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267 APPENDIX E-4 Owi Island Site â Case Study Site Response in the 1985 M 6.2 Chiba-Ibaragi Earthquake General This Appendix presents results of numerical modeling of the response of the Owi Island site in the 1985 M 6.2 Chiba-Ibaragi earthquake. Owi Island was constructed through the hydraulic deposition of sand, silt, and gravel over natural soil layers of clay, silt, and sand. As analyzed herein (acceleration history was recorded at 10 m b.g.s.), this case history is representative of a shallow soil profile site. Soil profile at the site is liquefiable, as identified by screening. 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-2. Model Selection Table E-1 lists the software and constitutive models used to calculate response of the Owi Island site in the 1985 M 6.2 Chiba-Ibaragi 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 LE-MC = Linear Elastic-Mohr Coulomb (also total stress analysis); S-I = Seed â 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). Chiba-Ibaragi Earthquake and Ground Motions Relevant information about the 1985 M 6.2 Chiba-Ibaragi earthquake and ground motions induced at the site is reproduced from Appendix B-3 in Table E-2.
268 Table E2. Chiba-Ibaragi Earthquake â Earthquake and Strong Motion Parameters at the Site. Earthquake Date M R PGA (N-S) ru Chiba-Ibaragi October 4, 1985 6.2 50 km Surface (SM2) 10 m b.g.s. (downhole; SM1) 6 m 14 m 0.072 g 0.043 g 2.6% 3.0% M = Moment Magnitude; R = Approximate site-to-source distance; PGA = Peak Ground Acceleration; ru = Maximum recorded excess pore water pressure normalized by the vertical effective stress; N-S = North-South (direction); SM = Strong Motion (Instrument). 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-2. The silty fine sand layer with Pore Water Pressure (PWP) transduced P2 in the middle has been identified as the âcriticalâ layer by screening. (a) (b) Figure E-1. Owi Island Site - Interpreted Soil Profile with Location of Strong Motion Instruments. Measured Shear Wave Velocity is from Ishihara et al. (1987). Advanced Laboratory Testing and Interpretation of the Results Table E-3 summarizes information on the available results of advanced laboratory testing of silty fine sand (applicable to all sands in the profile). Dynamic properties of silt were not measured. More information about this testing and how properties of silt were estimated is provided in Appendix B-2.
269 Table E-3 â Summary of Advanced Laboratory Testing Soil RC and TS Sand Y Silt N (MRD Curves Estimated by Ishihara et al., 1987) RC = Resonant Column; TS = Torsional Shear; Y = Available and used herein; N = Not Measured. MRD = Modulus Reduction and Damping (curves). Element Testing Table E-4 lists the results of CM sub-model testing, i.e., fitting of the modulus reduction and damping curves. The element testing of the results of undrained stress-controlled CyDSS testing was not possible as results of undrained CyDSS testing are not available. Table E-4 â Summary of Element Testing Material (Test Type) SHAKE2000 D-MOD2000 FLAC OpenSees Sand N/A MKZ LE-MC PM4SAND UBCSAND UCSDSAND3 UCSDSAND3 PM4SAND Silt N/A MKZ LE-MC UCSDCLAYPM4SILT 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. Program (i.e., SRA software) names are obscured are obscured for administrative reasons. (a) Sand
270 (b) Silt Figure E-2. CM Sub-Model Testing with the MKZ Model (Program 2). Modulus Reduction and Damping Curves for Sand and Silt are from Ishihara et al. (1987). (a) Sand (b) Silt Figure E-3. CM Sub-Model Testing with the UCSDSAND3 Model (Program 4). Modulus Reduction Curves are from Ishihara et al. (1987). SRA Model Development The site response analysis model of the Owi Island site is presented in Figure E-1. It includes idealized soil stratification, groundwater elevation, and an interpreted shear wave velocity profile (red line; 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. 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.
271 System Testing Figure E-4 documents the process of system testing (i.e., model testing at the soil profile level) for D-MOD2000 and OpenSeesPL. Upon completion of the system testing, for both programs, the Rayleigh damping model parameters assessed were fine-tuned in an iterative process. The Rayleigh damping model parameter (n) and the target viscous damping (D) selected for evaluation of the Owi Island site response to the 1985 M 6.2 Chiba-Ibaragi earthquake correspond to spectra indicated in âblackâ in Figure E-4. They are identical and were also used for calculations with FLAC. (a) Program 2 (MKZ) (b) Program 4 (UCSDSAND3) (c) Program 4 (PM4SAND) Figure E-4. System Testing with Program 2 and Program 4.
272 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-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 Select Software and CMs. 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-6. The recorded ground surface response is shown for reference.
273 (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.
274 Results - Response within Soil Profile Figure E-7 shows select results of the TSA in a profile view. Input PGA (recorded at approximately 10 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 Figure E-12. 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-7. Results of TSA - Recorded and Calculated Response. Figure E-8 shows select results of ESA in a profile view (results with excess PWP dissipation allowed). Recorded PGA values are shown for reference. An excess PWP response is
275 presented herein in the form of normalized PWP ratio (ru). Both ru and calculated shear stress are normalized with the initial vertical effective stress. Figure E-8 shows select results of TSA presented in the form of calculated stress-strain loops. (a) Program 2 (MKZ) (b) Program 3 (LE-MC) Figure E-8. Results of TSA - Calculated Stress-Strain Response at 5.9 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 10 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 Figure E-12(a). The calculated and inferred shear stress are normalized with the initial vertical effective stress. 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
276 (c) Peak Shear Strain (d) Normalized Excess PWP Figure E-9. Results of ESA - Recorded and Calculated Response. Figure E-10 shows select results of ESA as history of ru buildup. The recorded acceleration history is shown for reference. Calculated excess PWP response is notably overestimated with all but one model.
277 (a) (b) Figure E-10. (a) Comparison of recorded and calculated PWP ratio (ru) at a depth of 6 m; (b) acceleration time history recorded in the 1985 Chiba-Ibaragi earthquake at depth of 10 m. Figure E-11 shows select 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-11(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).
278 (a) Program 2 (MKZ) (b) Program 3 (PM4SAND) (c) Program 3 (UBCSAND) (d) Program 3 (UCSDSAND3) (e) Program 4 (UCSDSAND3) (f) Program 4 (PM4SAND) (g) Inferred from SM Records Figure E-11. Results of ESA - Calculated Stress-Strain Response at 5.9 m b.g.s.
279 Figure E-12(a) shows interpretation of site information in terms of ârecordedâ stress-strain loops. The interpretation is explained and documented in Appendix B-2. Figure E-12(b) shows select results of ESA presented in the form of the corresponding calculated stress-strain loops. (a) Interpreted Stress-Strain Loops (b) Calculated Stress-Strain Loops Figure E-12. Results of ESA â Interpreted and Calculated Stress-Strain Response at 5.9 m b.g.s. Figure E-13 is a "window" (5 to 12 seconds) of recorded and calculated time histories. The comparison is made at the ground surface. For select software-CM pair, recorded and calculated compare very well.
280 Figure E-13. Comparison of the Recorded and Calculated Free-Field Ground Surface Motions in the 1985 M 6.2 Chiba-Ibaragi Earthquake. References Ishihara, K., Anazawa, Y., and Kuwano, J. (1987). "Porewater Pressures and Ground Motions Monitored during the 1985 Chiba-Ibaragi Earthquake." S oi l s an d f oun d ati on s, The Japanese Geotechnical Society, Vol. 27, No. 3, pp. 13â30.
281 APPENDIX E-4 Attachment Site Response Model of the Owi Island Site. Layer Soil Type (Modeled as) Thickness (m) Depth (m) Vs (m/s) ksat (cm/s) γ (kN/m3) 1 Surface soil (Sand) 1.40 0.70 140 3.05E-06 17.9 2 Sandy silt (Silt) 1.40 2.10 210 3.05E-04 19.5 3 Sandy gravel (Sand) 0.70 3.15 210 3.96E-03 19.5 4 Fine sand with silt (Sand) 1.00 4.00 210 2.01E-03 18.0 5 Silty fine sand (Sand) 2.80 5.90 155 2.01E-03 17.0 6 Fine sand with silt (Sand) 1.50 8.05 100 2.01E-03 17.0 7 Silty with sand (Silt) 1.20 9.40 140 3.05E-05 17.0 Dw (m) H (m) (Vs)avg (m/s) Ts (s) fs (Hz) 1.50 10.00 161.3 0.248 4.03 Depth = depth of middle of the layer; Vs = soil shear wave velocity; k = saturated hydraulic conductivity; γ = saturated or wet soil unit weight; Dw = depth of groundwater table; H = total thickness of soil layer; (Vs)avg = weighted average of soil shear wave velocity; T = 1st natural period of the soil layer; fs = 1st natural frequency of the soil layer. Parameters and Coefficients of the MKZ Model (Program 2) Layer No. MKZ - Nonlinear Stress-Strain MKZ - PWP Dissipation γr (-) β s K2 m n Er (MPa) 1 0.00100 1.5 0.67 - - - - 2 0.00100 0.9 0.67 - - - 1E-8 3 0.00100 1.5 0.67 0.0025 0.43 0.62 - 4 0.00100 1.5 0.68 0.0025 0.43 0.62 - 5 0.00100 1.5 0.68 0.0025 0.43 0.62 - 6 0.00100 1.5 0.68 0.0025 0.43 0.62 - 7 0.00100 0.9 0.68 - - - 1E-8 Layer No. MKZ - PWP Generation (for cohesionless materials) ν f P F S γtv (%) 1 - - - - - - 2 - - - - - - 3 1 2 1.005 3 1.8 0.025 4 1 2 1.005 3 1.8 0.025 5 1 2 1.005 3 1.8 0.025 6 1 2 1.005 3 1.7 0.025 7 - - - - - - Layer No. MKZ - PWP Generation (for cohesion materials) OCR St ð«ð« A B C D γtv (%) 1 - - - - - - - - 2 1 0.075 0.495 7.6451 -14.7174 6.38 0.6922 0.1 3 - - - - - - - - 4 - - - - - - - - 5 - - - - - - - - 6 - - - - - - - - 7 1 0.075 0.495 7.6451 -14.7174 6.38 0.6922 0.1 Rayleigh Damping(2) ððð«ð« = 0.211 ððð«ð« = 6.57e-5 (1) PWP = Pore Water Pressure. Rayleigh damping coefficients, ððð«ð«, and ððð«ð«, are calculated by using the period of the soil layer as 0.248 s, the viscous damping, ðð, as %0.5, and the ðð value as 5.
282 Parameters and Coefficients of the LE-MC Model (Program 3) LE-MC Input Parameters Layer No. CM Ïd (T/m 3) n (-) G0 (MPa) K (MPa) Ï (deg) c (kPa) Ï (deg) 1 LE-MC 1.3296 0.4983 41.09 89.03 30 1E+06 0 2 LE-MC 1.5880 0.4007 87.67 189.94 30 1E+06 0 3 LE-MC 1.5880 0.4007 87.67 189.94 30 1E+06 0 4 LE-MC 1.3435 0.493 80.94 175.37 30 1E+06 0 5 LE-MC 1.1788 0.5552 41.64 90.21 30 1E+06 0 6 LE-MC 1.1788 0.5552 17.33 37.55 30 1E+06 0 7 LE-MC 1.1788 0.5552 33.97 73.60 30 1E+06 0 Layer No. LE-MC Input Parameters Tens. (kPa) K0 (-) k11 (m/s) k22 (m/s) k12 (m/s) Sat. (-) 1 1E+06 0.5 3.05E-06 3.05E-06 3.05E-06 1 2 1E+06 0.5 3.05E-04 3.05E-04 3.05E-04 1 3 1E+06 0.5 3.96E-03 3.96E-03 3.96E-03 1 4 1E+06 0.5 2.01E-03 2.01E-03 2.01E-03 1 5 1E+06 0.5 2.01E-03 2.01E-03 2.01E-03 1 6 1E+06 0.5 2.01E-03 2.01E-03 2.01E-03 1 7 1E+06 0.5 3.05E-05 3.05E-05 3.05E-05 1 Layer No. LE-MC Input Parameters Sig3 hysteretic damping (4) Rayleigh (5) a b x0 1 1.0000 -0.543 -0.982 0.5% @ 3.8 Hz 2 0.9999 -0.457 -0.433 3 1.0000 -0.543 -0.982 4 1.0000 -0.543 -0.982 5 1.0000 -0.543 -0.982 6 1.0000 -0.543 -0.982 7 0.9999 -0.457 -0.433 1. CM = Constitutive Model 2. LE-MC used for quasi-static stress initialization phase for all layers. 3. Initial bulk modulus calculated assuming Poisson's ratio 0.3 for all layers. 4. Fitted to MKZ model modulus reduction curves used in D-MOD2000 calibration. 5. Total, i.e., combined stiffness- and mass-proportional.
283 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 1.0000 -0.543 -0.982 1% @ 2 Hz - - - 2 LE-MC 0.9999 -0.457 -0.433 - - - 3 LE-MC 1.0000 -0.543 -0.982 - - - 4 LE-MC 1.0000 -0.543 -0.982 - - - 5 LE-MC 1.0000 -0.543 -0.982 - - - 6 PM4SAND - - - 0.58 266 0.86 7 LE-MC 0.9999 -0.457 -0.433 - - - 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)60cs (7) kGe kB kGp 1 LE-MC 1.0000 -0.5427 -0.9821 1% @ 2 Hz - - - - 2 LE-MC 0.9999 -0.4574 -0.4327 - - - - 3 LE-MC 1.0000 -0.5427 -0.9821 - - - - 4 LE-MC 1.0000 -0.5427 -0.9821 - - - - 5 LE-MC 1.0000 -0.5427 -0.9821 - - - - 6 UBCSAND - - - 14.92 393.5 852.6 800.0 7 LE-MC 0.9999 -0.4574 -0.4327 - - - - (1) CM = Constitutive Model (2) LE-MC used for quasi-static stress initialization phase for all layers. (3) Initial bulk modulus calculated assuming Poisson's ratio 0.3 for all layers. (4) Fitted to MKZ model modulus reduction curves used in D-MOD2000 calibration. (5) Based on Ziotopoulou (2010). (6) Total, i.e., combined stiffness- and mass-proportional. (7) "cs" denotes adjusted for "clean sand.".
284 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 1.0000 -0.5427 -0.9821 1% @ 2 Hz - 2 LE-MC 0.9999 -0.4574 -0.4327 - 3 LE-MC 1.0000 -0.5427 -0.9821 - 4 LE-MC 1.0000 -0.5427 -0.9821 - 5 LE-MC 1.0000 -0.5427 -0.9821 - 6 UCSDSAND3 - - - 14.92 7 LE-MC 0.9999 -0.4574 -0.4327 - (1) CM = Constitutive Model (2) LE-MC used for quasi-static stress initialization phase for all layers. (3) Initial bulk modulus calculated assuming Poisson's ratio 0.3 for all layers. (4) Fitted to MKZ model modulus reduction curves used in D-MOD2000 calibration. (5) Based on Ziotopoulou (2010). (6) Total, i.e., combined stiffness- and mass-proportional. (7) Input values correspond to "clean sand" ("cs") adjusted values.
285 Parameters and Coefficients of the UBCSAND 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-Sand3 0.0 70 30 1.5 10 20 2 U-Clay2 0.0 100 0 300 10 20 3 U-Sand3 0.0 150 30 1.5 10 20 4 U-Sand3 0.0 110 30 1.5 10 20 5 U-Sand3 0.0 70 30 1.5 10 20 6 U-Sand3 0.0 30 30 1.5 10 20 7 U-Clay2 0.0 100 0 110 10 20 Layer No. Parameters for the generation of pore water pressure Soil Stiffness ððð·ð·ð·ð· (°) ðððð ðððð ðððð ððð ð ðððð ðð ð©ð©ðð (MPa) ð®ð®ðððððð (MPa) 1 25.30 0.01 3.00 0.40 9.00 0.00 0.30 89.0 41.1 2 N/A N/A N/A N/A N/A N/A 0.40 408.9 87.6 3 25.30 0.01 3.00 0.40 9.00 0.00 0.30 189.9 87.6 4 25.30 0.01 3.00 0.40 9.00 0.00 0.30 175.3 80.9 5 25.30 0.01 3.00 0.40 9.00 0.00 0.30 90.2 41.6 6 25.30 0.01 3.00 0.40 9.00 0.00 0.30 37.5 17.3 7 N/A N/A N/A N/A N/A N/A 0.40 158.4 34.0 Layer No. ðððððððð (cm/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 3.05.E-06 2.20 5.50 1.83 0.3 3 -0.3 2 3.05.E-04 2.20 5.50 1.99 N/A N/A N/A 3 3.96.E-03 2.20 5.50 1.99 0.3 3 -0.3 4 2.01.E-03 2.20 5.50 1.84 0.3 3 -0.3 5 2.01.E-03 2.20 5.50 1.73 0.3 3 -0.3 6 2.01.E-03 2.20 5.50 1.73 0.3 3 -0.3 7 3.05.E-05 2.20 5.50 1.73 N/A N/A N/A 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 = 0.21 and ð·ð·ðð = 6.6e-5.
286 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 PM4SNAD 1.83 N/A 1465 0.63 3.05E-06 1.00 2.20 2 PM4SILT 1.99 4.5 2102 2.20 3.05E-04 1.00 2.20 3 PM4SAND 1.99 N/A 1707 0.63 3.96E-03 1.00 2.20 4 PM4SAND 1.84 N/A 1452 0.53 2.01E-03 1.00 2.20 5 PM4SAND 1.73 N/A 659 0.53 2.01E-03 1.00 2.20 6 PM4SAND 1.73 N/A 246 0.53 2.01E-03 1.00 2.20 7 PM4SILT 1.73 12.5 377 2.20 3.05E-05 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 = 0.21 and ð·ð·ðð = 0.00006.