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212 APPENDIX E-1 Wildlife Liquefaction Array Site Site Response in the 1987 M 6.2 Elmore Ranch Earthquake General This Appendix presents results of numerical modeling of the response of the Wildlife Liquefaction Array (WLA) site in the 1987 M 6.2 Elmore Ranch earthquake. The WLA site is representative of a deep soil profile site. The top, liquefiable portion of this site was inadvertently created by flooding in 1906. It did not liquefy prior to the Elmore Ranch Earthquake. The analysis documented herein was performed in general accordance with the Guidance for âEffective-Stress Site Response Analysisâ outlined in Section 8.2 of the main report. Detailed site characterization of the WLA site 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 1987 M 6.2 Elmore Ranch 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 Constitutive Models SHAKE2000 D-MOD2000 FLAC PLAXIS OpenSeesPL S-I MKZ LE-MC PM4SAND UBCSAND UCSDSAND3 HSsmall PM4SAND UBCSAND U-CLAY2 UCSDSAND3 PM4SAND PM4SILT CM = Constitutive Model; LE-MC = Linear Elastic-Mohr Coulomb; HSsmall = Hardening Soil; 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). 1987 M 6.2 Elmore Ranch Earthquake and Ground Motions Relevant information about the 1989 M 6.2 Elmore Ranch earthquake and ground motions induced at the site are presented in Table E-2.
213 Table E-2. Key Parameters of Input Motion. Earthquake Date and Time M R PGA (NS) ruIn-Hole (7.5 m b.g.s.) Surface Elmore Ranch November 24, 1987. 01:54 GMT 6.2 23 km 0.078 g 0.128 g 0.025* M = Moment Magnitude; R = Approximate site-to-source distance; PGA = Peak Ground Acceleration; NS = North- South; ru = pore water pressure ratio (peak pore water pressure normalized with the initial vertical effective- stress); * = Recorded in a centrifuge experiment. Ground motions, as recorded in the 1987 M 6.2 Elmore Ranch earthquake, are shown in Figure E-1. The corresponding acceleration response spectra are shown in Figure E-2. (a) (b) Figure E-1. Acceleration histories in the 1987 M 6.2 Elmore Ranch Earthquake (N-S) (a) Ground Surface; (b) 7.5 m Downhole.
214 Figure E-2. Acceleration Response Spectra in the 1987 M 6.2 Elmore Ranch Earthquake (N-S) (a) Ground Surface; (b) 7.5 m Downhole. Figure E-3 shows the recorded excess pore water pressure (PWP) at a depth of 2.5 m. This excess PWP was generated in a centrifuge experiment (see Appendix C-1). The WLA site profile was simulated in a laminar box that was excited by the motion shown in Figure E-1(b) at its base. Figure E-3. 1987 M 6.2 Elmore Ranch Earthquake - Normalized Excess PWP History Generated in the Centrifuge Experiment. 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-1. Interpreted and summarized information is presented in Figure E-4. The silty sand (âcriticalâ layer) did not liquefy in the 1987 M 6.2 Elmore Ranch earthquake.
215 (a) (b) Figure E-4. WLA site â Interpreted Soil Profile with Location of Strong Motion Instruments. Shear Wave Velocity is from Bierschwale and Stokoe (1984) (see 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 â Summary of Advanced Laboratory Testing Soil RC and TS CyDSS Note Clay Y - - Silty Sand Y Y (Stress and Strain-Controlled) âCriticalâ Layer 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. Element Testing Table E-4 lists the results of element tests 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 herein. Program (i.e., SRA software) names into which CMs are embedded are obscured for administrative reasons.
216 Table E-4 â Summary of Element Testing Soil SHAKE2000 D-MOD2000 FLAC PLAXIS OpenSeesPL Clay N/A MKZ - - U-CLAY2 Silty Sand N/A MKZ LE-MC HSsmall UCSDSAND3 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-5 and E-6. Additional information is presented in Appendix D-3. (a) Clay (b) Silty Sand Figure E-5. CM Sub-Model Testing with the MKZ Model as implemented in Program 2. Modulus Reduction and Damping Curves were Developed as a Part of Site Exploration (Appendix B-1).
217 (a) Clay (b) Silty Sand Figure E-6. CM Sub-Model Testing with the UCSDSAND3 Model as implemented in Program 4. Modulus Reduction and Damping Curves were Developed as a Part of Site Exploration (Appendix B-1). (a) Silty Sand Figure E-7. CM Sub-Model Testing with the LE-MC Model as implemented in Program 3. Silty Sand Modulus Reduction and Damping Curves were Developed as a Part of Site Exploration (Appendix B-1). (a) Silty Sand
218 Figure E-8. CM Sub-Model Testing with the HSsmall Model as implemented in Program 5. Silty Sand Modulus Reduction and Damping Curves were Developed as a Part of Site Exploration (Appendix B-1). Figure E-7 shows evolution of stress-strain response as calculated from the results of CM sub- model testing presented in Figure E-5(b). Calculations were performed in total-stress mode for a range of shear strains. (a) (b) (c) (d) (e) Figure E-7. Stress-Strain Loops in WLA Site Silty Sand (MKZ Model): (a) Peak Shear Strain = 0.001%; (b) 0.01%; (c) 0.1%; (d) 1%; and (e) 10%. 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-8.
219 (a) (b) (c) Figure E-8. WLA Site - Comparison of Measured and Calculated Stress-Strain Response in a CyDSS Stress-Controlled Test on â Intactâ Specimen of Silty Sand. SRA Model Development The site response analysis model of the WLA site is presented in Figure E-4. It includes idealized soil stratification, groundwater elevation, and an interpreted shear wave velocity profile (âblueâ line in Figure E-4(b); corresponds to layering as input in the SRA model). Input motion was applied as a âwithinâ motion in SHAKE2000 and OpenSeesPL analyses. In D-MOD2000, the transmitting base option was used. In FLAC, the applied acceleration history option was used. Program (i.e., SRA software) names are further obscured are obscured for administrative reasons. The basic material properties, i.e., material properties that are not software-specific are provided for each layer in the Attachment.
220 System Testing Figure E-9 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 assumed Rayleigh damping model parameters were refined. The fine-tuning was performed with the Elmore Ranch in-hole record scaled to Peak Ground Acceleration (PGA) of 0.05 g. The results of the fine-tuning are shown in Figure E-9. The best match Rayleigh damping model parameter (n) and the target viscous damping (D) correspond to spectra indicated in âblack.â (a) Program 2 (MKZ) (b) Program 4 (UCSDSAND3) (c) Program 4 (PM4SAND) Figure E-9. System Testing with Program 2 (MKZ) and Program 4 (UCSDSAND3 and PM4SAND).
221 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-10. 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-10. Results of TSA â Recorded and Calculated Surface Response with Selected Software and CMs.
222 The Effective Stress Analysis (ESA) was performed without and with excess PWP (PWP) dissipation. The results of ESA with excess PWP dissipation allowed are presented in Figure E- 11. The recorded ground surface response is shown for reference. (a) Program 2 (MKZ) (b) Program 3 (PM4SAND) (c) Program 3 (UBCSAND) (d) Program 3 (UCSDSAND3)
223 (e) Program 5 (HSsmall) (f) Program 5 (PM4SAND) (g) Program 5 (UBCSAND) (h) Program 4 (UCSDSAND3) (i) Program 4 (PM4SAND) Figure E-11. Results of ESA â Recorded and Calculated Surface Response with Select Software and CMs.
224 Figure E-12 shows selected results of the TSA in a profile view. Input PGA (recorded at approximately 8 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 shear stress and strain response is reproduced from the Main Report as Figure E-16(g). The calculated and inferred shear stress are normalized with the initial vertical effective stress. (a) Peak Ground Acceleration (b) Normalized Peak Shear Stress (c) Peak Shear Strain Figure E-12. Results of TSA Recorded and Calculated Response. Results - Response within Soil Profile
225 Figure E-13 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. (a) Program 2 (MKZ) (b) Program 3 (LE-MC) Figure E-13. Results of TSA - Calculated Stress-Strain Response at 6 m b.g.s. Figure E-14 shows selected results of the ESA in a profile view (results with excess PWP dissipation allowed). Input PGA (recorded at approximately 8 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- 16(g). As noted above, excess PWP response was not recorded during the 1987 M 6.2 Elmore Ranch earthquake. However, excess PWP record was generated in a centrifuge experiment (see Appendix C-1). 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
226 (c) Peak Shear Strain (d) Normalized Excess PWP Figure E-14. Results of ESA - Recorded and Calculated Response. Figure E-15 shows select results of ESA as history of ru buildup. The recorded acceleration history is shown for reference. (a)
227 (b) Figure E-15. Effective-Stress Response of â Criticalâ Layer: (a) Calculated Excess PWP at 5.5 m b.g.s.; (b) Input Motion (Shown for Reference). Figure E-16 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-16(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 (UBCSAND) (d) Program 3 (UCSDSAND3) (e) Program 4 (UCSDSAND3) (f) Program 4 (PM4SAND)
228 (g) Inferred from SM Records Figure E-16. Results of ESA - Calculated Stress-Strain Response at 6 m b.g.s. Reference Bierschwale, J. G., and Stokoe, K. H. (1984). A n al y ti cal ev al uati on l i q uef acti on poten ti al of san d s sub j ected to the 1 981 W estm orel an d E arthq uak e. G eotech. E n g . Report 95 -6 6 3 , University of Texas, Civil Engineering Department.
229 APPENDIX E-1 - ATTACHMENT
230 Site Response Model of the Original WLA Site Layer No. Soil Type Thickness (m) Depth* (m) Vs (m/s) ksat (cm/s) γ (kN/m3) 1 Silt (WSA) 1.50 0.75 84 3.05E-06 17.0 2 Silt (WSA) 1.00 2.00 107 3.05E-04 18.9 3 Sand (WSA) 1.00 3.00 107 3.05E-04 19.4 4 Sand (WSB) 1.45 4.22 110 2.13E-03 19.4 5 Sand (WSB) 1.00 5.45 116 2.13E-03 19.4 6 Sand (WSB) 1.30 6.60 125 2.13E-03 19.4 7 Sand (WSB) 0.70 7.60 152 3.05E-05 19.4 Dw (m) H (m) (Vs)avg (m/s) T (s) fs (Hz) 1.50 7.95 111.1 0.286 3.49 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. 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 0.001 1.70 0.67 - - - 2 0.001 1.70 0.67 - - - 3 0.001 1.70 0.67 0.0025 0.43 0.62 4 0.001 1.50 0.68 0.0025 0.43 0.62 5 0.001 1.50 0.68 0.0025 0.43 0.62 6 0.001 1.50 0.68 0.0025 0.43 0.62 7 0.001 1.50 0.68 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 Rayleigh Damping (2) ððð«ð« = 0.1829 ððð«ð« = 7.591e-5 (1) PWP = Porewater Pressure. (2) Rayleigh damping coefficients, ððð«ð«, and ððð«ð«, are calculated for: Ts = 0.286 s, ðð = 0.5%, and ðð = 5. 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 1.1814 0.5542 13.57 29.39 30 1E+06 0 2 LE-MC 1.4928 0.4367 21.95 47.56 30 1E+06 0 3 LE-MC 1.5675 0.4085 22.48 48.71 30 1E+06 0 4 LE-MC 1.5675 0.4085 23.80 51.57 30 1E+06 0
231 5 LE-MC 1.5675 0.4085 26.50 57.42 30 1E+06 0 6 LE-MC 1.5675 0.4085 30.84 66.82 30 1E+06 0 7 LE-MC 1.5675 0.4085 45.86 99.36 30 1E+06 0 Layer No. LE-MC Input Parameters Tens. (kPa) K0 (-) k11 (cm/s) k22 (cm/s) k12 (cm/s) Sat. (-) 1 1E+06 0.5 3.05E-06 3.05E-06 0.00E+00 1 2 1E+06 0.5 3.05E-04 3.05E-04 0.00E+00 1 3 1E+06 0.5 3.05E-04 3.05E-04 0.00E+00 1 4 1E+06 0.5 2.13E-03 2.13E-03 0.00E+00 1 5 1E+06 0.5 2.13E-03 2.13E-03 0.00E+00 1 6 1E+06 0.5 2.13E-03 2.13E-03 0.00E+00 1 7 1E+06 0.5 3.05E-05 3.05E-05 0.00E+00 1 Layer No. LE-MC Input Parameters Sig3 hysteretic damping (4) Rayleigh (5) a b x0 1 0.9998 -0.648 -1.343 0.867% @ 3.4 Hz 2 0.9998 -0.648 -1.343 3 0.9998 -0.648 -1.343 4 1.0000 -0.639 -1.259 5 1.0000 -0.639 -1.259 6 1.0000 -0.639 -1.259 7 1.0000 -0.639 -1.259 (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) Stiffness-proportional. Parameters and Coefficients of the PM4SAND Model (Program 3) Layer No. CM Sig3 (three parameters stress- strain model) (4) Rayleigh Damping (5,6) PM4SAND non-default parameters (5) a b x0 Dr Go hpo 1 LE-MC 0.9998 -0.648 -1.343 1% @ 2 Hz - - - 2 LE-MC 0.9998 -0.648 -1.343 - - - 3 PM4SAND - - - 0.38 350 1.90 4 PM4SAND - - - 0.58 266 0.86 5 PM4SAND - - - 0.58 266 0.86 6 PM4SAND - - - 0.58 266 0.86 7 LE-MC 1.0000 -0.639 -1.259 - - - (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) Based on Ziotopoulou (2010). (5) Total, i.e., combined stiffness- and mass-proportional.
232 Parameters and Coefficients of the UBCSAND Model (Program 3) Layer No. CM Sig3 (three parameters stress- strain model) (4) Rayleigh damping (5,6) UBCSAND non-default parameter (5) a b x0 (N1)60c s (7) kGe kB kGp 1 LE-MC 0.9998 -0.6479 -1.3433 1% @ 2 Hz - - - - 2 LE-MC 0.9998 -0.6479 -1.3433 - - - - 3 UBCSAND - - - 9.55 472.6 1024.0 500 4 UBCSAND - - - 14.92 393.5 852.6 800 5 UBCSAND - - - 14.92 393.5 852.6 800 6 UBCSAND - - - 14.92 393.5 852.6 800 7 LE-MC 1.0000 -0.6387 -1.2589 - - - - (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) Based on Ziotopoulou (2010). (5) Total, i.e., combined stiffness- and mass-proportional. (6) "cs" denotes adjusted for "clean sand." Parameters and Coefficients of the UCSDSAND3 Model (Program 3) Layer No. CM Sig3 (three parameters stress- strain model) (4) Rayleigh (5,6) UCSDSAND3 non- default params a b x0 (N1)60 (4,6,7) 1 LE-MC 0.9998 -0.6479 -1.3433 1% @ 2 Hz - 2 LE-MC 0.9998 -0.6479 -1.3433 - 3 UCSDSAND3 - - - 9.55 4 UCSDSAND3 - - - 14.92 5 UCSDSAND3 - - - 14.92 6 UCSDSAND3 - - - 14.92 7 LE-MC 1.0000 -0.6387 -1.2589 - (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) Based on Ziotopoulou (2010). (5) Total, i.e., combined stiffness- and mass-proportional. (6) Input values correspond to "clean sand" ("cs") adjusted values. 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-Clay2 0.0 101 0 6 10 20 2 U-Clay2 0.0 101 0 9.5 10 20 3 U-Clay2 0.0 101 0 10 10 20 4 U-Sand3 0.0 18 30 1.73 10 20 5 U-Sand3 0.0 20 30 1.73 10 20
233 6 U-Sand3 0.0 20 30 1.73 10 20 7 U-Clay2 0.0 101 0 21 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 - - - - - - 0.49 605.8 12.2 2 - - - - - - 0.49 1089.8 21.9 3 - - - - - - 0.49 1116.1 22.5 4 25.40 0.02 4.00 0.30 12.50 1.00 0.30 51.5 23.8 5 25.30 0.02 4.00 0.30 12.50 1.00 0.30 57.4 26.5 6 25.30 0.02 4.00 0.30 12.50 1.00 0.30 66.8 30.8 7 - - - - - - 0.49 2276.7 45.8 Layer No. ðððððððð (cm/s) ð©ð©ðð(GPa) ð©ð©ðð(GPa) ðð (Mg/m 3) Parameters for soil dilation ð ð ðð ð ð ðð ð ð ðð 1 3.05E-06 2.20 3.97 1.73 - - - 2 3.05E-04 2.20 5.04 1.93 - - - 3 3.05E-04 2.20 5.39 1.97 - - - 4 2.13E-03 2.20 5.39 1.97 0.3 3 -0.3 5 2.13E-03 2.20 5.39 1.97 0.3 3 -0.3 6 2.13E-03 2.20 5.39 1.97 0.3 3 -0.3 7 3.05E-05 2.20 5.39 1.97 - - - 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 = 1.82 and ð·ð·ðð = 0.00078. 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 (cm/s) ðððð (Mg/m3) ð©ð©ðð(GPa) 1 PM4SILT 1.73 36.3 580 1.20 3.05E-06 1.00 2.20 2 PM4SILT 1.93 25.1 548 1.20 3.05E-04 1.00 2.20 3 PM4SAND 1.97 N/A 360 0.53 3.05E-04 1.00 2.20 4 PM4SAND 1.97 N/A 420 0.53 2.13E-03 1.00 2.20 5 PM4SAND 1.97 N/A 421 0.45 2.13E-03 1.00 2.20 6 PM4SAND 1.97 N/A 452 0.45 2.13E-03 1.00 2.20 7 PM4SILT 1.97 30.6 533 1.20 3.05E-05 1.00 2.20 CM = constitutive model; 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 = 0.36 and ð·ð·ðð = 0.00016.