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305 APPENDIX E-6 Treasure Island Site Site Response in the 1989 M 6.9 Loma Prieta Earthquake General This Appendix presents results of numerical modeling of the response of the Treasure Island (TI) site in the 1989 M 6.9 Loma Prieta earthquake. The TI site is representative of a deep soil profile / bedrock outcrop Strong Motion (SM) pair. This is an inferred soil liquefaction site. The analysis documented herein was performed in general accordance with the âGuidance for Effective-Stress Site Response Analysisâ outlined in Section 8.2 of the main report. Relevant information about recorded ground motions is provided in Appendix B-4. Model Selection Table E-1 lists the software and constitutive models used to calculate response of the TI site in the 1989 M 6.9 Loma Prieta 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 OpenSeesPL S-I MKZ LE-MC PM4SAND UBCSAND UCSDSAND3 UCSDSAND3 UCSDCLAY PM4SAND PM4SILT CM = Constitutive Model; LE-MC = Linear Elastic-Mohr Coulomb; 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 and OpenSeesPL). 1989 M 6.9 Loma Prieta Earthquake and Ground Motions Relevant information about the 1989 M 6.9 Loma Prieta earthquake and ground motions induced at the site is reproduced from Appendix B-4 in Table E-2.
306 Table E-2. Loma Prieta Earthquake â Earthquake and Strong Motion Parameters at the Site. Earthquake Date M R PGA (N-S) ru Loma Prieta October 17, 1989 6.9 70-75 km Yerba Buena Island (Outcrop) TI (Soft Soil) Hydraulic Fill 0.067 g 0.159 g > 0.95 (Inferred) M = Moment Magnitude; R = Approximate site-to-source distance; PGA = Peak Ground Acceleration (larger of the two horizontal components); ru = Maximum recorded excess pore water pressure normalized by the vertical effective stress; N-S = North-South (direction). Site Exploration and Characterization Relevant information about the site, including site location and layout, results of site characterization efforts, and relevant earthquake and strong motion information is provided in the site characterization report that is enclosed as Appendix B-4. Interpreted and summarized information is presented in Figure E-1. The fill (mostly silty sand) was liquified in the 1989 M 6.9 Loma Prieta Earthquake. A portion of the fill below groundwater table has been identified as the âcriticalâ layer accordingly. (a) (b) Figure E-1. TI Site â Interpreted Soil Profile with Location of Strong Motion Instruments. Measured Shear Wave Velocity is from Gibbs et al. (1992).
307 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 D-1. Table E-3 â Summary of Advanced Laboratory Testing Soil RC and TS CyDSS Note Fill (Liquefiable Sand) Y - âCriticalâ Layer Young Bay Mud (YBM) Y - - Medium Dense Sand (MDS) Y Y(1) - Old Bay Mud (OBM) Y - - (1) CyDSS test results are available only for the MDS (Stress-Controlled only). These test results are presented in Appendix D-1. 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, including in Appendix D-1 (the element testing of the results of undrained stress-controlled CyDSS testing of medium dense sand, MDS). 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 â Summary of Element Testing Material (Test Type) SHAKE2000 D-MOD2000 FLAC OpenSeesPL Fill (Liquefiable Sand) N/A MKZ LE-MC PM4SAND UBCSAND UCSDSAND3 UCSDSAND3 PM4SAND Young Bay Mud (YBM) N/A MKZ LE-MC UCSDCLAY PM4SILT Medium Dense Sand (MDS) N/A MKZ LE-MC PM4SAND UBCSAND UCSDSAND3 UCSDSAND3 PM4SAND Old Bay Mud (OBM) N/A MKZ LE-MC UCSDCLAY PM4SILT 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-2 and E-3. Additional information is presented in Appendix D-3.
308 (a) Fill (Sand) (b) Young Bay Mud (c) Medium Dense Sand (d) Old Bay Mud Figure E-2. CM Sub-Model Testing with the MKZ Model (Program 2). Measured Modulus Reduction and Damping Curves are from Hwang and Stokoe (1993).
309 (a) Fill (Sand) (b) Young Bay Mud (c) Medium Dense Sand (d) Old Bay Mud Figure E-2. CM Sub-Model Testing with the UCSDSAND3 Model (Program 4). Measured Modulus Reduction and Damping Curves are from Hwang and Stokoe (1993). Selected results of element testing (results for 30th cycle of stress-controlled undrained CyDSS testing of MDS) are reproduced from Appendix D-1 in Figure E-3. (a) UCSDSAND3 (b) PM4SAND Figure E-3 Element Testing of MDS with the UCSDSAND3 and PM4SAND Models (Reproduced from Appendix D-1).
310 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). SRA Model Development The site response analysis model of the TI site is presented in Figure E-1. It includes idealized soil stratification, groundwater elevation, and an interpreted shear wave velocity profile (âredâ line; also corresponds to layering as input in the SRA model). Input motion was applied as an âoutcropâ motion in SHAKE2000 and OpenSeesPL analyses. In D-MOD2000, the transmitting base option was used. In FLAC, the applied shear stress 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-4 documents the process of system testing (i.e., model testing at the soil profile level) for Programs 2 and 4. Upon completion of the system testing, for both programs, the Rayleigh damping model parameters assessed were fine-tuned in an iterative process. The fine-tuning was performed with the Yerba Buena island record from the 1989 M 6.9 Loma Prieta earthquake scaled to Peak Ground Acceleration (PGA) of 0.02 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 âblackâ in Figure E-4. Note that the n = 5 and D = 5% pair provides the best match for both programs and all three CMs considered.
311 (a) Program 2 (MKZ) (b) Program 4 (UCSDSAND3) (c) Program 4 (PM4SAND) Figure E-4. System Testing with Program 2 (MKZ) and Program 4 (UCSDSAND3 and PM4SAND).
312 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 selected software are presented in Figure E-5. The recorded ground surface response is shown for reference. (a) Program 1 (S-I) (b) Program 2 (MKZ) (c) Program 3 (LE-MC) Figure E-5. Results of TSA â Recorded and Calculated Surface Response with Selected Software and CMs. The Effective Stress Analysis (ESA) was performed without and with excess Pore Water Pressure (PWP) dissipation. The results of ESA with excess PWP dissipation allowed are presented in Figure E-6. The recorded ground surface response is shown for reference.
313 (a) Program 2 (MKZ) (b) Program 3 (PM4SAND) (c) Program 3 (UBCSAND) (d) Program 3 (UCSDSAND3) (e) Program 4 (UCSDSAND3) (f) Program 4 (PM4SAND) Figure E-6. Results of ESA â Recorded and Calculated Surface Response with excess PWP Dissipation Allowed.
314 Results - Response within Soil Profile Figure E-11 shows selected results of the TSA in a profile view. Input PGA (recorded as outcrop and read as an âwithin motionâ from SHAKE at approximately 90 m b.g.s.) and PGA recorded within the profile are shown for reference. (a) Peak Ground Acceleration (b) Normalized Peak Shear Stress (c) Peak Shear Strain Figure E-7. Results of TSA - Recorded and Calculated Response. Figure E-8 shows selected results of TSA presented in the form of stress-strain loops calculated in the middle of the submerged portion of the âcriticalâ layer.
315 (a) Program 2 (MKZ) (b) Program 3 (LE-MC) Figure E-8. Results of TSA - Calculated Stress-Strain Response at 8.7 m b.g.s. Figure E-9 shows selected results of the ESA in a profile view (results with excess PWP dissipation allowed). Input PGA (âwithinâ value from SHAKE) and PGA recorded within the profile are shown for reference. As noted above, excess PWP response was not recorded during the 1989 M 6.9 Loma Prieta earthquake. However, the site liquefied and, therefore, presence of excess PWP within submerged fill (âCriticalâ Layer) has been inferred. 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. (a) Peak Ground Acceleration (b) Normalized Peak Shear Stress
316 (c) Peak Shear Strain (d) Normalized Excess PWP Figure E-9. Results of ESA - Recorded and Calculated Response. Figure E-10 shows selected results of ESA as history of ru buildup. The recorded acceleration history is shown for reference. Like in Figure E-9(d) above, ru ⥠0.95 signals the onset of soil liquefaction. (a)
317 (b) Figure E-10. (a) Calculated Excess PWP Response at 6 m b.g.s.; (b) Input (Bedrock) Motion (Shown for Reference). Figure E-11 shows selected results of ESA presented in the form of stress-strain loops calculated in the middle of the submerged portion of the âcriticalâ layer. (a) Program 2 (MKZ) (b) Program 3 (PM4SAND) (c) Program 3 (UBCSAND) (d) Program 3 (UCSDSAND3) (e) Program 4 (UCSDSAND3) (f) Program 4 (PM4SAND) Figure E-11. Results of ESA - Calculated Stress-Strain Response at 8.7 m b.g.s.
318 References 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 92-287, US Geological Survey, Menlo Park, California. Hwang, S. K., and Stokoe, K. H. (1993). âDynamic properties of undisturbed soil samples from Treasure Island, California,â Research Report, Geotechnical Engineering Center, Civil Engineering Department, University of Texas at Austin.
319 APPENDIX E-6 Attachment Site Response Model of the TI Site Layer No. Soil Type Thickness (m) Depth* (m) Vs (m/s) ksat (cm/s) γ (kN/m3) ξtar 1 Fill 0.80 0.40 252 1.00E-01 19.7 0.005 2 Fill 0.80 1.20 252 1.00E-01 19.7 0.005 3 Fill 1.60 2.40 134 1.00E-01 19.7 0.005 4 Fill 1.60 4.00 134 1.00E-01 19.7 0.005 5 Fill 1.60 5.60 134 1.00E-01 19.7 0.005 6 Fill 1.60 7.20 134 1.00E-01 19.7 0.005 7 Fill 1.33 8.66 170 1.00E-01 19.7 0.005 8 Fill 1.33 9.99 170 1.00E-01 19.7 0.005 9 Fill 1.33 11.31 170 1.00E-01 19.7 0.005 10 YBM 1.33 12.64 170 1.00E-07 19.7 0.005 11 YBM 1.41 14.00 176 1.00E-07 14.8 0.005 12 YBM 1.41 15.41 176 1.00E-07 14.8 0.005 13 YBM 1.41 16.82 176 1.00E-07 14.8 0.005 14 YBM 1.41 18.23 176 1.00E-07 14.8 0.005 15 YBM 1.41 19.64 176 1.00E-07 14.8 0.005 16 YBM 1.41 21.05 176 1.00E-07 14.8 0.005 17 YBM 1.41 22.46 176 1.00E-07 14.8 0.005 18 YBM 1.41 23.87 176 1.00E-07 14.8 0.005 19 YBM 1.41 25.28 176 1.00E-07 14.8 0.005 20 YBM 1.41 26.69 176 1.00E-07 14.8 0.005 21 YBM 1.41 28.10 176 1.00E-07 14.8 0.005 22 MDS 2.48 30.04 317 1.00E-01 20.7 0.005 23 MDS 2.48 32.52 317 1.00E-01 20.7 0.005 24 MDS 2.48 35.00 317 1.00E-01 20.7 0.005 25 MDS 2.48 37.48 317 1.00E-01 20.7 0.005 26 MDS 2.48 39.96 317 1.00E-01 20.7 0.005 27 OBM 2.29 42.35 267 1.00E-08 17.5 0.005 28 OBM 2.29 44.64 267 1.00E-08 17.5 0.005 29 OBM 2.29 46.93 267 1.00E-08 17.5 0.005 30 OBM 2.29 49.23 267 1.00E-08 17.5 0.005 31 OBM 2.29 51.52 267 1.00E-08 17.5 0.005 32 OBM 2.29 53.81 267 1.00E-08 17.5 0.005 33 OBM 2.29 56.11 267 1.00E-08 17.5 0.005 34 OBM 2.29 58.40 267 1.00E-08 17.5 0.005 35 OBM 2.29 60.69 267 1.00E-08 17.5 0.005 36 OBM 2.29 62.99 267 1.00E-08 17.5 0.005 37 OBM 2.29 65.28 267 1.00E-08 17.5 0.005 38 OBM 2.29 67.57 267 1.00E-08 17.5 0.005 39 OBM 2.29 69.87 267 1.00E-08 17.5 0.005 40 OBM 2.29 72.16 267 1.00E-08 17.5 0.005 41 OBM 2.29 74.45 267 1.00E-08 17.5 0.005 42 MDS 2.75 76.98 369 1.00E-02 21.4 0.005 43 MDS 2.75 79.73 369 1.00E-02 21.4 0.005 44 OBM 2.33 82.27 386 1.00E-08 17.5 0.005 45 OBM 2.33 84.60 386 1.00E-08 17.5 0.005 46 OBM 2.33 86.93 386 1.00E-08 17.5 0.005
320 Dw (m) H (m) (Vs)avg (m/s) Ts (s) fs (Hz) 1.60 88.10 258.1 1.365 0.73 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. YBM = Young Bay Mud; MDS = Medium Dense Sand; OBM = Old Bay Mud; 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 0.0011 1.49 0.71 0.0025 0.43 0.62 2 0.0011 1.49 0.71 0.0025 0.43 0.62 3 0.0011 1.49 0.71 0.0025 0.43 0.62 4 0.0011 1.49 0.71 0.0025 0.43 0.62 5 0.0011 1.49 0.71 0.0025 0.43 0.62 6 0.0011 1.49 0.71 0.0025 0.43 0.62 7 0.0011 1.49 0.71 0.0025 0.43 0.62 8 0.0011 1.49 0.71 0.0025 0.43 0.62 9 0.0011 1.49 0.71 0.0025 0.43 0.62 10 0.0034 1.40 0.80 N/A N/A N/A 11 0.0034 1.40 0.80 N/A N/A N/A 12 0.0034 1.40 0.80 N/A N/A N/A 13 0.0034 1.40 0.80 N/A N/A N/A 14 0.0034 1.40 0.80 N/A N/A N/A 15 0.0034 1.40 0.80 N/A N/A N/A 16 0.0034 1.40 0.80 N/A N/A N/A 17 0.0034 1.40 0.80 N/A N/A N/A 18 0.0034 1.40 0.80 N/A N/A N/A 19 0.0034 1.40 0.80 N/A N/A N/A 20 0.0034 1.40 0.80 N/A N/A N/A 21 0.0034 1.40 0.80 N/A N/A N/A 22 0.0032 1.44 0.69 0.0025 0.43 0.62 23 0.0032 1.44 0.69 0.0025 0.43 0.62 24 0.0032 1.44 0.69 0.0025 0.43 0.62 25 0.0032 1.44 0.69 0.0025 0.43 0.62 26 0.0032 1.44 0.69 0.0025 0.43 0.62 27 0.0023 1.44 0.69 N/A N/A N/A 28 0.0023 1.44 0.69 N/A N/A N/A 29 0.0023 1.44 0.69 N/A N/A N/A 30 0.0023 1.44 0.69 N/A N/A N/A 31 0.0023 1.44 0.69 N/A N/A N/A 32 0.0023 1.44 0.69 N/A N/A N/A 33 0.0023 1.44 0.69 N/A N/A N/A 34 0.0023 1.44 0.69 N/A N/A N/A 35 0.0023 1.44 0.69 N/A N/A N/A 36 0.0023 1.44 0.69 N/A N/A N/A 37 0.0023 1.44 0.69 N/A N/A N/A 38 0.0023 1.44 0.69 N/A N/A N/A 39 0.0023 1.44 0.69 N/A N/A N/A 40 0.0023 1.44 0.69 N/A N/A N/A 41 0.0023 1.44 0.69 N/A N/A N/A 42 0.0032 1.44 0.69 0.0025 0.43 0.62 43 0.0032 1.44 0.69 0.0025 0.43 0.62
321 44 0.0023 1.44 0.69 N/A N/A N/A 45 0.0023 1.44 0.69 N/A N/A N/A 46 0.0023 1.44 0.69 N/A N/A N/A Layer No. MKZ - PWP Generation ν f P F S γtv (%) 1 1.0 1.0 1.0 10.9 1.7 0.017 2 1.0 1.0 1.0 10.9 1.7 0.017 3 1.0 1.0 1.0 10.9 1.7 0.017 4 1.0 1.0 1.0 10.9 1.7 0.017 5 1.0 1.0 1.0 10.9 1.7 0.017 6 1.0 1.0 1.0 10.9 1.7 0.017 7 1.0 1.0 1.0 10.9 1.7 0.017 8 1.0 1.0 1.0 10.9 1.7 0.017 9 1.0 1.0 1.0 10.9 1.7 0.017 10 1.0 N/A N/A N/A N/A 1.000 11 1.0 N/A N/A N/A N/A 1.000 12 1.0 N/A N/A N/A N/A 1.000 13 1.0 N/A N/A N/A N/A 1.000 14 1.0 N/A N/A N/A N/A 1.000 15 1.0 N/A N/A N/A N/A 1.000 16 1.0 N/A N/A N/A N/A 1.000 17 1.0 N/A N/A N/A N/A 1.000 18 1.0 N/A N/A N/A N/A 1.000 19 1.0 N/A N/A N/A N/A 1.000 20 1.0 N/A N/A N/A N/A 1.000 21 1.0 N/A N/A N/A N/A 1.000 22 1.0 1.0 1.1 9.1 1.0 0.081 23 1.0 1.0 1.1 9.1 1.0 0.081 24 1.0 1.0 1.1 9.1 1.0 0.081 25 1.0 1.0 1.1 9.1 1.0 0.081 26 1.0 1.0 1.1 9.1 1.0 0.081 27 1.0 N/A N/A N/A N/A 0.100 28 1.0 N/A N/A N/A N/A 0.100 29 1.0 N/A N/A N/A N/A 0.100 30 1.0 N/A N/A N/A N/A 0.100 31 1.0 N/A N/A N/A N/A 0.100 32 1.0 N/A N/A N/A N/A 0.100 33 1.0 N/A N/A N/A N/A 0.100 34 1.0 N/A N/A N/A N/A 0.100 35 1.0 N/A N/A N/A N/A 0.100 36 1.0 N/A N/A N/A N/A 0.100 37 1.0 N/A N/A N/A N/A 0.100 38 1.0 N/A N/A N/A N/A 0.100 39 1.0 N/A N/A N/A N/A 0.100 40 1.0 N/A N/A N/A N/A 0.100 41 1.0 N/A N/A N/A N/A 0.100 42 1.0 1.0 1.1 9.1 1.0 0.081 43 1.0 1.0 1.1 9.1 1.0 0.081 44 N/A N/A N/A N/A N/A 1.000 45 N/A N/A N/A N/A N/A 1.000
322 46 N/A N/A N/A N/A N/A 1.000 MKZ - PWP Generation Layer No. A B C D 1 N/A N/A N/A N/A 2 N/A N/A N/A N/A 3 N/A N/A N/A N/A 4 N/A N/A N/A N/A 5 N/A N/A N/A N/A 6 N/A N/A N/A N/A 7 N/A N/A N/A N/A 8 N/A N/A N/A N/A 9 N/A N/A N/A N/A 10 7.6 -14.7 6.4 0.7 11 7.6 -14.7 6.4 0.7 12 7.6 -14.7 6.4 0.7 13 7.6 -14.7 6.4 0.7 14 7.6 -14.7 6.4 0.7 15 7.6 -14.7 6.4 0.7 16 7.6 -14.7 6.4 0.7 17 7.6 -14.7 6.4 0.7 18 7.6 -14.7 6.4 0.7 19 7.6 -14.7 6.4 0.7 20 7.6 -14.7 6.4 0.7 21 7.6 -14.7 6.4 0.7 22 N/A N/A N/A N/A 23 N/A N/A N/A N/A 24 N/A N/A N/A N/A 25 N/A N/A N/A N/A 26 N/A N/A N/A N/A 27 14.6 -30.5 18.4 -2.5 28 14.6 -30.5 18.4 -2.5 29 14.6 -30.5 18.4 -2.5 30 14.6 -30.5 18.4 -2.5 31 14.6 -30.5 18.4 -2.5 32 14.6 -30.5 18.4 -2.5 33 14.6 -30.5 18.4 -2.5 34 14.6 -30.5 18.4 -2.5 35 14.6 -30.5 18.4 -2.5 36 14.6 -30.5 18.4 -2.5 37 14.6 -30.5 18.4 -2.5 38 14.6 -30.5 18.4 -2.5 39 14.6 -30.5 18.4 -2.5 40 14.6 -30.5 18.4 -2.5 41 14.6 -30.5 18.4 -2.5 42 N/A N/A N/A N/A 43 N/A N/A N/A N/A 44 13.0 -26.3 15.4 -2.0 45 13.0 -26.3 15.4 -2.0 46 13.0 -26.3 15.4 -2.0
323 Rayleigh Damping(2) ððð«ð« = 3.8 ððð«ð« = 3.66-e4 Rayleigh damping coefficients are calculated for: Ts = 1.378 s, the viscous damping as 0.5%, and n = 5. Parameters and Coefficients of the LE-MC Model (Program 3) LE-MC Input Parameters Layer No.(5) CM Ïd (T/m 3) Rayleigh (6) a b x0 1 LE-MC 1.59 1.00 -0.62 -1.20 0.5% @ 0.73 Hz 2 LE-MC 1.59 1.00 -0.62 -1.20 3 LE-MC 1.59 1.00 -0.62 -1.20 4 LE-MC 0.80 1.00 -0.55 -0.65 5 LE-MC 1.75 1.00 -0.63 -0.73 6 LE-MC 1.23 1.00 -0.63 -0.88 7 LE-MC 1.23 1.00 -0.63 -0.88 8 LE-MC 1.23 1.00 -0.63 -0.88 9 LE-MC 1.23 1.00 -0.63 -0.88 10 LE-MC 1.87 1.00 -0.63 -0.73 11 LE-MC 1.23 1.00 -0.63 -0.88 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. 3. Fitted to MKZ model modulus reduction curves used in D-MOD2000 calibration. 4. Layers 1 through 11 were subdivided into 46 sublayers based on D-MOD2000 discretization. 5. Total, i.e., combined stiffness- and mass-proportional. Parameters and Coefficients of the PM4SAND Model (Program 3) Sublayer No. CM (1,2) Sig3 (three parameters stress-strain model) Rayleigh Damping (3) PM4SAND non-default parameters a b x0 Dr (4) Go (5) hpo (6) 2_1 PM4SAND - - - 0.5% @ 0.73 Hz 0.42 719 0.7 2_2 PM4SAND - - - 0.38 454 0.9 2_3 PM4SAND - - - 0.36 520 0.9 2_4 PM4SAND - - - 0.34 609 0.8 3_1 PM4SAND - - - 0.39 564 0.9 3_2 PM4SAND - - - 0.38 675 0.8 3_3 PM4SAND - - - 0.37 721 0.7 (1) LE-MC used for quasi-static stress initialization phase for all layers. Except for sublayers listed, all layers and sublayers used LE-MC model. (2) Total, i.e., combined stiffness- and mass-proportional. (3) Selected based on (N1)60 profile. (4) Selected based on Vs profile. (5) Selected based on (N1)60 profile and Ziotopoulou (2010) input values. Parameters and Coefficients of the UBCSAND model (Program 3) Sublayer No. CM (1,2) Sig3 (three parameters stress-strain model) Rayleigh damping (3) UBCSAND non-default parameter
324 a b x0 (N1)60-cs kGe (4) kB (5) kGp (6) 2_1 UBCSAND - - - 0.5% @ 0.73 Hz 8.0 719 1558 750 2_2 UBCSAND - - - 6.8 454 983 410 2_3 UBCSAND - - - 6.0 520 1128 420 2_4 UBCSAND - - - 5.4 609 1320 450 3_1 UBCSAND - - - 7.0 564 1222 520 3_2 UBCSAND - - - 6.6 675 1462 590 3_3 UBCSAND - - - 6.2 721 1562 600 (1) LE-MC used for quasi-static stress initialization phase for all layers. Except for sublayers listed, all layers and sublayers used LE-MC model. (2) Total, i.e., combined stiffness- and mass-proportional. (3) Selected based on Vs profile. (4) Assumes Poisson's ratio 0.3. (5) Selected based on (N1)60 profile and Ziotopoulou (2010) input values for Port Island and Wildlife Site. Parameters and coefficients of UCSDSAND3 model (Program 4) Layer No. CM ð«ð« (m) Parameters of modulus reduction curve ð ð ð·ð·ððâ²(kPa) ðð (°) ðððð (kPa) ð¸ð¸ðððððð,ðð(%) ðµðµðððð 1 -0.80 U-Sand3 0.0 70 30 1.5 10 20 2 -3.20 U-Sand3 0.0 30 30 1.5 10 20 3 -4.80 U-Sand3 0.0 25 30 1.5 10 20 4 -6.40 U-Sand3 0.0 30 30 1.5 10 20 5 -8.00 U-Sand3 0.0 40 30 1.5 10 20 6 -10.65 U-Sand3 0.0 60 30 1.5 10 20 7 -11.98 U-Sand3 0.0 70 30 1.5 10 20 8 -13.30 U-Clay2 0.0 100 0 100 10 20 9 -14.71 U-Clay2 0.0 100 0 100 10 20 10 -16.12 U-Clay2 0.0 100 0 100 10 20 11 -18.94 U-Clay2 0.0 100 0 100 10 20 12 -20.35 U-Clay2 0.0 100 0 100 10 20 13 -21.76 U-Clay2 0.0 100 0 100 10 20 14 -23.17 U-Clay2 0.0 100 0 100 10 20 15 -24.58 U-Clay2 0.0 100 0 100 10 20 16 -25.99 U-Clay2 0.0 100 0 100 10 20 17 -27.40 U-Clay2 0.0 100 0 100 10 20 18 -28.81 U-Clay2 0.0 100 0 100 10 20 19 -31.29 U-Sand3 0.0 700 38 0.01 10 20 20 -33.77 U-Sand3 0.0 450 38 0.01 10 20 21 -36.25 U-Sand3 0.0 500 38 0.01 10 20 22 -38.73 U-Sand3 0.0 400 38 0.01 10 20 23 -41.21 U-Sand3 0.0 325 38 0.01 10 20 24 -43.51 U-Clay2 0.0 100 0 150 10 20 25 -45.80 U-Clay2 0.0 100 0 150 10 20 26 -78.37 U-Sand3 0.0 500 35 5 10 20 27 -83.46 U-Clay2 0.0 100 0 150 10 20 Layer No. Parameters for generation of PWP Soil Stiffness ððð·ð·ð·ð· (°) ðððð ðððð ðððð ððð ð ðððð ðð ð©ð©ðð (MPa) ð®ð®ðððððð (MPa) 1 20.40 0.03 5.00 0.20 16.00 2.00 0.30 170.6 78.7
325 2 20.40 0.03 5.00 0.20 16.00 2.00 0.30 84.4 39.0 3 20.40 0.03 5.00 0.20 16.00 2.00 0.30 63.1 29.1 4 20.40 0.03 5.00 0.20 16.00 2.00 0.30 82.0 37.9 5 20.40 0.03 5.00 0.20 16.00 2.00 0.30 106.2 49.0 6 20.40 0.03 5.00 0.20 16.00 2.00 0.30 134.9 62.3 7 20.40 0.03 5.00 0.20 16.00 2.00 0.30 152.2 70.3 8 N/A N/A N/A N/A N/A N/A 0.40 195.0 41.8 9 N/A N/A N/A N/A N/A N/A 0.40 168.0 36.0 10 N/A N/A N/A N/A N/A N/A 0.40 224.1 48.0 11 N/A N/A N/A N/A N/A N/A 0.40 234.2 50.2 12 N/A N/A N/A N/A N/A N/A 0.40 314.3 67.3 13 N/A N/A N/A N/A N/A N/A 0.40 285.3 61.1 14 N/A N/A N/A N/A N/A N/A 0.40 165.8 35.5 15 N/A N/A N/A N/A N/A N/A 0.40 181.3 38.8 16 N/A N/A N/A N/A N/A N/A 0.40 209.3 44.8 17 N/A N/A N/A N/A N/A N/A 0.40 211.7 45.4 18 N/A N/A N/A N/A N/A N/A 0.40 376.4 80.7 19 24.00 0.01 1.00 0.60 4.60 -1.00 0.30 606.5 279.9 20 24.00 0.01 1.00 0.60 4.60 -1.00 0.30 418.4 193.1 21 24.00 0.01 1.00 0.60 4.60 -1.00 0.30 460.7 212.7 22 24.00 0.01 1.00 0.60 4.60 -1.00 0.30 355.0 163.8 23 24.00 0.01 1.00 0.60 4.60 -1.00 0.30 294.4 135.9 24 N/A N/A N/A N/A N/A N/A 0.48 2361.6 95.7 25 N/A N/A N/A N/A N/A N/A 0.48 3077.9 124.8 26 37.20 0.00 0.00 0.80 2.20 0.00 0.30 637.5 294.3 27 N/A N/A N/A N/A N/A N/A 0.48 6447.8 261.4 Layer No. ðððððððð (m/s) ð©ð©ðð(GPa) ð©ð©ðð(GPa) ðð (Mg/m3) Parameters for soil dilation ð ð ðð ð ð ðð ð ð ðð 1 1.00.E-05 2.20 5.50 1.99 0.15 3 -0.2 2 1.00.E-05 2.20 5.50 1.99 0.15 3 -0.2 3 1.00.E-05 2.20 5.50 1.99 0.15 3 -0.2 4 1.00.E-05 2.20 5.50 1.99 0.15 3 -0.2 5 1.00.E-05 2.20 5.50 1.99 0.15 3 -0.2 6 1.00.E-05 2.20 5.50 1.99 0.15 3 -0.2 7 1.00.E-05 2.20 5.50 1.99 0.15 3 -0.2 8 1.00.E-09 2.20 5.50 1.50 N/A N/A N/A 9 1.00.E-09 2.20 5.50 1.50 N/A N/A N/A 10 1.00.E-09 2.20 5.50 1.50 N/A N/A N/A 11 1.00.E-09 2.20 5.50 1.50 N/A N/A N/A 12 1.00.E-09 2.20 5.50 1.50 N/A N/A N/A 13 1.00.E-09 2.20 5.50 1.50 N/A N/A N/A 14 1.00.E-09 2.20 5.50 1.50 N/A N/A N/A 15 1.00.E-09 2.20 5.50 1.50 N/A N/A N/A 16 1.00.E-09 2.20 5.50 1.50 N/A N/A N/A 17 1.00.E-09 2.20 5.50 1.50 N/A N/A N/A 18 1.00.E-09 2.20 5.50 1.50 N/A N/A N/A 19 1.00.E-06 2.20 5.50 2.03 0.45 3 -0.4 20 1.00.E-06 2.20 5.50 2.03 0.45 3 -0.4 21 1.00.E-06 2.20 5.50 2.03 0.45 3 -0.4 22 1.00.E-06 2.20 5.50 2.03 0.45 3 -0.4
326 23 1.00.E-06 2.20 5.50 2.03 0.45 3 -0.4 24 1.00.E-10 2.20 5.50 1.76 N/A N/A N/A 25 1.00.E-10 2.20 5.50 1.76 N/A N/A N/A 26 1.00.E-04 2.20 5.50 2.16 0.6 3 0.5 27 1.00.E-10 2.20 5.50 1.76 N/A N/A N/A D = depth of bottom of element ðð = pressure dependent coefficient; ððððâ² = reference mean effective pressure; ðð = model friction angle; ð ð 0 = model cohesion; ð¾ð¾ðððððð,ðð = maximum shear strain at reference pressure; ðððððð = number of yield surface; ðððððð = phase transformation angle; ðððð, ðððð, ðððð, ðððð, ðððð = contraction parameters; ðð = Poissonâs ratio; ðµðµðð = bulk modulus; ðºðºðððððð = small-strain shear modulus; ððð ð ððð ð = soil permeability; ðµðµðð = bulk modulus of water; ðµðµðð = combined bulk modulus; ðð = soil density; ðððð, ðððð, ðððð = soil dilation parameters. Rayleigh damping parameters: ð¶ð¶ðð = 0.04 and ð·ð·ðð = 0.0004. Parameters and Coefficients of the PM4SAND model (Program 4) Layer No. CM ðð (Mg/m3) Primary parameter Fluid properties ðððð(ððð·ð·ðð) ð®ð®ðð ðððððð ðððððððð (m/s) ðððð (Mg/m3) ð©ð©ðð(GPa) 1 PM4SAND 1.99 N/A 3559 0.45 1.00E-03 1.00 2.20 2 PM4SAND 1.99 N/A 2055 0.45 1.00E-03 1.00 2.20 3 PM4SAND 1.99 N/A 790 0.42 1.00E-03 1.00 2.20 4 PM4SAND 1.99 N/A 500 0.45 1.00E-03 1.00 2.20 5 PM4SAND 1.99 N/A 575 0.51 1.00E-03 1.00 2.20 6 PM4SAND 1.99 N/A 673 0.50 1.00E-03 1.00 2.20 7 PM4SAND 1.99 N/A 624 0.45 1.00E-03 1.00 2.20 8 PM4SAND 1.99 N/A 747 0.48 1.00E-03 1.00 2.20 9 PM4SAND 1.99 N/A 798 0.53 1.00E-03 1.00 2.20 10 PM4SILT 1.50 59.00 343 2.20 1.00E-07 1.00 2.20 11 PM4SILT 1.50 59.00 285 2.20 1.00E-07 1.00 2.20 12 PM4SILT 1.50 59.00 368 2.20 1.00E-07 1.00 2.20 13 PM4SILT 1.50 59.00 356 2.20 1.00E-07 1.00 2.20 14 PM4SILT 1.50 59.00 360 2.20 1.00E-07 1.00 2.20 15 PM4SILT 1.50 59.00 469 2.20 1.00E-07 1.00 2.20 16 PM4SILT 1.50 59.00 413 2.20 1.00E-07 1.00 2.20 17 PM4SILT 1.50 59.00 233 2.20 1.00E-07 1.00 2.20 18 PM4SILT 1.50 59.00 248 2.20 1.00E-07 1.00 2.20 19 PM4SILT 1.50 59.00 279 2.20 1.00E-07 1.00 2.20 20 PM4SILT 1.50 59.00 275 2.20 1.00E-07 1.00 2.20 21 PM4SILT 1.50 59.00 478 2.20 1.00E-07 1.00 2.20 22 PM4SAND 2.09 N/A 2373 0.63 1.00E-04 1.00 2.20 23 PM4SAND 2.09 N/A 1549 0.63 1.00E-04 1.00 2.20 24 PM4SAND 2.09 N/A 1622 0.63 1.00E-04 1.00 2.20 25 PM4SAND 2.09 N/A 1195 0.63 1.00E-04 1.00 2.20 26 PM4SAND 2.09 N/A 950 0.63 1.00E-04 1.00 2.20 27 PM4SILT 1.76 134.00 383 2.20 1.00E-08 1.00 2.20 28 PM4SILT 1.76 134.00 481 2.20 1.00E-08 1.00 2.20 29 PM4SILT 1.76 134.00 465 2.20 1.00E-08 1.00 2.20 30 PM4SILT 1.76 134.00 451 2.20 1.00E-08 1.00 2.20 31 PM4SILT 1.76 134.00 437 2.20 1.00E-08 1.00 2.20 32 PM4SILT 1.76 134.00 424 2.20 1.00E-08 1.00 2.20 33 PM4SILT 1.76 178.00 412 2.20 1.00E-08 1.00 2.20
327 34 PM4SILT 1.76 178.00 401 2.20 1.00E-08 1.00 2.20 35 PM4SILT 1.76 178.00 390 2.20 1.00E-08 1.00 2.20 36 PM4SILT 1.76 178.00 381 2.20 1.00E-08 1.00 2.20 37 PM4SILT 1.76 178.00 371 2.20 1.00E-08 1.00 2.20 38 PM4SILT 1.76 178.00 362 2.20 1.00E-08 1.00 2.20 39 PM4SILT 1.76 216.00 354 2.20 1.00E-08 1.00 2.20 40 PM4SILT 1.76 216.00 346 2.20 1.00E-08 1.00 2.20 41 PM4SILT 1.76 216.00 339 2.20 1.00E-08 1.00 2.20 42 PM4SAND 2.16 N/A 1510 0.63 1.00E-02 1.00 2.20 43 PM4SAND 2.16 N/A 1473 0.63 1.00E-02 1.00 2.20 44 PM4SILT 1.76 262.00 645 2.20 1.00E-08 1.00 2.20 45 PM4SILT 1.76 262.00 633 2.20 1.00E-08 1.00 2.20 46 PM4SILT 1.76 262.00 621 2.20 1.00E-08 1.00 2.20 ðð = soil density; ððð¢ð¢ = undrained shear strength; ðºðº0 = shear modulus coefficient; âðððð = contraction rate parameter; ððð ð ððð ð = permeability; ððð¤ð¤ = water density; ðµðµðð = soil and water combined bulk modulus. Rayleigh damping parameters: ð¶ð¶ðð = 0.04 and ð·ð·ðð = 4 à 10â4.