Prediction of co-seismic soil slope instability with finite element methods
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(2) Appendix D . D.1.2. Height: 10 m . . i (°) . 32 . H/L . FS 1.03 . 0.625 1.1 . 30 . 0.58 1.36 . 25 . 20 . 15 . 10 . . 2 . 0.47 . 0.36 . 0.27 . 0.18 . 1.71 . 2.29 . 3.41 . f (Hz) . PHAc (g) . 1 . 0.1 . 2 . 0.2 . 4 . 0.2 . 6 . 0.7 . 1 . 0.15 . 2 . 0.3 . 4 . 0.25 . 6 . 0.75 . 1 . 0.2 . 2 . 0.7 . 4 . 0.4 . 6 . 0.8 . 1 . 0.3 . 2 . 1 . 4 . 0.7 . 6 . 0.85 . 1 . 1 . 2 . 1.3 . 4 . 0.8 . 6 . 1.25 . 1 . 1 . 2 . 1.3 . 4 . 0.9 . 6 . 1.5 .
(3) Slope Critical Accelerations (Tables): Sands . D.1.3. Height: 20 m . . i (°) . 29 . 25 . 20 . 15 . 10 . H/L . 0.55 . 0.47 . 0.36 . 0.27 . 0.18 . FS . 1.04 . 1.28 . 1.63 . 2.21 . 3.35 . f (Hz) . PHAc (g) . 1 . 0.05 . 2 . 0.25 . 4 . 0.25 . 6 . 0.6 . 1 . 0.07 . 2 . 0.5 . 4 . 0.4 . 6 . 0.75 . 1 . 0.1 . 2 . 0.75 . 4 . 0.5 . 6 . 1 . 1 . 0.9 . 2 . 1 . 4 . 0.6 . 6 . 1.25 . 1 . 1 . 2 . 1 . 4 . 0.75 . 6 . 1.35 . . 3 .
(4) Appendix D . D.1.4. Height: 40 m . . i (°) . 28 . 25 . 20 . 15 . 10 . . 4 . H/L . 0.53 . 0.47 . 0.36 . 0.27 . 0.18 . FS . 1.07 . 1.21 . 1.58 . 2.17 . 3.31 . f (Hz) . PHAc (g) . 1 . 0.2 . 2 . 0.1 . 4 . 0.3 . 6 . 1.1 . 1 . 0.25 . 2 . 0.2 . 4 . 0.4 . 6 . 1.25 . 1 . 0.3 . 2 . 0.25 . 4 . 0.5 . 6 . 1.25 . 1 . 0.6 . 2 . 0.6 . 4 . 0.6 . 6 . 1.25 . 1 . 1 . 2 . 0.75 . 4 . 0.7 . 6 . 1.25 .
(5) Slope Critical Accelerations (Tables): Sands . D.2. Sand 2: “medium dense sand” . D.2.1. Height: 5 m . i (°) . H/L . FS . f (Hz) . PHAc (g) . 1 . n.m.1 . 2 . n.m.1 . 4 . n.m.1 . 38 . 0.78 . 1.01 . 6 . n.m.1 . 35 . 0.7 . 1.11 . 1 . 0.25 . 2 . 0.3 . 4 . 0.35 . 6 . 0.9 . 1 . 0.4 . 2 . 0.5 . 4 . 0.5 . 6 . 1.5 . 1 . 0.5 . 2 . 1.0 . 4 . 0.75 . 6 . ‐ . 30 . 25 . 0.58 . 0.47 . 1.33 . 1.56 . n.m.1 Not measurable due to marginal static stability . 5 .
(6) Appendix D . D.2.2. Height: 10 m . i (°) . 34 . 30 . 25 . 20 . 15 . 10 . . 6 . H/L . FS . f (Hz) . PHAc (g) . 1 . 0.15 . 2 . 0.2 . 4 . 0.25 . 0.68 . 1.02 . 6 . 0.6 . 1 . 0.2 . 2 . 0.3 . 4 . 0.35 . 0.58 . 1.19 . 6 . 0.75 . 1 . 0.25 . 2 . 0.5 . 0.47 . 1.46 . 4 . 0.45 . 6 . 1.0 . 1 . 0.3 . 2 . 1.0 . 4 . 0.6 . 6 . 1.4 . 1 . 0.75 . 0.36 . 0.27 . 0.18 . 1.84 . 2.46 . 3.7 . 2 . ‐ . 4 . 0.75 . 6 . 1.5 . 1 . ‐ . 2 . ‐ . 4 . 0.9 . 6 . ‐ .
(7) Slope Critical Accelerations (Tables): Sands . D.2.3. Height: 20 m . i (°) . 32 . 25 . 20 . 15 . 10 . H/L . 0.62 . 0.47 . 0.36 . 0.27 . 0.18 . FS . 1.02 . 1.38 . 1.78 . 2.4 . 3.62 . f (Hz) . PHAc (g) . 1 . 0.05 . 2 . 0.25 . 4 . 0.25 . 6 . 0.6 . 1 . 0.1 . 2 . 0.75 . 4 . 0.5 . 6 . 0.8 . 1 . 0.15 . 2 . 1.0 . 4 . 0.6 . 6 . 1.0 . 1 . 0.75 . 2 . ‐ . 4 . 0.7 . 6 . 1.3 . 1 . ‐ . 2 . ‐ . 4 . 0.8 . 6 . 1.5 . . 7 .
(8) Appendix D . D.2.4. Height: 40 m . i (°) . 31 . 25 . 20 . 15 . 10 . . 8 . H/L . 0.6 . 0.47 . 0.36 . 0.27 . 0.18 . FS . 1.02 . 1.34 . 1.72 . 2.36 . 3.59 . f (Hz) . PHAc (g) . 1 . 0.1 . 2 . 0.1 . 4 . 0.3 . 6 . 0.9 . 1 . 0.2 . 2 . 0.2 . 4 . 0.5 . 6 . 1.25 . 1 . 0.3 . 2 . 0.25 . 4 . 0.6 . 6 . 1.3 . 1 . 0.6 . 2 . 0.6 . 4 . 0.7 . 6 . 1.4 . 1 . 1.0 . 2 . 0.8 . 4 . 0.9 . 6 . 1.5 .
(9) Slope Critical Accelerations (Tables): Sands . D.3. Sand 3: “dense sand” . D.3.1. Height: 5 m . i (°) . 50 . 45 . 40 . 35 . 30 . H/L . 1.19 . 1 . 0.83 . 0.7 . 0,58 . FS . 1.02 . 1.2 . 1.4 . 1.55 . 1.73 . f (Hz) . PHAc (g) . 1 . 0.5 . 2 . 0.5 . 4 . 0.6 . 6 . 1.25 . 1 . 1.25 . 2 . 1.25 . 4 . 0.75 . 6 . 1.5 . 1 . 1.5 . 2 . 1.5 . 4 . 1 . 6 . ‐ . 1 . ‐ . 2 . 1.5 . 4 . 1.25 . 6 . ‐ . 1 . ‐ . 2 . 1.5 . 4 . 1.5 . 6 . ‐ . . 9 .
(10) Appendix D . D.3.2. Height: 10 m . I (°) . 43 . 40 . 35 . 30 . 25 . 20 . 15 . 10 . 10 . H/L . 0.93 . 0.84 . 0.7 . 0.58 . 0.47 . 0.36 . 0.27 . 0.18 . FS . 1.07 . 1.13 . 1.35 . 1.59 . 1.95 . 2.48 . 3.28 . 4.95 . f (Hz) . PHAc (g) . 1 . 0.3 . 2 . 0.3 . 4 . 0.6 . 6 . 1.1 . 1 . 0.5 . 2 . 0.5 . 4 . 0.65 . 6 . 1.3 . 1 . 0.5 . 2 . 0.7 . 4 . 0.8 . 6 . 1.5 . 1 . 0.6 . 2 . 0.9 . 4 . 0.9 . 6 . 1.5 . 1 . 0.8 . 2 . 1.4 . 4 . 1 . 6 . 1.5 . 1 . 1.5 . 2 . 1.5 . 4 . 1.1 . 6 . 1.5 . 1 . ‐ . 2 . ‐ . 4 . 1.2 . 6 . ‐ . 1 . ‐ . 2 . ‐ . 4 . 1.3 . 6 . ‐ .
(11) Slope Critical Accelerations (Tables): Sands . D.3.3. Height: 20 m . . I (°) . 40 . 35 . 30 . 25 . 20 . 15 . 10 . H/L . 0.84 . 0.7 . 0.58 . 0.47 . 0.36 . 0.27 . 0.18 . FS . 1.07 . 1.26 . 1.53 . 1.88 . 2.39 . 3.22 . 4.87 . f (Hz) . PHAc (g) . 1 . 0.1 . 2 . 0.25 . 4 . 0.6 . 6 . 1.1 . 1 . 0.15 . 2 . 0.5 . 4 . 0.75 . 6 . 1.25 . 1 . 0.2 . 2 . 0.8 . 4 . 0.85 . 6 . 1.5 . 1 . 0.25 . 2 . 1.2 . 4 . 0.95 . 6 . 1.5 . 1 . 0.5 . 2 . 1.5 . 4 . 1.1 . 6 . 1.5 . 1 . 1.25 . 2 . ‐ . 4 . 1.2 . 6 . 1.5 . 1 . ‐ . 2 . ‐ . 4 . 1.3 . 6 . ‐ . . 11 .
(12) Appendix D . D.3.4. Height: 40 m . I (°) . 38 . 35 . 30 . 25 . 20 . 15 . 10 . . 12 . H/L . 0.78 . 0.7 . 0.58 . 0.47 . 0.36 . 0.27 . 0.18 . FS . 1.05 . 1.23 . 1.48 . 1.83 . 2.35 . 3.18 . 4.84 . f (Hz) . PHAc (g) . 1 . 0.3 . 2 . 0.2 . 4 . 0.5 . 6 . 1 . 1 . 0.2 . 2 . 0.25 . 4 . 0.6 . 6 . 1.3 . 1 . 0.25 . 2 . 0.25 . 4 . 0.8 . 6 . 1.4 . 1 . 0.4 . 2 . 0.4 . 4 . 0.9 . 6 . 1.5 . 1 . 0.6 . 2 . 0.4 . 4 . 1 . 6 . 1.5 . 1 . 1.5 . 2 . 0.6 . 4 . 1 . 6 . 1.5 . 1 . 1.5 . 2 . 1 . 4 . 1.25 . 6 . ‐ .
(13) Appendix E – Slope Critical Accelerations (Tables): Clays E.1. Clay 1: “Soft (NC)” . E.1.1. Height: 5 m . i (°) . 18 . 15 . 10 . E.1.2 i (°) . 14 . 10 . H/L . 0.32 . 0.27 . 0.18 . FS . f (Hz) . PHAc (g) . 1 . 0.01 . 2 . 0.05 . 4 . 0.05 . 6 . 0.2 . 1 . 0.01 . 2 . 0.07 . 4 . 0.1 . 6 . 0.3 . 1 . 0.03 . 2 . 0.15 . 4 . 0.2 . 1.54 . 6 . 0.4 . FS . f (Hz) . PHAc (g) . 1 . 0.01 . 2 . 0.05 . 4 . 0.1 . 6 . 0.2 . 1 . 0.05 . 2 . 0.1 . 4 . 0.2 . 6 . 0.3 . 1.04 . 1.17 . Height: 10 m H/L . 0.25 . 0.18 . 1.04 . 1.38 . . unclear failure . . . apparent no failure but shear strains level reached . . . 13 .
(14) Appendix E . E.1.3 i (°) . 13 . 10 . . 14 . Height: 20 m H/L . 0.23 . 0.18 . FS . 1.03 . 1.3 . f (Hz) . PHAc (g) . 1 . 0.03 . 2 . 0.03 . 4 . 0.05 . 6 . 0.2 . 1 . 0.1 . 2 . 0.05 . 4 . 0.15 . 6 . 0.4 .
(15) Slope Critical Accelerations (Tables): Clays . E.2. Clay 2: “Medium stiff” . E.2.1. Height: 5 m . i (°) . 70 . 60 . 50 . 40 . 30 . 20 . 15 . 10 . H/L . 2.75 . 1.73 . 1.19 . 0.83 . 0.58 . 0.36 . 0.27 . 0.18 . FS . 1.05 . 1.14 . 1.26 . 1.32 . 1.53 . 1.86 . 2.18 . 2.88 . f (Hz) . PHAc (g) . 1 . 0.05 . 2 . 0.15 . 4 . 0.15 . 6 . 0.25 . 1 . 0.1 . 2 . 0.2 . 4 . 0.2 . 6 . 0.3 . 1 . 0.2 . 2 . 0.25 . 4 . 0.25 . 6 . 0.4 . 1 . 0.3 . 2 . 0.3 . 4 . 0.3 . 6 . 0.5 . 1 . 0.5 . 2 . 0.35 . 4 . 0.35 . 6 . 0.6 . 1 . 0.9 . 2 . 0.4 . 4 . 0.4 . 6 . 0.65 . 1 . 1.5 . 2 . 0.45 . 4 . 0.45 . 6 . 0.7 . 1 . ‐ . 2 . 1.25 . 4 . 0.75 . 6 . 0.75 . . 15 .
(16) Appendix E . E.2.2. i (°) . 40 . 35 . 0.84 . 0.7 . 0.58 . 20 . 0.36 . 10 . 16 . H/L . 30 . 15 . . Height: 10 m . 0.27 . 0.18 . FS . 1.01 . 1.07 . 1.14 . 1.49 . 1.84 . 2.39 . f (Hz) . PHAc (g) . 1 . 0.03 . 2 . 0.1 . 4 . 0.15 . 6 . 0.5 . 1 . 0.1 . 2 . 0.15 . 4 . 0.2 . 6 . 0.6 . 1 . 0.13 . 2 . 0.2 . 4 . 0.25 . 6 . 0.7 . 1 . 0.28 . 2 . 0.3 . 4 . 0.4 . 6 . 0.8 . 1 . ‐ . 2 . 0.4 . 4 . 0.45 . 6 . 0.85 . 1 . ‐ . 2 . 0.75 . 4 . 0.6 . 6 . 0.9 .
(17) Slope Critical Accelerations (Tables): Clays . E.2.3. i (°) . 25 . 20 . 15 . 10 . Height: 20 m . H/L . 0.47 . 0.36 . 0.27 . 0.18 . FS . f (Hz) . PHAc (g) . 1.05 . 1 . 0.07 . . 2 . 0.15 . . 4 . 0.45 . . 6 . 0.75 . 1.22 . 1 . 0.3 . . 2 . 0.3 . . 4 . 0.5 . . 6 . 0.8 . 1.41 . 1 . ‐ . . 2 . 0.4 . . 4 . 0.55 . . 6 . 0.85 . 1.54 . 1 . ‐ . . 2 . 1 . . 4 . 0.6 . . 6 . 0.9 . . 17 .
(18) Appendix E . E.3. Clay 3: “Stiff (OC)” . E.3.1. Height: 5 m . i (°) . 89 . 18 . 50 . FS . 1.1 . 80 . 5.56 . 1.46 . 70 . 2.75 . 1.61 . 60 . . H/L . 1.73 . 1.75 . f (Hz) . PHAc (g) . 1 . 1 . 2 . 1 . 4 . 0.5 . 6 . 0.75 . 1 . ‐ . 2 . 1.5 . 4 . 1 . 6 . 1.5 . 1 . ‐ . 2 . 1.5 . 4 . 1.25 . 6 . 1.5 . 1 . ‐ . 2 . ‐ . 4 . 1.5 . 6 . ‐ .
(19) Slope Critical Accelerations (Tables): Clays . E.3.2. i (°) . 75 . 60 . 50 . 40 . 35 . 30 . Height: 10 m . H/L . 3.73 . 1.73 . 1.19 . 0.84 . 0.70 . 0.58 . FS . 1.06 . 1.24 . 1.36 . 1.52 . 1.61 . 1.71 . f (Hz) . PHAc (g) . 1 . 0.25 . 2 . 0.25 . 4 . 0.5 . 6 . 1.25 . 1 . 0.5 . 2 . 0.5 . 4 . 0.75 . 6 . 1.5 . 1 . 1.5 . 2 . 0.75 . 4 . 1 . 6 . 1.5 . 1 . 1.5 . 2 . 1 . 4 . 1.1 . 6 . 1.5 . 1 . ‐ . 2 . 1.25 . 4 . 1.25 . 6 . ‐ . 1 . ‐ . 2 . 1.5 . 4 . 1.5 . 6 . ‐ . . 19 .
(20) Appendix E . E.3.3. i (°) . 40 . 30 . 25 . 20 . 15 . . 20 . Height: 20 m . H/L . 0.84 . 0.58 . 0.47 . 0.36 . 0.27 . FS . 1.03 . 1.17 . 1.3 . 1.38 . 1.44 . f (Hz) . PHAc (g) . 1 . 0.1 . 2 . 0.25 . 4 . 0.5 . 6 . 1.5 . 1 . 0.4 . 2 . 0.5 . 4 . 1.5 . 6 . 1.5 . 1 . 1 . 2 . 0.75 . 4 . 1.5 . 6 . ‐ . 1 . 1.25 . 2 . 1.25 . 4 . ‐ . 6 . ‐ . 1 . ‐ . 2 . 1.5 . 4 . ‐ . 6 . ‐ .
(21) Appendix F – Parametric analysis: Univariate and Bivariate F.1. Univariate analysis: Distributions . F.1.1. All data . (a) u, log u i‐ Cohesive soils . ii‐ Non‐cohesive soils . . 21 .
(22) Appendix F (b) Input frequency (f) . . i‐ Clays . . ii‐ Sands . (c) PHAc, log PHAc i‐ Cohesive soils . . 22 . .
(23) Parametric analysis: Univariate and Bivariate ii‐ Non‐cohesive soils . (d) i, log i i‐ Cohesive soils . . . 23 .
(24) Appendix F ii‐ Non‐cohesive soils . (e) Ts, log Ts i‐ Cohesive soils . . 24 . .
(25) Parametric analysis: Univariate and Bivariate ii‐ Non‐cohesive soils . (f) vs30, log vs30 i‐ Cohesive soils . . . 25 .
(26) Appendix F ii‐ Non‐cohesive soils . . 26 .
(27) Parametric analysis: Univariate and Bivariate . F.1.2. M = 7.25 . (a) u, log u i‐ Cohesive soils . . ii‐ Non‐cohesive soils . . . 27 .
(28) Appendix F (b) Input frequency (f) . . i‐ Clays . ii‐ Sands . (c) PHAc, log PHAc i‐ Cohesive soils . . 28 . .
(29) Parametric analysis: Univariate and Bivariate ii‐ Non‐cohesive soils . (d) i, log i i‐ Cohesive soils . . . 29 .
(30) Appendix F ii‐ Non‐cohesive soils . (e) Ts, log Ts i‐ Cohesive soils . . 30 . .
(31) Parametric analysis: Univariate and Bivariate ii‐ Non‐cohesive soils . (f) vs30, log vs30 i‐ Cohesive soils . . . 31 .
(32) Appendix F ii‐ Non‐cohesive soils . (g) Ia, log Ia i‐ Cohesive soils . . 32 . .
(33) Parametric analysis: Univariate and Bivariate ii‐ Non‐cohesive soils . . . 33 .
(34) Appendix F . F.1.3. One soil case: “Clay 2” . (a) u, log u . (a) Input frequency (f) . . i‐ Clays . . 34 .
(35) Parametric analysis: Univariate and Bivariate . (c) PHAc, log PHAc . (d) i, log i . . . 35 .
(36) Appendix F (e) FS, log FS . (f) Ts, log Ts . . 36 . .
(37) Parametric analysis: Univariate and Bivariate (g). vs30, log vs30 . . . 37 .
(38) Appendix F . F.1.4. Per PHAc . F.1.4.1 PHAc = 0.1 g (a) log u . i‐ Cohesive soils. . ii‐ Non‐cohesive soils. (b) Input frequency (f) . i‐ Cohesive soils . 38 . ii‐ Non‐cohesive soils. .
(39) Parametric analysis: Univariate and Bivariate . (c) log i . i‐ Cohesive soils . ii‐ Non‐cohesive soils. . (d) log Ts . i‐ Cohesive soils . ii‐ Non‐cohesive soils . 39 .
(40) Appendix F (e) log vs30 . i‐ Cohesive soils PHAc = 0.2 g (a) log u . i‐ Cohesive soils. ii‐ Non‐cohesive soils. . 40 . .
(41) Parametric analysis: Univariate and Bivariate (b) Input frequency (f) . i‐ Cohesive soils. ii‐ Non‐cohesive soils. (c) log i . i‐ Cohesive soils . ii‐ Non‐cohesive soils . 41 .
(42) Appendix F (d) log Ts . i‐ Cohesive soils (e) log vs30 . i‐ Cohesive soils . 42 . ii‐ Non‐cohesive soils. .
(43) Parametric analysis: Univariate and Bivariate . F.1.4.2 PHAc = 0.25 g (a) log u . i‐ Non‐cohesive soils (b) Input frequency (f) . i‐ Non‐cohesive soils . 43 .
(44) Appendix F . (c) log i . i‐ Non‐cohesive soils (d) log Ts . i‐ Non‐cohesive soils . 44 . .
(45) Parametric analysis: Univariate and Bivariate F.1.4.3 PHAc = 0.3 g (a) log u . i‐ Cohesive soils. ii‐ Non‐cohesive soils. (b) Input frequency (f) . i‐ Cohesive soils. ii‐ Non‐cohesive soils. . . 45 .
(46) Appendix F . (c) log i . i‐ Cohesive soils . ii‐ Non‐cohesive soils. (d) log Ts . i‐ Cohesive soils . 46 . ii‐ Non‐cohesive soils .
(47) Parametric analysis: Univariate and Bivariate (e) log vs30 . i‐ Cohesive soils F.1.4.4 PHAc = 0.4 g (a) log u . i‐ Cohesive soils . ii‐ Non‐cohesive soils . 47 .
(48) Appendix F (b) Input frequency (f) . i‐ Cohesive soils. ii‐ Non‐cohesive soils. (c) log i . i‐ Cohesive soils . 48 . ii‐ Non‐cohesive soils . .
(49) Parametric analysis: Univariate and Bivariate (d) log Ts . i‐ Cohesive soils . ii‐ Non‐cohesive soils. . (e) log vs30 . i‐ Cohesive soils . 49 .
(50) Appendix F . F.1.4.5 PHAc = 0.5 g (a) log u . i‐ Cohesive soils. ii‐ Non‐cohesive soils. (b) Input frequency (f) . i‐ Cohesive soils . 50 . ii‐ Non‐cohesive soils.
(51) Parametric analysis: Univariate and Bivariate . (c) log i . i‐ Cohesive soils . ii‐ Non‐cohesive soils. (d) log Ts . i‐ Cohesive soils . ii‐ Non‐cohesive soils . 51 .
(52) Appendix F (e) log vs30 . i‐ Cohesive soils. . 52 .
(53) Parametric analysis: Univariate and Bivariate . F.1.5. Skewness . All data Variable . M = 7.25 . Clays (n=105) 0.088 . Sands (n=161) ‐0.084 . Clays (n=) ‐0.044 . Sands (n=) 0.139 . f . 0.217 . 0.17 . 0.159 . 0.418 . H . 0.741 . 0.288 . 0.832 . 0.355 . u . 1.822 . 2.217 . 1.790 . 0.730 . log u . 0.377 . ‐0.017 . 0.311 . ‐0.432 . PHAc . 0.662 . 0.603 . ‐0.052 . 0.371 . log PHAc . ‐1.033 . 0.613 . ‐0.277 . 0.201 . I . 1.046 . ‐0.043 . 0.788 . 0.843 . log i . 0.215 . ‐0.98 . ‐0.019 . 0.197 . Ts . 0.605 . 0.316 . 0.805 . 0.372 . log Ts . 0.102 . 0.325 . 0.346 . ‐0.223 . vs30 . 0.325 . 0.179 . 0.493 . 0.432 . log vs30 . ‐0.227 . 0.153 . 0.012 . 0.401 . Ia . ‐ . ‐ . 0.046 . 0.446 . log Ia . ‐ . ‐ . ‐0.293 . 0.157 . Soil type . . 53 .
(54) Appendix F . F.2 F.2.1. Box‐and‐whisker plots All data . (a) General i‐ Cohesive soils . . . 54 . .
(55) Parametric analysis: Univariate and Bivariate ii‐ Non‐cohesive soils . . . 55 .
(56) Appendix F (b) Displacements per categorical variable (b‐1) Per soil type i‐ Cohesive soils . ii‐ Non‐cohesive soils . . 56 . . .
(57) Parametric analysis: Univariate and Bivariate (b‐2) Per input frequency (f) i‐ Cohesive soils . ii‐ Non‐cohesive soils . . . . 57 .
(58) Appendix F (b‐3) Per slope height (H) i‐ Cohesive soils . . ii‐ Non‐cohesive soils . . 58 . .
(59) Parametric analysis: Univariate and Bivariate F.2.2. M = 7.25 . (a) General i‐ Cohesive soils . ii‐ Non‐cohesive soils 59 .
(60) Appendix F . . (b) Displacements per categorical variable (b‐1) Per soil type . i‐ Cohesive soils . 60 . ii‐ Non‐cohesive soils .
(61) Parametric analysis: Univariate and Bivariate (b‐1) Per input frequency (f) . i‐ Cohesive soils (b‐1) Per slope height (H) . ii‐ Non‐cohesive soils. i‐ Cohesive soils . ii‐ Non‐cohesive soils. . . 61 .
(62) Appendix F . F.2.3 . . 62 . One soil case: “Clay 2” .
(63) Parametric analysis: Univariate and Bivariate . F.2.4. Per critical acceleration . (a) PHAc = 0.1 g . i‐ Cohesive soils (b) PHAc = 0.2 g . ii‐ Non‐cohesive soils. i‐ Cohesive soils. ii‐ Non‐cohesive soils. 63 .
(64) Appendix F (c) PHAc = 0.25 g . i‐ Non‐cohesive soils (d) PHAc = 0.3 g . i‐ Cohesive soils . 64 . ii‐ Non‐cohesive soils.
(65) Parametric analysis: Univariate and Bivariate (e) PHAc = 0.4 g . i‐ Cohesive soils (f) PHAc = 0.5 g . ii‐ Non‐cohesive soils. i‐ Cohesive soils . ii‐ Non‐cohesive soils. . 65 .
(66)
(67) Appendix F – Parametric analysis: Univariate and Bivariate F.3. Univariate analysis: Distributions . F.3.1. All data . (a) u, log u i‐ Cohesive soils . ii‐ Non‐cohesive soils . . 67 .
(68) Appendix F (b) Input frequency (f) . . i‐ Clays . . ii‐ Sands . (c) PHAc, log PHAc i‐ Cohesive soils . . 68 . .
(69) Parametric analysis: Univariate and Bivariate ii‐ Non‐cohesive soils . (d) i, log i i‐ Cohesive soils . . . 69 .
(70) Appendix F ii‐ Non‐cohesive soils . (g) Ts, log Ts i‐ Cohesive soils . . 70 . .
(71) Parametric analysis: Univariate and Bivariate ii‐ Non‐cohesive soils . (h) vs30, log vs30 i‐ Cohesive soils . . . 71 .
(72) Appendix F ii‐ Non‐cohesive soils . . 72 .
(73) Parametric analysis: Univariate and Bivariate . F.3.2. M = 7.25 . (a) u, log u i‐ Cohesive soils . . ii‐ Non‐cohesive soils . . . 73 .
(74) Appendix F (c) Input frequency (f) . . i‐ Clays . ii‐ Sands . (c) PHAc, log PHAc i‐ Cohesive soils . . 74 . .
(75) Parametric analysis: Univariate and Bivariate ii‐ Non‐cohesive soils . (d) i, log i i‐ Cohesive soils . . . 75 .
(76) Appendix F ii‐ Non‐cohesive soils . (h) Ts, log Ts i‐ Cohesive soils . . 76 . .
(77) Parametric analysis: Univariate and Bivariate ii‐ Non‐cohesive soils . (i) vs30, log vs30 i‐ Cohesive soils . . . 77 .
(78) Appendix F ii‐ Non‐cohesive soils . (j) Ia, log Ia i‐ Cohesive soils . . 78 . .
(79) Parametric analysis: Univariate and Bivariate ii‐ Non‐cohesive soils . . . 79 .
(80) Appendix F . F.3.3. One soil case: “Clay 2” . (a) u, log u . (c) Input frequency (f) . . i‐ Clays . . 80 .
(81) Parametric analysis: Univariate and Bivariate . (c) PHAc, log PHAc . (d) i, log i . . . 81 .
(82) Appendix F (h) FS, log FS . (i) Ts, log Ts . . 82 . .
(83) Parametric analysis: Univariate and Bivariate (j). vs30, log vs30 . . . 83 .
(84) Appendix F . F.3.4. Per PHAc . F.3.4.1 PHAc = 0.1 g (a) log u . i‐ Cohesive soils. . ii‐ Non‐cohesive soils. (d) Input frequency (f) . i‐ Cohesive soils . 84 . ii‐ Non‐cohesive soils. .
(85) Parametric analysis: Univariate and Bivariate . (c) log i . i‐ Cohesive soils . ii‐ Non‐cohesive soils. . (f) log Ts . i‐ Cohesive soils . ii‐ Non‐cohesive soils . 85 .
(86) Appendix F (g) log vs30 . i‐ Cohesive soils PHAc = 0.2 g (a) log u . i‐ Cohesive soils. ii‐ Non‐cohesive soils. . 86 . .
(87) Parametric analysis: Univariate and Bivariate (c) Input frequency (f) . i‐ Cohesive soils. ii‐ Non‐cohesive soils. (c) log i . i‐ Cohesive soils . ii‐ Non‐cohesive soils . 87 .
(88) Appendix F (f) log Ts . i‐ Cohesive soils (g) log vs30 . i‐ Cohesive soils . 88 . ii‐ Non‐cohesive soils. .
(89) Parametric analysis: Univariate and Bivariate . F.3.4.2 PHAc = 0.25 g (a) log u . i‐ Non‐cohesive soils (c) Input frequency (f) . i‐ Non‐cohesive soils . 89 .
(90) Appendix F . (c) log i . i‐ Non‐cohesive soils (e) log Ts . i‐ Non‐cohesive soils . 90 . .
(91) Parametric analysis: Univariate and Bivariate F.3.4.3 PHAc = 0.3 g (a) log u . i‐ Cohesive soils. ii‐ Non‐cohesive soils. (c) Input frequency (f) . i‐ Cohesive soils. ii‐ Non‐cohesive soils. . . 91 .
(92) Appendix F . (c) log i . i‐ Cohesive soils . ii‐ Non‐cohesive soils. (f) log Ts . i‐ Cohesive soils . 92 . ii‐ Non‐cohesive soils .
(93) Parametric analysis: Univariate and Bivariate (g) log vs30 . i‐ Cohesive soils F.3.4.4 PHAc = 0.4 g (a) log u . i‐ Cohesive soils . ii‐ Non‐cohesive soils . 93 .
(94) Appendix F (c) Input frequency (f) . i‐ Cohesive soils. ii‐ Non‐cohesive soils. (c) log i . i‐ Cohesive soils . 94 . ii‐ Non‐cohesive soils . .
(95) Parametric analysis: Univariate and Bivariate (f) log Ts . i‐ Cohesive soils . ii‐ Non‐cohesive soils. . (g) log vs30 . i‐ Cohesive soils . 95 .
(96) Appendix F . F.3.4.5 PHAc = 0.5 g (a) log u . i‐ Cohesive soils. ii‐ Non‐cohesive soils. (c) Input frequency (f) . i‐ Cohesive soils . 96 . ii‐ Non‐cohesive soils.
(97) Parametric analysis: Univariate and Bivariate . (c) log i . i‐ Cohesive soils . ii‐ Non‐cohesive soils. (f) log Ts . i‐ Cohesive soils . ii‐ Non‐cohesive soils . 97 .
(98) Appendix F (g) log vs30 . i‐ Cohesive soils. . 98 .
(99) Parametric analysis: Univariate and Bivariate . F.3.5. Skewness . All data Variable . M = 7.25 . Clays (n=105) 0.088 . Sands (n=161) ‐0.084 . Clays (n=) ‐0.044 . Sands (n=) 0.139 . f . 0.217 . 0.17 . 0.159 . 0.418 . H . 0.741 . 0.288 . 0.832 . 0.355 . u . 1.822 . 2.217 . 1.790 . 0.730 . log u . 0.377 . ‐0.017 . 0.311 . ‐0.432 . PHAc . 0.662 . 0.603 . ‐0.052 . 0.371 . log PHAc . ‐1.033 . 0.613 . ‐0.277 . 0.201 . I . 1.046 . ‐0.043 . 0.788 . 0.843 . log i . 0.215 . ‐0.98 . ‐0.019 . 0.197 . Ts . 0.605 . 0.316 . 0.805 . 0.372 . log Ts . 0.102 . 0.325 . 0.346 . ‐0.223 . vs30 . 0.325 . 0.179 . 0.493 . 0.432 . log vs30 . ‐0.227 . 0.153 . 0.012 . 0.401 . Ia . ‐ . ‐ . 0.046 . 0.446 . log Ia . ‐ . ‐ . ‐0.293 . 0.157 . Soil type . . 99 .
(100) Appendix F . F.4 F.4.1. Box‐and‐whisker plots All data . (a) General i‐ Cohesive soils . . . 100 . .
(101) Parametric analysis: Univariate and Bivariate ii‐ Non‐cohesive soils . . . 101 .
(102) Appendix F (b) Displacements per categorical variable (b‐1) Per soil type i‐ Cohesive soils . ii‐ Non‐cohesive soils . . 102 . . .
(103) Parametric analysis: Univariate and Bivariate (b‐2) Per input frequency (f) i‐ Cohesive soils . ii‐ Non‐cohesive soils . . . . 103 .
(104) Appendix F (b‐3) Per slope height (H) i‐ Cohesive soils . . ii‐ Non‐cohesive soils . . 104 . .
(105) Parametric analysis: Univariate and Bivariate F.4.2. M = 7.25 . (a) General i‐ Cohesive soils . ii‐ Non‐cohesive soils 105 .
(106) Appendix F . . (b) Displacements per categorical variable (b‐1) Per soil type . i‐ Cohesive soils . 106 . ii‐ Non‐cohesive soils .
(107) Parametric analysis: Univariate and Bivariate (b‐1) Per input frequency (f) . i‐ Cohesive soils (b‐1) Per slope height (H) . ii‐ Non‐cohesive soils. i‐ Cohesive soils . ii‐ Non‐cohesive soils. . . 107 .
(108) Appendix F . F.4.3 . . 108 . One soil case: “Clay 2” .
(109) Parametric analysis: Univariate and Bivariate . F.4.4. Per critical acceleration . (a) PHAc = 0.1 g . i‐ Cohesive soils (b) PHAc = 0.2 g . ii‐ Non‐cohesive soils. i‐ Cohesive soils. ii‐ Non‐cohesive soils. 109 .
(110) Appendix F (c) PHAc = 0.25 g . i‐ Non‐cohesive soils (d) PHAc = 0.3 g . i‐ Cohesive soils . 110 . ii‐ Non‐cohesive soils.
(111) Parametric analysis: Univariate and Bivariate (e) PHAc = 0.4 g . i‐ Cohesive soils (f) PHAc = 0.5 g . ii‐ Non‐cohesive soils. i‐ Cohesive soils . ii‐ Non‐cohesive soils. . 111 .
(112)
(113) Appendix G – Multiple regression: Residuals for model adequacy (normal probability and standardized residuals vs. standardized predicted response plots) G.1. M‐independent dataset . . (a) General form of multiple regression (eqs. 4.4, 4.5): Clay slopes i‐ log PHAc, log vs30 (eq. 4.4) . (a) . (b). ii‐. (a) . log i, log PHAc (eq. 4.4) . (b). 113 .
(114) Appendix G iii‐. log vs30, log PHAc, log i (eq. 4.5) . (a) . (b). iv‐. (a) . . 114 . log vs30, log PHAc, f (eq. 4.5) . (b).
(115) Multiple regression: Residuals for model adequacy v‐. log i, log PHAc, f (eq. 4.5) . (a) . (b). (b) General form of multiple regression (eq. 4.4): Sand slopes i‐ f, H (eq. 4.4) . (a) . (b). ii‐. f, log Ts (eq. 4.4) . 115 .
(116) Appendix G . (a) . (b). (c) 2nd and 3rd order polynomial forms (eqs. 4.6, 4.7, 4.8): Clay slopes i‐ log vs30, log PHAc (eq. 4.6) . (a) . (b). ii‐. 116 . log PHAc, log vs30 (eq. 4.6) .
(117) Multiple regression: Residuals for model adequacy (a) . (b). 117 .
(118) Appendix G iii‐. (a) . 118 . log PHAc, log vs30 (eq. 4.7) . (b).
(119) Multiple regression: Residuals for model adequacy iv‐. log PHAc, log vs30 (eq. 4.8) . (a) . (b). v‐. (a) . log vs30, log PHAc, (eq. 4.8) . (b). 119 .
(120) Appendix G vi‐. log PHAc, log i (eq. 4.6) . (a) . (b). vii‐. (a) . 120 . log i, log PHAc (eq. 4.6) . (b).
(121) Multiple regression: Residuals for model adequacy viii‐. log PHAc, log i (eq. 4.7) . (a) . (b). ix‐. (a) . log PHAc, log i (eq. 4.8) . (b). . 121 .
(122) Appendix G . G.1 . M‐dependent dataset (M=7.25): Clay slopes . (a) General form of multiple regression (eqs. 4.4, 4.5) i‐. log vs30, log PHAc (eq. 4.4) . (a) . (b). ii‐. log vs30, log Ia (eq. 4.4) . (a) . (b). iii‐. 122 . log i, log PHAc (eq. 4.4) .
(123) Multiple regression: Residuals for model adequacy . (a) . (b). iv‐. log i, log Ia (eq. 4.4) . (a) . (b). v‐. (a) . log PHAc, log Ia (eq. 4.4) . (b). vi‐. log PHAc, log vs30, log Ia (eq. 4.5) . 123 .
(124) Appendix G . (a) . (b). vii‐. log i, log PHAc, log Ia (eq. 4.5) . (a) . (b). viii‐. log vs30, log i, log PHAc (eq. 4.5) . . (a) . (b). ix‐ 124 . log vs30, log i, log Ia (eq. 4.5) .
(125) Multiple regression: Residuals for model adequacy . (a) . (b). (b) 2nd and 3rd order polynomial forms (eqs. 4.6, 4.7, 4.8) i‐ log PHAc, (log PHAc)2, log Ia (eq. 4.6) . (a) . (b). ii‐. log Ia, (log Ia)2, log PHAc (eq. 4.6) . 125 .
(126) Appendix G . (a) . (b). iii‐. (a) . log Ia, (log Ia)2, log PHAc, (log PHAc)2 (eq. 4.7) . (b). iv‐. (a) . log Ia, log PHAc, (log PHAc)2, (log PHAc)3 (eq. 4.8) . (b). v‐. 126 . log Ia, (log Ia)2, (log Ia)3, log PHAc (eq. 4.8) .
(127) Multiple regression: Residuals for model adequacy . (a) . (b). vi‐. (a) . log vs30, (log vs30)2, log PHAc (eq. 4.6) . (b). vii‐. (a) . log vs30, log PHAc, (log PHAc)2 (eq. 4.6) . (b). viii‐. log vs30, (log vs30)2, log PHAc, (log PHAc)2 (eq. 4.7) . 127 .
(128) Appendix G . (a) . (b). ix‐. (a) . log vs30, log PHAc, (log PHAc)2, (log PHAc)3 (eq. 4.8) . (b). x‐. (a) . log vs30, (log vs30)2, (log vs30)3, log PHAc (eq. 4.8) . (b). xi‐. 128 . log Ia, , (log Ia)2, log vs30 (eq. 4.6) .
(129) Multiple regression: Residuals for model adequacy (a) . (b). (c) Two predictors with interaction term (eq. 4.9) i‐ log Ia, log PHAc (eq. 4.9) . (a) . (b). ii‐. (a) . log Ia, log PHAc (eq. 4.9) . (b). . 129 .
(130) Appendix G . G.2 Soil‐dependent dataset (“Clay 2”) (a) General form of multiple regression (eqs. 4.4, 4.5) i‐ log PHAc, vs30 (eq. 4.4) (a) . (b). (b) 2nd and 3rd order polynomial forms (eqs. 4.6, 4.7, 4.8) iii‐ log PHAc, vs30 (eq. 4.4) (a) . . 130 . (b).
(131) . Appendix H – Parameters and results from the Californian and USGS simplified approaches and FE method G.3. PHAc, ky per frequency . G.3.1. f = 1 Hz . (a) Cohesive soils Soil type Clay 1 . H (m) . i (°) . FS . PHAc (g) . Ky . 20 . 10 . 1.3 . 0.1 . 0.052 . 60 . 1.14 . 0.1 . 0.121 . 50 . 1.26 . 0.2 . 0.199 . 40 . 1.32 . 0.3 . 0.206 . 30 . 1.53 . 0.5 . 0.265 . 35 . 1.07 . 0.1 . 0.040 . 30 . 1.14 . 0.13 . 0.070 . 10 . 20 . 1.49 . 0.28 . 0.168 . 20 . 20 . 1.22 . 0.3 . 0.075 . 75 . 1.06 . 0.25 . 0.058 . 60 . 1.24 . 0.5 . 0.208 . 40 . 1.03 . 0.1 . 0.019 . 30 . 1.17 . 0.4 . 0.085 . 5 . Clay 2 . 10 . Clay 3 . 20 . 131 .
(132) Appendix H (b) Non‐cohesive soils Soil type . H (m) . i (°) . FS . PHAc (g) . Ky . 35 . 1.03 . 0.25 . 0.017 . 30 . 0.5 . 0.100 . 32 . 1.2 1.03 . 0.1 . 0.016 . 30 . 1.1 . 0.15 . 0.050 . 25 . 1.36 . 0.2 . 0.152 . 10 . 20 . 1.71 . 0.3 . 0.243 . 20 . 20 . 1.63 . 0.1 . 0.215 . 28 . 1.07 . 0.2 . 0.033 . 25 . 1.21 . 0.25 . 0.089 . 40 . 20 . 1.58 . 0.3 . 0.198 . 35 . 1.11 . 0.25 . 0.063 . 5 . 30 . 0.4 . 0.165 . 30 . 1.33 1.19 . 0.2 . 0.095 . 25 . 1.46 . 0.25 . 0.194 . 5 . Sand 1 . 10 . 20 . 1.84 . 0.3 . 0.287 . 25 . 1.38 . 0.1 . 0.161 . 20 . 1.78 . 0.15 . 0.267 . 31 . 1.02 . 0.1 . 0.010 . 25 . 1.34 . 0.2 . 0.144 . 40 . 20 . 1.72 . 0.3 . 0.246 . 5 . 50 . 1.02 . 0.5 . 0.015 . 43 . 1.07 . 0.3 . 0.048 . 40 . 0.5 . 0.084 . 35 . 1.13 1.35 . 0.5 . 0.201 . 40 . 1.07 . 0.1 . 0.045 . 35 . 1.26 . 0.15 . 0.149 . 30 . 1.53 . 0.2 . 0.265 . 25 . 1.88 . 0.25 . 0.372 . 20 . Sand 2 . 10 . 20 . Sand 3 . 132 . 40 . 20 . 2.39 . 0.5 . 0.475 . 38 . 1.05 . 0.3 . 0.031 . 35 . 1.23 . 0.2 . 0.132 . 30 . 1.48 . 0.25 . 0.240 . 25 . 1.83 . 0.4 . 0.351 .
(133) Parameters and results from the Californian and USGS simplified approaches… . G.3.2. f = 2 Hz . (a) Cohesive soils Soil type . Clay 1 . H (m) . i (°) . FS . PHAc (g) . Ky . 5 . 10 . 1.54 . 0.15 . 0.094 . 10 . 10 . 1.38 . 0.1 . 0.066 . 70 . 1.05 . 0.15 . 0.047 . 60 . 1.14 . 0.2 . 0.121 . 50 . 1.26 . 0.25 . 0.199 . 40 . 1.32 . 0.3 . 0.206 . 30 . 1.53 . 0.35 . 0.265 . 20 . 1.86 . 0.4 . 0.294 . 15 . 2.18 . 0.45 . 0.305 . 40 . 1.01 . 0.1 . 0.006 . 35 . 1.07 . 0.15 . 0.040 . 30 . 1.14 . 0.2 . 0.070 . 20 . 1.49 . 0.3 . 0.168 . 15 . 1.84 . 0.4 . 0.217 . 25 . 1.05 . 0.15 . 0.021 . 20 . 1.22 . 0.3 . 0.075 . 15 . 1.41 . 0.4 . 0.106 . 75 . 1.06 . 0.25 . 0.058 . 10 . 60 . 1.24 . 0.5 . 0.208 . 20 . 40 . 1.03 . 0.25 . 0.019 . 20 . 30 . 1.17 . 0.5 . 0.085 . 5 . 10 . Clay 2 . Clay 3 . 20 . 133 .
(134) Appendix H (b) Non‐cohesive soils Soil type . H (m) . 5 . i (°) . FS . PHAc (g) . Ky . 35 . 1.03 . 0.25 . 0.017 . 30 . 1.2 1.03 . 0.5 . 0.100 . 0.2 . 0.016 . 0.3 . 0.050 . 32 10 . 20 . Sand 1 . 40 . 5 . 30 29 . 1.04 . 0.25 . 0.019 . 25 . 1.28 . 0.5 . 0.118 . 28 . 1.07 . 0.1 . 0.033 . 25 . 1.21 . 0.2 . 0.089 . 20 . 1.58 . 0.25 . 0.198 . 35 . 1.11 . 0.3 . 0.063 . 30 . 1.33 1.02 . 0.5 . 0.165 . 0.2 . 0.011 . 0.3 . 0.095 . 0.5 . 0.194 . 34 30 . Sand 2 . 134 . 1.46 . 25 . 20 . 32 . 1.02 . 0.25 . 0.011 . 31 . 1.02 . 0.1 . 0.010 . 25 . 1.34 . 0.2 . 0.144 . 40 . 20 . 1.72 . 0.25 . 0.246 . 5 . 50 . 1.02 . 0.5 . 0.015 . 43 . 1.07 . 0.3 . 0.048 . 40 . 1.13 . 0.5 . 0.084 . 40 . 1.07 . 0.25 . 0.045 . 35 . 1.26 . 0.5 . 0.149 . 38 . 1.05 . 0.2 . 0.031 . 35 . 1.23 . 0.25 . 0.132 . 30 . 1.48 . 0.25 . 0.240 . 25 . 1.83 . 0.4 . 0.351 . 20 . 2.35 . 0.4 . 0.462 . 20 . Sand 3 . 1.19 . 10 . 10 . . 1.1 . 40 .
(135) Parameters and results from the Californian and USGS simplified approaches… . G.3.3. f = 4 Hz . (a) Cohesive soils Soil type . i (°) . FS . PHAc (g) . Ky . 15 . 1.17 . 0.1 . 0.044 . 10 . 1.54 . 0.2 . 0.094 . 14 . 1.04 . 0.1 . 0.010 . 10 . 10 . 1.38 . 0.2 . 0.066 . 20 . 10 . 1.3 . 0.15 . 0.052 . 70 . 1.05 . 0.15 . 0.047 . 60 . 1.14 . 0.2 . 0.121 . 50 . 1.26 . 0.25 . 0.199 . 40 . 1.32 . 0.3 . 0.206 . 30 . 1.53 . 0.35 . 0.265 . 20 . 1.86 . 0.4 . 0.294 . 15 . 2.18 . 0.45 . 0.305 . 40 . 1.01 . 0.15 . 0.006 . 35 . 1.07 . 0.2 . 0.040 . 30 . 1.14 . 0.25 . 0.070 . 20 . 1.49 . 0.4 . 0.168 . 15 . 1.84 . 0.45 . 0.217 . 25 . 1.05 . 0.45 . 0.021 . 20 . 1.22 . 0.5 . 0.075 . 20 . 15 . 1.41 . 0.55 . 0.106 . 5 . 89 . 1.1 . 0.5 . 0.100 . 10 . 75 . 1.06 . 0.5 . 0.058 . 20 . 40 . 1.03 . 0.5 . 0.019 . H (m) . 5 . Clay 1 . 5 . 10 . Clay 2 . Clay 3 . 135 .
(136) Appendix H (b) Non‐cohesive soils Soil type . H (m) . 5 . 10 . 20 . Sand 1 . 40 . 5 . 10 . 20 . Sand 2 . Sand 3 . . 136 . 40 . 40 . i (°) . FS . PHAc (g) . Ky . 35 . 1.03 . 0.25 . 0.017 . 30 . 1.2 . 0.5 . 0.100 . 32 . 1.03 . 0.2 . 0.016 . 30 . 1.1 . 0.25 . 0.050 . 25 . 1.36 . 0.4 . 0.152 . 29 . 1.04 . 0.25 . 0.019 . 25 . 1.28 . 0.4 . 0.118 . 20 . 1.63 . 0.5 . 0.215 . 28 . 1.07 . 0.3 . 0.033 . 25 . 1.21 . 0.4 . 0.089 . 20 . 1.58 . 0.5 . 0.198 . 35 . 1.11 . 0.35 . 0.063 . 30 . 1.33 . 0.5 . 0.165 . 34 . 1.02 . 0.25 . 0.011 . 30 . 1.19 . 0.35 . 0.095 . 25 . 1.46 . 0.45 . 0.194 . 32 . 1.02 . 0.25 . 0.011 . 25 . 1.38 . 0.5 . 0.161 . 31 . 1.02 . 0.3 . 0.010 . 25 . 1.34 . 0.5 . 0.144 . 38 . 1.05 . 0.5 . 0.031 . 35 . 1.23 . 0.6 . 0.132 . 30 . 1.48 . 0.8 . 0.240 . 25 . 1.83 . 0.9 . 0.351 . 20 . 2.35 . 1 . 0.462 . 15 . 3.18 . 1 . 0.564 . 10 . 4.84 . 1.25 . 0.667 .
(137) Parameters and results from the Californian and USGS simplified approaches… . G.3.4. f = 6 Hz . (a) Cohesive soils Soil type . Clay 1 . Clay 2 . H (m) . i (°) . FS . PHAc (g) . Ky . 5 . 18 . 1.04 . 0.2 . 0.012 . 5 . 15 . 1.17 . 0.3 . 0.044 . 5 . 10 . 1.54 . 0.4 . 0.094 . 10 . 14 . 1.04 . 0.2 . 0.010 . 10 . 10 . 1.38 . 0.3 . 0.066 . 20 . 13 . 1.03 . 0.2 . 0.007 . 20 . 10 . 1.3 . 0.4 . 0.052 . 5 . 70 . 1.05 . 0.25 . 0.047 . 5 . 60 . 1.14 . 0.3 . 0.121 . 5 . 50 . 1.26 . 0.4 . 0.199 . 5 . 40 . 1.32 . 0.5 . 0.206 . 10 . 40 . 1.01 . 0.5 . 0.006 . . 137 .
(138) Appendix H . G.4 G.4.1. Maximum horizontal equivalent acceleration (MHEA) f = 1 Hz . (a) Cohesive soils MHEA (g) . Soil type . H (m) . i (°) . FS . PHAc (g) . Ky . Ts (s) . Tm (s) . NRF . A . Clay 2 . 5 . 30 . 1.53 . 0.5 . 0.265 . 0.2 . 0.52 . 0.91 . 0.46 . 0.52 . . . 50 . 1.26 . 0.2 . 0.199 . 0.2 . 0.56 . 1.2 . 0.24 . 0.29 . . 10 . 20 . 1.49 . 0.25 . 0.168 . 0.32 . 0.55 . 1.14 . 0.29 . 0.23 . Clay 3 . 10 . 60 . 1.24 . 0.5 . 0.208 . 0.25 . 0.52 . 0.91 . 0.46 . 0.43 . . 75 . 1.06 . 0.25 . 0.058 . 0.25 . 0.55 . 1.14 . 0.29 . 0.28 . 20 30 *NRF r. 1.17 . 0.4 . 0.085 . 0.42 . 0.53 . 0.99 . 0.4 . 0.25 . . A MHEA = PHA B. T MHEA PHAr NFR exp 0.624 0.7831 ln s Tm . 138 . . B .
(139) Parameters and results from the Californian and USGS simplified approaches… (b) Non‐cohesive soils MHEA (g) . Soil type . H (m) . i (°) . FS . PHAc (g) . Ky . Ts (s) . Tm (s) . NRF . A . B . Sand 1 . 5 . 30 . 1.2 . 0.5 . 0.1 . 0.1 . 0.52 . 0.91 . 0.46 . 0.89 . . . 35 . 1.03 . 0.25 . 0.017 . 0.1 . 0.55 . 1.14 . 0.29 . 0.58 . . 10 . 25 . 1.36 . 0.2 . 0.152 . 0.21 . 0.56 . 1.2 . 0.24 . 0.28 . . 40 . 25 . 1.21 . 0.25 . 0.089 . 0.82 . 0.55 . 1.14 . 0.29 . 0.11 . . . 28 . 1.07 . 0.2 . 0.033 . 0.82 . 0.56 . 1.2 . 0.24 . 0.10 . Sand 2 . 5 . 30 . 1.33 . 0.4 . 0.165 . 0.1 . 0.53 . 0.99 . 0.4 . 0.78 . . . 35 . 1.11 . 0.25 . 0.063 . 0.1 . 0.55 . 1.14 . 0.29 . 0.58 . . 10 . 25 . 1.46 . 0.25 . 0.194 . 0.2 . 0.55 . 1.14 . 0.29 . 0.34 . . . 30 . 1.19 . 0.2 . 0.095 . 0.2 . 0.56 . 1.2 . 0.24 . 0.29 . . 40 . 25 . 1.34 . 0.2 . 0.144 . 0.78 . 0.56 . 1.2 . 0.24 . 0.10 . Sand 3 . 5 . 50 . 1.02 . 0.5 . 0.015 . 0.09 . 0.52 . 0.91 . 0.46 . 0.96 . . 10 . 35 . 1.35 . 0.5 . 0.201 . 0.18 . 0.52 . 0.91 . 0.46 . 0.56 . . . 40 . 1.13 . 0.5 . 0.084 . 0.18 . 0.52 . 0.91 . 0.46 . 0.56 . . 20 . 20 . 2.39 . 0.5 . 0.475 . 0.36 . 0.52 . 0.91 . 0.46 . 0.33 . . . 25 . 1.88 . 0.25 . 0.372 . 0.36 . 0.55 . 1.14 . 0.29 . 0.21 . . . 30 . 1.53 . 0.2 . 0.265 . 0.36 . 0.56 . 1.2 . 0.24 . 0.18 . . 40 . 25 . 1.83 . 0.4 . 0.351 . 0.72 . 0.53 . 0.99 . 0.4 . 0.17 . . . 30 . 1.48 . 0.25 . 0.24 . 0.72 . 0.55 . 1.14 . 0.29 . 0.12 . . . 35 . 1.23 . 0.2 . 0.132 . 0.72 . 0.56 . 1.2 . 0.24 . 0.11 . . 139 .
(140) Appendix H . G.4.2. f = 2 Hz . (a) Cohesive soils MHEA (g) . Soil type . H (m) . i (°) . FS . PHAc (g) . Ky . Ts (s) . Tm (s) . NRF . A . B . Clay 2 . 5 . 15 . 2.18 . 0.45 . 0.305 . 0.2 . 0.53 . 0.95 . 0.43 . 0.49 . . . 20 . 1.86 . 0.4 . 0.294 . 0.2 . 0.53 . 0.99 . 0.4 . 0.46 . . . 30 . 1.53 . 0.35 . 0.265 . 0.2 . 0.54 . 1.04 . 0.36 . 0.42 . . . 50 . 1.26 . 0.25 . 0.199 . 0.2 . 0.55 . 1.14 . 0.29 . 0.34 . . . 60 . 1.14 . 0.2 . 0.121 . 0.2 . 0.56 . 1.2 . 0.24 . 0.29 . . 10 . 15 . 1.84 . 0.4 . 0.217 . 0.32 . 0.53 . 0.99 . 0.4 . 0.31 . 30 . 1.14 . 0.2 . 0.07 . 0.32 . 0.56 . 1.2 . 0.24 . 0.20 . . . . 20 . 15 . 1.41 . 0.4 . 0.106 . 0.49 . 0.53 . 0.99 . 0.4 . 0.23 . Clay 3 . 10 . 60 . 1.24 . 0.5 . 0.208 . 0.25 . 0.52 . 0.91 . 0.46 . 0.43 . . . 75 . 1.06 . 0.25 . 0.058 . 0.25 . 0.55 . 1.14 . 0.29 . 0.28 . . 20 . 30 . 1.17 . 0.5 . 0.085 . 0.42 . 0.52 . 0.91 . 0.46 . 0.29 . . . 40 . 1.03 . 0.25 . 0.019 . 0.42 . 0.55 . 1.14 . 0.29 . 0.19 . . 140 .
(141) Parameters and results from the Californian and USGS simplified approaches… (b) Non‐cohesive soils MHEA (g) . Soil type . H (m) . i (°) . FS . PHAc (g) . Ky . Ts (s) . Tm (s) . NRF . A . B . Sand 1 . 5 . 30 . 1.2 . 0.5 . 0.1 . 0.1 . 0.52 . 0.91 . 0.46 . 0.89 . . . 35 . 1.03 . 0.25 . 0.017 . 0.1 . 0.55 . 1.14 . 0.29 . 0.58 . . 10 . 32 . 1.03 . 0.2 . 0.016 . 0.21 . 0.56 . 1.2 . 0.24 . 0.28 . . 20 . 25 . 1.28 . 0.5 . 0.118 . 0.41 . 0.52 . 0.91 . 0.46 . 0.29 . . . 29 . 1.04 . 0.25 . 0.019 . 0.41 . 0.55 . 1.14 . 0.29 . 0.19 . . 40 . 20 . 1.58 . 0.25 . 0.198 . 0.82 . 0.55 . 1.14 . 0.29 . 0.11 . . . 25 . 1.21 . 0.2 . 0.089 . 0.82 . 0.56 . 1.2 . 0.24 . 0.10 . Sand 2 . 5 . 30 . 1.33 . 0.5 . 0.165 . 0.1 . 0.52 . 0.91 . 0.46 . 0.89 . . 10 . 25 . 1.46 . 0.5 . 0.194 . 0.2 . 0.52 . 0.91 . 0.46 . 0.52 . . . 34 . 1.02 . 0.2 . 0.011 . 0.2 . 0.56 . 1.2 . 0.24 . 0.29 . . 20 . 32 . 1.02 . 0.25 . 0.011 . 0.39 . 0.55 . 1.14 . 0.29 . 0.20 . . 40 . 20 . 1.72 . 0.25 . 0.246 . 0.78 . 0.55 . 1.14 . 0.29 . 0.12 . . . 25 . 1.34 . 0.2 . 0.144 . 0.78 . 0.56 . 1.2 . 0.24 . 0.10 . Sand 3 . 5 . 50 . 1.02 . 0.5 . 0.015 . 0.09 . 0.52 . 0.91 . 0.46 . 0.96 . . 10 . 40 . 1.13 . 0.5 . 0.084 . 0.18 . 0.52 . 0.91 . 0.46 . 0.56 . . 20 . 35 . 1.26 . 0.5 . 0.149 . 0.36 . 0.52 . 0.91 . 0.46 . 0.33 . . . 40 . 1.07 . 0.25 . 0.045 . 0.36 . 0.55 . 1.14 . 0.29 . 0.21 . . 40 . 20 . 2.35 . 0.4 . 0.462 . 0.72 . 0.53 . 0.99 . 0.4 . 0.17 . . . 25 . 1.83 . 0.4 . 0.351 . 0.72 . 0.53 . 0.99 . 0.4 . 0.17 . . . 30 . 1.48 . 0.25 . 0.24 . 0.72 . 0.55 . 1.14 . 0.29 . 0.12 . . . 35 . 1.23 . 0.25 . 0.132 . 0.72 . 0.55 . 1.14 . 0.29 . 0.12 . . . 38 . 1.05 . 0.2 . 0.031 . 0.72 . 0.56 . 1.2 . 0.24 . 0.11 . . 141 .
(142) Appendix H . G.4.3. f = 4 Hz . (a) Cohesive soils MHEA (g) . Soil type . H (m) . i (°) . FS . PHAc (g) . Ky . Ts (s) . Tm (s) . NRF . A . B . Clay 1 . 5 . 10 . 1.54 . 0.2 . 0.094 . 0.29 . 0.56 . 1.2 . 0.24 . 0.22 . . 10 . 10 . 1.38 . 0.2 . 0.066 . 0.42 . 0.56 . 1.2 . 0.24 . 0.16 . Clay 2 . 5 . 15 . 2.18 . 0.45 . 0.305 . 0.2 . 0.53 . 0.95 . 0.43 . 0.49 . . . 20 . 1.86 . 0.4 . 0.294 . 0.2 . 0.53 . 0.99 . 0.4 . 0.46 . . . 30 . 1.53 . 0.35 . 0.265 . 0.2 . 0.54 . 1.04 . 0.36 . 0.42 . . . 50 . 1.26 . 0.25 . 0.199 . 0.2 . 0.55 . 1.14 . 0.29 . 0.34 . . . 60 . 1.14 . 0.2 . 0.121 . 0.2 . 0.56 . 1.2 . 0.24 . 0.29 . . 10 . 15 . 1.84 . 0.45 . 0.217 . 0.32 . 0.53 . 0.95 . 0.43 . 0.34 . . . 20 . 1.49 . 0.4 . 0.168 . 0.32 . 0.53 . 0.99 . 0.4 . 0.31 . . . 30 . 1.14 . 0.25 . 0.07 . 0.32 . 0.55 . 1.14 . 0.29 . 0.23 . . . 35 . 1.07 . 0.2 . 0.04 . 0.32 . 0.56 . 1.2 . 0.24 . 0.20 . . 20 . 15 . 1.41 . 0.55 . 0.106 . 0.49 . 0.52 . 0.89 . 0.48 . 0.27 . . . 20 . 1.22 . 0.5 . 0.075 . 0.49 . 0.52 . 0.91 . 0.46 . 0.26 . . . 25 . 1.05 . 0.45 . 0.021 . 0.49 . 0.53 . 0.95 . 0.43 . 0.24 . Clay 3 . 5 . 89 . 1.1 . 0.5 . 0.1 . 0.15 . 0.52 . 0.91 . 0.46 . 0.65 . . 10 . 75 . 1.06 . 0.5 . 0.058 . 0.25 . 0.52 . 0.91 . 0.46 . 0.43 . . 20 . 40 . 1.03 . 0.5 . 0.019 . 0.42 . 0.52 . 0.91 . 0.46 . 0.29 . . 142 .
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