSAND3 and the results of stress-controlled undrained CyDSS testing of an “intact” specimen of silty sand are reproduced as Figure E-5.

333 (a) Stress-Strain (b) Excess PWP Response Figure E-5. WLA Site - Comparison of Measured and Calculated Response. Measured = CyDSS Strain-Controlled Test on “ Intact” Specimen of Silty Sand. (See Appendix D-2). The parameters of constitutive models developed by CM sub-model testing and by element testing are presented in a series of tables enclosed as an attachment. Also included in these tables are program-specific parameters that do not classify as parameters of CMs. These program-specific parameters include initial estimates of viscous damping (SHAKE2000), and Rayleigh damping model parameters (D-MOD2000, FLAC, and OpenSeesPL). Model Development The site response analysis model of the centrifuge experiment is presented in Figure E-6. It includes idealized soil stratification, groundwater elevation, and an interpreted shear wave velocity profile (“blue” line; corresponds to Vs profile as input in the SRA model). (a) (b) Figure E-6. Centrifuge Experiment – Instrumented Laminar Box and Interpreted Soil Profile. Refer for Appendix C-1 for Information on Vs Profile.

334 The input motion was applied as a “within” motion in SHAKE2000 and OpenSeesPL analyses and as rigid boundary in D-MOD2000. 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-7 documents selected system testing (i.e., model testing at the soil profile level) for Programs 2 and 4 (program names are obscured are obscured for administrative reasons). Upon completion of the system testing, for both programs, the Rayleigh damping model parameters assessed were fine-tuned in an iterative process. The Olympia WHTL (EW) Motion was scaled down to 0.05 g prior to the iterations. The Rayleigh damping model parameter (n) and the target viscous damping (D) that were selected for evaluation of the laminar box response to the Olympia WHTL (EW) Motion correspond to spectra indicated in “black.” (a) Program 2 (MKZ) (b) Program 4 (UCSDSAND3)

335 (c) Program 4 (PM4SAND) Figure E-7. System Testing with Program 2 (MKZ) and Program 4 (UCSDSAND3 and PM4SAND). 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 selected software are presented in Figure E-8. The recorded ground surface response is shown for reference. (a) Program 1 (S-I) (b) Program 2 (MKZ)

336 (c) Program 3 (LE-MC) Figure E-8. Results of TSA – Recorded and Calculated Surface Response with Selected Software and CMs. The Effective Stress Analysis (ESA) was performed without and with excess PWP dissipation. The results of ESA with selected software and with excess PWP dissipation allowed are presented in Figure E-9. The recorded ground surface response is shown for reference. (a) Program 2 (MKZ) (b) Program 3 (PM4SAND)

337 (c) Program 3 (UCSDSAND3) (d) Program 5 (PM4SAND) (e) Program 4 (UCSDSAND3) (f) Program 4 (PM4SAND) Figure E-9. Results of ESA – Recorded and Calculated Surface Response with Selected Software and CMs. Response within Soil Profile Figure E-10 shows selected results of the TSA in a profile view. Input PGA (applied at the base of 7 m high laminar box) and PGA recorded within the model profile are shown for reference along with inferred peak stress and strain response. This inferred peak stress and strain response is reproduced from Figure E-14(g). The calculated and inferred shear stress are normalized with the initial vertical effective stress.

338 (a) Peak Ground Acceleration (b) Normalized Peak Shear Stress (c) Peak Shear Strain Figure E-10. Results of TSA - Recorded and Calculated Response. Figure E-11 shows selected results of TSA presented in a form of stress-strain loops calculated in the middle of the submerged portion of the “critical” layer.

339 (a) Program 2 (MKZ) (b) Program 3 (LE-MC) Figure E-11. Results of TSA - Calculated Stress-Strain Response at 5.1 m b.g.s. Figure E-12 shows selected results of the ESA in a profile view (results with excess PWP dissipation allowed). Input PGA (applied at a depth of 7 m) 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 Figure E-14(g). 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. The ru ≥ 0.95 was recorded at a depth of 4.2 m and was matched by virtually all calculations. (a) Peak Ground Acceleration (b) Normalized Peak Shear Stress

340 (c) Peak Shear Strain (d) Normalized Excess PWP Figure E-12. Results of ESA - Recorded and Calculated Response. Figure E-13 shows selected results of ESA as history of ru buildup. The recorded acceleration history is shown for reference. Results of calculations are reported for a range of depths (5.1 m to 5.5 m) which is modeling-dependent (different numerical modeler selected different mesh/grid density within the profile). (a)

341 (b) Figure E-13. (a) Calculated Excess PWP Response at 6 m b.g.s.; (b) Input (Bedrock) Motion is Shown for Reference. Figure E-14 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-14(g) shows stress-strain loops as inferred from the interpretation of Newton’s second law, closely spaced Strong Motion (SM) records, and unit weight of soil between the SM instruments (i.e., a proxy for mass density). (a) Program 2 (MKZ) (b) Program 3 (PM4SAND) (c) Program 3 (UCSDSAND3) (d) Program 5 (PM4SAND) (e) Program 4 (UCSDSAND3) (f) Program 4 (PM4SAND)

342 (g) Inferred from SM Records Figure E-14. Results of ESA - Calculated Stress-Strain Response at 5.1 m b.g.s.

343 APPENDIX E-7 Attachment Laminar Box Response Model Layer No. Soil Type Thickness (m) Depth* (m) Vs (m/s) ksat (cm/s) γ (kN/m3) 1 Lean Clay 0.73 0.37 100 3.00E-04 18.4 2 Lean Clay 0.77 1.12 100 3.00E-04 18.4 3 Lean Clay 0.63 1.82 100 3.00E-04 18.4 4 Lean Clay 0.96 2.62 100 3.00E-04 18.4 5 Silty Sand 0.85 3.52 125 3.00E-03 18.4 6 Silty Sand 0.80 4.35 125 3.00E-03 18.4 7 Silty Sand 0.76 5.13 175 3.00E-03 18.4 8 Silty Sand 0.76 5.89 175 3.00E-03 18.4 9 Silty Sand 0.73 6.64 175 3.00E-03 18.4 Dw (m) H (m) (Vs)avg (m/s) Ts (s) fs (Hz) 1.50 7.00 130.0 0.215 4.64 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; Ts = 1st mode period; fs = 1st mode frequency. 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 0.0025 0.43 0.62 2 0.00100 1.70 0.67 0.0025 0.43 0.62 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 0.00100 1.50 0.68 0.0025 0.43 0.62 9 0.00100 1.50 0.68 0.0025 0.43 0.62 Layer No. MKZ - PWP Generation ν f P F S γtv (%) 1 3.50 2.00 1.04 2.60 1.70 0.02 2 3.50 2.00 1.04 2.60 1.70 0.02 3 3.50 2.00 1.04 2.60 1.70 0.02 4 3.50 2.00 1.04 2.60 1.70 0.02 5 3.50 2.00 1.04 2.60 1.70 0.02 6 3.50 2.00 1.04 2.60 1.70 0.02 7 3.50 2.00 1.04 2.60 1.70 0.02 8 3.50 2.00 1.04 2.60 1.70 0.02 9 3.50 2.00 1.04 2.60 1.70 0.02 Rayleigh Damping (2) 𝛂𝛂𝐫𝐫 = 0.24 𝛃𝛃𝐫𝐫 = 5.70-e5 (1) PWP = Pore Water Pressure. (2) Rayleigh damping coefficients are calculated by using Ts = 0.215 s, the viscous damping as 0.5%, and n = 5.

344 Table E-5. Parameters and coefficients of the UCSDSAND3 Model (Program 4) Layer No. CM Parameters of modulus reduction curve 𝒅𝒅 𝑷𝑷𝒓𝒓′(kPa) 𝝋𝝋 (°) 𝒔𝒔𝟎𝟎 (kPa) 𝜸𝜸𝒎𝒎𝒎𝒎𝒎𝒎,𝒓𝒓(%) 𝑵𝑵𝒀𝒀𝒀𝒀 1 U-Clay1 0.001 0.00 9.50 10 20 1 2 U-Clay1 0.001 0.00 9.50 10 20 2 3 U-Clay1 0.001 0.00 9.50 10 20 3 4 U-Clay1 0.001 0.00 9.50 10 20 4 5 UCSDSAND3 0.001 30.00 0.01 10 20 5 6 UCSDSAND3 0.001 30.00 0.01 10 20 6 7 UCSDSAND3 0.001 30.00 0.01 10 20 7 8 UCSDSAND3 0.001 30.00 0.01 10 20 8 9 UCSDSAND3 0.001 30.00 0.01 10 20 9 Layer No. Parameters for generation of PWP Soil Stiffness 𝝋𝝋𝑷𝑷𝑷𝑷 (°) 𝒄𝒄𝒎𝒎 𝒄𝒄𝒃𝒃 𝒄𝒄𝒄𝒄 𝒄𝒄𝒅𝒅 𝒄𝒄𝒆𝒆 𝝂𝝂 𝑩𝑩𝒓𝒓 (MPa) 𝑮𝑮𝒎𝒎𝒎𝒎𝒎𝒎 (MPa) 1 N.A. N.A. N.A. N.A. N.A. N.A. 0.49 930.51 18.74 2 N.A. N.A. N.A. N.A. N.A. N.A. 0.49 930.51 18.74 3 N.A. N.A. N.A. N.A. N.A. N.A. 0.49 930.51 18.74 4 N.A. N.A. N.A. N.A. N.A. N.A. 0.49 930.51 18.74 5 29 0.01 1.50 0.55 5.70 -0.75 0.30 63.43 29.27 6 29 0.01 1.50 0.55 5.70 -0.75 0.30 63.43 29.27 7 29 0.01 1.50 0.55 5.70 -0.75 0.30 124.32 57.38 8 29 0.01 1.50 0.55 5.70 -0.75 0.30 124.32 57.38 9 29 0.01 1.50 0.55 5.70 -0.75 0.30 124.32 57.38 Layer No. 𝒌𝒌𝒔𝒔𝒎𝒎𝒔𝒔 (m/s) 𝑩𝑩𝒇𝒇(GPa) 𝑩𝑩𝒆𝒆(GPa) 𝝆𝝆 (Mg/m3) Parameters for soil dilation 𝒅𝒅𝒎𝒎 𝒅𝒅𝒃𝒃 𝒅𝒅𝒄𝒄 1 0.00 2.20 4.42 1.00 N.A. N.A. N.A. 2 0.00 2.20 4.42 1.00 N.A. N.A. N.A. 3 0.00 2.20 4.42 1.00 N.A. N.A. N.A. 4 0.00 2.20 4.42 1.00 N.A. N.A. N.A. 5 0.00 2.20 4.49 1.00 0.41 3.00 -0.38 6 0.00 2.20 4.49 1.00 0.41 3.00 -0.38 7 0.00 2.20 4.49 1.00 0.41 3.00 -0.38 8 0.00 2.20 4.49 1.00 0.41 3.00 -0.38 9 0.00 2.20 4.49 1.00 0.41 3.00 -0.38 CM = constitutive model; D = depth of bottom of element 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 = 0.04 and 𝜷𝜷𝒓𝒓 = 0.0004.

345 Parameters and Coefficients of the LE-MC model (Program 3) Layer No. LE-MC Input Parameters CM ρd (T/m3) n (-) G0 (MPa) K (MPa) Φ (deg) c (kPa) ψ (deg) 1 LE-MC 1.3725 0.4975 18,735 40,655 30 1e6 0 2 LE-MC 1.3725 0.4975 18,735 40,655 30 1e6 0 3 LE-MC 1.3725 0.4975 18,735 40,655 30 1e6 0 4 LE-MC 1.3725 0.4975 18,735 40,655 30 1e6 0 5 LE-MC 1.3802 0.4898 29,274 63,524 30 1e6 0 6 LE-MC 1.3802 0.4898 29,274 63,524 30 1e6 0 7 LE-MC 1.3802 0.4898 57,376 124,507 30 1e6 0 8 LE-MC 1.3802 0.4898 57,376 124,507 30 1e6 0 9 LE-MC 1.3802 0.4898 57,376 124,507 30 1e6 0 Layer No. LE-MC Input Parameters Tens. (kPa) K0 (-) k11 (cm/s) k22 (cm/s) k12 (cm/s) Sat. (-) 1 1e6 0.5 3.0E-04 3.0E-04 0 1 2 1e6 0.5 3.0E-04 3.0E-04 0 1 3 1e6 0.5 3.0E-04 3.0E-04 0 1 4 1e6 0.5 3.0E-04 3.0E-04 0 1 5 1e6 0.5 3.0E-03 3.0E-03 0 1 6 1e6 0.5 3.0E-03 3.0E-03 0 1 7 1e6 0.5 3.0E-03 3.0E-03 0 1 8 1e6 0.5 3.0E-03 3.0E-03 0 1 9 1e6 0.5 3.0E-03 3.0E-03 0 1 Layer No. LE-MC Input Parameters Sig3 hysteretic damping Rayleigh a b x0 1 0.99985 -0.64799 -1.34361 0.5% @ 4.7 Hz 2 0.99985 -0.64799 -1.34361 3 0.99985 -0.64799 -1.34361 4 0.99985 -0.64799 -1.34361 5 1.00000 -0.63868 -1.25892 6 1.00000 -0.63868 -1.25892 7 1.00000 -0.63868 -1.25892 8 1.00000 -0.63868 -1.25892 9 1.00000 -0.63868 -1.25892 (1) LE-MC used for quasi-static stress initialization phase for all layers. (2) Initial bulk modulus calculated assuming Poisson's ratio 0.3 for all layers.

346 Parameters and Coefficients of the PM4SAND Model (Program 3) Layer No. CM Sig3 (three parameters stress- strain model) Rayleigh Damping PM4SAND non-default parameters a b x0 Dr Go hpo 1 LE-MC 0.99985 -0.64799 -1.34361 0.5% @ 4.7 Hz - - - 2 LE-MC 0.99985 -0.64799 -1.34361 - - - 3 LE-MC 0.99985 -0.64799 -1.34361 - - - 4 LE-MC 0.99985 -0.64799 -1.34361 - - - 5 PM4SAND - - - 0.69 552 0.55 6 PM4SAND - - - 0.69 552 0.55 7 PM4SAND - - - 0.69 552 0.55 8 PM4SAND - - - 0.69 552 0.55 9 PM4SAND - - - 0.69 552 0.55 (1) LE-MC used for quasi-static stress initialization phase for all layers. (2) Initial bulk modulus calculated assuming Poisson's ratio 0.3 for all layers. Parameters and Coefficients of the UCSDSAND3 Model (Program 3) Layer No. CM Sig3 (three parameters stress- strain model) Rayleigh UCSDSAND3 non- default params a b x0 (N1)60 1 LE-MC 0.99985 -0.64799 -1.34361 0.5% @ 4.7 Hz - 2 LE-MC 0.99985 -0.64799 -1.34361 - 3 LE-MC 0.99985 -0.64799 -1.34361 - 4 LE-MC 0.99985 -0.64799 -1.34361 - 5 UCSDSAND3 - - - 22.5 6 UCSDSAND3 - - - 22.5 7 UCSDSAND3 - - - 22.5 8 UCSDSAND3 - - - 22.5 9 UCSDSAND3 - - - 22.5 (1) LE-MC used for quasi-static stress initialization phase for all layers. (2) Initial bulk modulus calculated assuming Poisson's ratio = 0.3 for all layers.

Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation Get This Book
×
 Seismic Site Response Analysis with Pore Water Pressure Generation: Resources for Evaluation
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

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.

READ FREE ONLINE

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  6. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  7. ×

    View our suggested citation for this chapter.

    « Back Next »
  8. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!