Figure 1
Relationship between PL and Fs based on Bayesian mapping function using the original version of the simplified procedure. PL = probability of liquefaction.
Figure 2
Bayesian mapping function along the case history data base using the original version of the simplified procedure. CSR = cyclic stress ratio.
Figure 3
Relationship between PL and Fs based on Bayesian mapping function using the corrected version of the simplified procedure. PL = probability of liquefaction.
Figure 4
Bayesian mapping function along the case history data base using the corrected version of the simplified procedure. CSR = cyclic stress ratio.
Figure 5
Relationship between PL and Fs based on Bayesian mapping function using the corrected version of the simplified procedure. PL = probability of liquefaction.
Figure 6
Bayesian mapping function along the case history data base using the corrected version of the simplified procedure with Eq. (17). CSR = cyclic stress ratio.
Figure 7
Comparison of the original and the adjusted CRR-N160cs curves. CRR = cyclic resistance ratio.
Figure 8
Profile of soil according to the depth (Nantou site).
Figure 9
Safety factor according to the depth computed by the original and corrected versions of the simplified method (Nantou site).
Figure 10
Maximum shear stress according to depth with dynamic and simplified analysis (Yuanlin site).
Figure 11
Profile of soil and shear wave velocity according to the depth (petrochemical zone site).
Figure 12
Safety factor according to the depth computed by the original and corrected versions of the simplified method (Coastal roadSkikda site).
Figure 13
Maximum shear stress according to the depth with dynamic and simplified analysis (Coastal road Skikda site).
Table 1
Summary of updated Cetin etal.’s (2016) field performance case history parameters (20 cases retained for validation).
| Case | Earthquake | Site | Liq? | Depth (m) | GWT (m) | σv (kPa) | σ′v (kPa) | amax (g) | CSR | Mw | MSF | Kσ | FC % | N | Cs | cR | CB | CE | CN | N160CS | CRR_Youd for ml=7,5σ’v =1atm | CRRSM | FSSM | CRR_Adj. for ml=7,5 sigpv0 = 1atm | CRRSMC | FSSMC |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 6 | 1964 Niigata | Arayamo-tomachi | Yes | 3.3 | 1 | 56 | 34 | 0.09 | 0.09 | 7.6 | 0.967 | 1.31 | 5 | 4.4 | 1 | 0.86 | 1 | 1.22 | 1.72 | 8.4 | 0.099 | 0.126 | 1.397 | 0.121 | 0.153 | 0.607 |
| 24 | 1975 Haicheng | Panjin Ch. F. P. | Yes | 8 | 1.5 | 148 | 85 | 0.13 | 0.13 | 7 | 1.193 | 1.041 | 67 | 8.1 | 1 | 1 | 1 | 0.83 | 1.09 | 10.9 | 0.121 | 0.151 | 1.158 | 0.149 | 0.185 | 0.631 |
| 25 | 1975 Haicheng | Ying Kou G. F. P. | Yes | 7 | 1.5 | 130 | 76 | 0.2 | 0.2 | 7 | 1.193 | 1.071 | 48 | 12.4 | 1 | 0.98 | 1 | 1 | 1.16 | 17.9 | 0.191 | 0.244 | 1.218 | 0.239 | 0.305 | 0.864 |
| 26 | 1975 Haicheng | Ying Kou P. P. | Yes | 7.5 | 1.5 | 139 | 80 | 0.2 | 0.18 | 7 | 1.193 | 1.057 | 20 | 10.3 | 1 | 0.99 | 1 | 1 | 1.12 | 13.6 | 0.146 | 0.185 | 1.025 | 0.182 | 0.229 | 0.723 |
| 30 | 1976 Tangshan | Coastal Region | Yes | 4.5 | 1.1 | 83 | 50 | 0.13 | 0.13 | 7.6 | 0.967 | 1.189 | 12 | 9.45 | 1 | 0.9 | 1 | 1 | 1.43 | 13.5 | 0.145 | 0.167 | 1.285 | 0.181 | 0.208 | 0.706 |
| 47 | 1978 Miyagiken-Oki | Nakamura 4 | Yes | 4 | 0.5 | 75 | 40 | 0.12 | 0.14 | 6.5 | 1.442 | 1.257 | 5 | 5.6 | 1 | 0.89 | 1 | 1 | 1.59 | 8.4 | 0.099 | 0.180 | 1.286 | 0.121 | 0.219 | 0.660 |
| 58 | 1978 Miyagiken-Oki | Hiyori-18 | Yes | 3.3 | 2.4 | 57 | 49 | 0.24 | 0.18 | 7.7 | 0.935 | 1.195 | 20 | 9.1 | 1 | 0.86 | 1 | 1.09 | 1.43 | 14.4 | 0.154 | 0.172 | 0.956 | 0.192 | 0.214 | 0.750 |
| 70 | 1978 Miyagiken-Oki | Yuriage Br-2 | Yes | 2.4 | 1.3 | 43 | 32 | 0.24 | 0.21 | 7.7 | 0.935 | 1.33 | 7 | 11.4 | 1 | 0.82 | 1 | 1.12 | 1.79 | 19.5 | 0.209 | 0.260 | 1.239 | 0.262 | 0.325 | 0.976 |
| 81 | 1979 Imperia’ Valley | Radio Tower B1 | Yes | 4.3 | 2 | 72 | 50 | 0.18 | 0.16 | 6.53 | 1.426 | 1.189 | 43.5 | 4.45 | 1 | 0.86 | 1 | 1.13 | 1.42 | 9.7 | 0.110 | 0.187 | 1.171 | 0.135 | 0.229 | 0.765 |
| 83 | 1979 Imperia’ Valley | River Park A | Yes | 1.1 | 0.3 | 18 | 10 | 0.16 | 0.18 | 6.53 | 1.426 | 1.778 | 91 | 2.65 | 1 | 0.66 | 1 | 1.13 | 2 | 7.3 | 0.090 | 0.228 | 1.269 | 0.109 | 0.275 | 0.763 |
| 95 | 1983 Nihonkai-Chubu | Takeda Ele.Sch. | Yes | 4.5 | 0.4 | 80 | 40 | 0.12 | 0.13 | 7.1 | 1.151 | 1.257 | 0 | 7.85 | 1 | 0.9 | 1 | 1.22 | 1.6 | 14.3 | 0.153 | 0.222 | 1.704 | 0.191 | 0.276 | 0.896 |
| 97 | 1983 Nihonkai-Chubu | Aomori Station | Yes | 5.8 | 0 | 108 | 52 | 0.12 | 0.14 | 7.7 | 0.935 | 1.178 | 3 | 9 | 1 | 0.94 | 1 | 1.22 | 1.4 | 15 | 0.160 | 0.176 | 1.259 | 0.200 | 0.220 | 0.663 |
| 122 | 1987 Superstition Hills | Wildlife B | Yes | 4.7 | 0.9 | 86 | 49 | 0.2 | 0.19 | 6.54 | 1.42 | 1.195 | 26.2 | 7.85 | 1 | 0.88 | 1 | 1.13 | 1.44 | 14.1 | 0.151 | 0.257 | 1.350 | 0.188 | 0.319 | 0.953 |
| 132 | 1989 Loma Prieta | P007-2 | Yes | 6.2 | 3 | 118 | 88 | 0.22 | 0.17 | 6.93 | 1.224 | 1.032 | 3 | 12.7 | 1 | 0.93 | 1 | 0.92 | 1.08 | 13.3 | 0.143 | 0.181 | 1.066 | 0.178 | 0.225 | 0.794 |
| 134 | 1989 Loma Prieta | POR-2&3&4 | Yes | 4.9 | 3.5 | 79 | 65 | 0.15 | 0.09 | 6.93 | 1.224 | 1.114 | 50 | 3.15 | 1 | 0.89 | 1 | 0.92 | 1.24 | 6.8 | 0.086 | 0.117 | 1.304 | 0.103 | 0.141 | 0.752 |
| 135 | 1989 Lama Prieta | Sandholdt UC-B10 | Yes | 3.2 | 1.7 | 58 | 43 | 0.26 | 0.22 | 6.93 | 1.224 | 1.235 | 2 | 9.15 | 1 | 0.81 | 1 | 1.25 | 1.53 | 14.8 | 0.158 | 0.239 | 1.086 | 0.197 | 0.298 | 0.893 |
| 139 | 1989 Lama Prieta | Treasure Island | Yes | 5.3 | 1.5 | 91 | 55 | 0.18 | 0.17 | 6.93 | 1.224 | 1.161 | 20 | 5.05 | 1 | 0.9 | 1 | 1.13 | 1.36 | 9.8 | 0.111 | 0.158 | 0.931 | 0.136 | 0.194 | 0.609 |
| 140 | 1989 Lama Prieta | Wood Marine UC-B4 | Yes | 1.8 | 1 | 31 | 24 | 0.25 | 0.21 | 6.93 | 1.224 | 1.429 | 35 | 5.75 | 1 | 0.72 | 1 | 1 | 2 | 11.9 | 0.130 | 0.228 | 1.085 | 0.161 | 0.282 | 0.865 |
| 143 | 1989 Lama Prieta | Marine Laboratory UC-B2 Yes | Yes | 3.5 | 2.5 | 63 | 53 | 0.26 | 0.2 | 6.93 | 1.224 | 1.172 | 3 | 13 | 1 | 0.83 | 1 | 1 | 1.38 | 15.4 | 0.164 | 0.235 | 1.177 | 0.205 | 0.294 | 0.969 |
| 210 | 1995 Hyogo ken-Na nbu | Torishima Dike | Yes | 4.8 | 0 | 86 | 39 | 0.25 | 0.29 | 6.9 | 1.238 | 1.265 | 20 | 8.5 | 1 | 0.91 | 1 | 1.22 | 1.61 | 17.5 | 0.186 | 0.292 | 1.006 | 0.233 | 0.365 | 0.812 |
[i] CRRSM=CRRYoud*MSF*Kσ; CRRSMC=CRRAdj*MSF*Kσ
[ii] CRRYoud: cyclic resistance ratio computed by Youd etal. (2001)
[iii] CRRAdj: cyclic resistance ratio computed by the proposed model in this study
[iv] FSSM: safety factor computed by the simplified method
[v] FSSMC: safety factor computed by the corrected simplified method
[vi] Liq?:Yes= liquefaction; No= no liquefaction