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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 âvoidâ 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 âreplicaâ 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) â 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 â 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 â Summary of Advanced Laboratory Testing Soil RC and TS CyDSS Note Clay Y - - Silty Sand Y Y (Stress and Strain-Controlled) âCriticalâ 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 â 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 âintactâ 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 â Intactâ 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 (âblueâ line; corresponds to Vs profile as input in the SRA model). (a) (b) Figure E-6. Centrifuge Experiment â 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 âwithinâ 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 âblack.â (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 â 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 â 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 âcriticalâ 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 âcriticalâ layer. Figure E-14(g) shows stress-strain loops as inferred from the interpretation of Newtonâs 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) ððð«ð« = 0.24 ððð«ð« = 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 ð ð ð·ð·ððâ²(kPa) ðð (°) ðððð (kPa) ð¸ð¸ðððððð,ðð(%) ðµðµðððð 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 ððð·ð·ð·ð· (°) ðððð ðððð ðððð ððð ð ðððð ðð ð©ð©ðð (MPa) ð®ð®ðððððð (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. 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 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 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.
345 Parameters and Coefficients of the LE-MC model (Program 3) Layer No. LE-MC Input Parameters CM Ïd (T/m3) n (-) G0 (MPa) K (MPa) Φ (deg) c (kPa) Ï (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.