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234 APPENDIX E-2 Wildlife Liquefaction Array Site Site Response in the 1987 M 6.6 Superstition Hills Earthquake General This Appendix presents results of numerical modeling of the response of the Wildlife Liquefaction Array (WLA) site in the 1987 M 6.6 Superstition Hills earthquake. The WLA site is representative of a deep soil profile site. The analysis documented herein differs from its counterpart presented in Appendix E-1 only in input motion. Select information is reproduced from Appendix E-1 for convenience. The analysis was performed in general accordance with the âGuidance for Effective Stress Site Response Analysisâ outlined in Section 8.2 of the main report. Detailed site characterization is provided in Appendix B-1. Model Selection Table E-1 lists the software and constitutive models used to calculate response of the WLA site in the 1987 M 6.6 Superstition Hills earthquake. Detailed information about the selected software is provided in Section 4.2 of the main report. Detailed information about the selected constitutive models (CMs) is provided in Section 4.3 of the main report. Table E-1. Selected Software and CMs SHAKE2000 D-MOD2000 FLAC PLAXIS OpenSeesPL S-I MKZ LE-MC PM4SAND UBCSAND UCSDSAND3 HSsmall PM4SAND UBCSAND U-CLAY2 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 6.6 Superstition Hills Earthquake and Ground Motions Relevant information about the 1987 M 6.6 Superstition Hills earthquake and the corresponding ground motions induced at the WLA site are presented in Table E-2.
235 Table E-2. Key Parameters of Input Motion. Earthquake Date and Time M R PGA (N-S) ruIn-Hole (7.5 m b.g.s.) Surface Superstition Hills November 24, 1987. 13:15 GMT 6.6 31 km 0.171 g 0.205 g ⥠M = Moment Magnitude; R = Approximate site-to-source distance; PGA = Peak Ground Acceleration; N-S = North- South; ru = pore water pressure ratio (peak pore water pressure normalized with the initial vertical effective stress). Ground motions, as recorded in the 1987 M 6.6 Superstition Hills earthquake in the North- South direction are shown in Figure E-1. The corresponding acceleration response spectra are shown in Figure E-2. (a) (b) Figure E-1. Acceleration Histories Recorded in the 1987 Superstition Hills Earthquake: (a) Ground Surface; (b) 7.5 m Downhole.
236 Figure E-2. Acceleration Response Spectra in the 1987 M 6.6 Superstition Hills Earthquake: (a) Ground Surface; (b) 7.5 m Downhole. Figure E-3 presents the normalized PWP response of the WLA site silty sand layer ("Unit Bâ; âcriticalâ layer) in the 1987 M 6.6 Superstition Hills earthquake. The normalization is with the initial vertical effective stress, and these normalized values are referred to as the PWP ratio (ru). Figure E-3. Normalized Excess PWP Recorded at the WLA Site in the 1987 M 6.6 Superstition Hills Earthquake. 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. Silty sand (i.e., âcriticalâ layer) liquefied in the 1987 M 6.6 Superstition Hills earthquake. Excess PWP was recorded in piezometers P1, P2, P4 and in P5.
237 (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 (Refer to Appendix E-1) 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 CyDSS test results are available only for silty sand (Stress- and Strain-Controlled); see Appendix C-2. 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-2. The CM sub-model testing is documented in Appendix E-1. 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).
238 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; 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. 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-5 documents the process of system testing (i.e., model testing at the soil profile level) for Programs 2 and 4 (program names are obscured for administrative reasons). 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-5. 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)
239 (c) Program 4 (PM4SAND) Figure E-5. System Testing with Program 2 ( MKZ) and Program 4 (UCSDSAND3 and PM4SAND). 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-6. The recorded input motion and recorded ground surface response are shown for reference. (a) Program 1 (S-I) (b) Program 2 (MKZ)
240 (c) Program 3 (LE-MC) (d) Program 5 (HS small) Figure E-6. Results of TSA â Recorded and Calculated Surface Response with Select Software and CMs. The Effective Stress Analysis (ESA) was performed without and with excess PWP dissipation. The results of ESA with excess PWP dissipation allowed are presented in Figure E-7. The recorded input motion and recorded ground surface response are shown for reference. (a) Program 2 (MKZ) (b) Program 3 (PM4SAND)
241 (c) Program 3 (UBCSAND) (d) Program 3 (UCSDSAND3) (e) Program 5 (PM4SAND) (f) Program 5 (UBCSAND) (g) Program 4 (UCSDSAND3) (h) Program 4 (PM4SAND) Figure E-7. Results of ESA â Recorded and Calculated Surface Response.
242 At the WLA site, the âcriticalâ layer is confined by two low-hydraulic conductivity layers (âclayâ and âlean clayâ layers; see Figure E-4). Therefore, the effects of excess PWP dissipation are expected to be small. This is shown in Figure E-8 where very small difference is spectra calculated with and without excess PWP dissipation allowed. (a) Program 2 (MKZ) (b) Program 4 (UCSDSAND3) Figure E-8. Results of ESA â Evaluation of the Effects of Excess PWP Dissipation. Results - Response within Soil Profile Figure E-8 shows select 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 stress and strain response is reproduced from the main report as Figure E-16(i). The calculated and inferred shear stress are normalized with the initial vertical effective stress. (a) Peak Ground Acceleration (b) Normalized Peak Shear Stress
243 (c) Peak Shear Strain Figure E-8. Results of TSA - Recorded and Calculated Response. Figure E-9 shows select results of TSA presented in a 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-9. Results of TSA - Calculated Stress-Strain Response at 6 m b.g.s. Figure E-10 shows select 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-13(i). An excess PWP response is presented herein in the form of normalized pore water pressure (PWP) ratio
244 (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 (c) Peak Shear Strain (d) Normalized Excess PWP Figure E-10. Results of ESA - Recorded and Calculated Response.
245 Figure E-11 shows select results of ESA as history of ru buildup. The recorded acceleration history is shown for reference. Note that calculated excess PWP response is not only software dependent, but also advanced CM-dependent. (a) (b) Figure E-12. Effective Stress Response of Critical Layer: (a) Calculated Excess PWP at 4.8 m b.g.s. (Installed Depth of Piezometer P1); (b) Input Motion (Shown for Reference). Figure E-13 shows select results of ESA presented in a form of stress-strain loops calculated in the middle of the submerged portion of the âcriticalâ layer. Figure E-13(i) 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).
246 (a) Program 2 (MKZ) (b) Program 3 (PM4SAND) (c) Program 3 (UBCSAND) (d) Program 3 (UCSDSAND3) (e) Program 5 (PM4SAND) (f) Program 5 (UBCSAND) (g) Program 4 (UCSDSAND3) (h) Program 4 (PM4SAND) (i) Inferred from SM Records Figure E-13. Results of ESA - Calculated Stress-Strain Response at 6 m b.g.s. Reference Bierschwale, J. G., and Stokoe, K. H. (1984), âAnalytical Evaluation of Liquefaction Potential of Sands Subjected to the 1981 Westmoreland Earthquake , â T echn i cal Report N o. 95 -6 6 3 , Civil Engineering Department, University of Texas at Austin, Austin, Texas.