Question 6.12: Figure 6.13 shows the subsoil profile at Kawagishi-cho in Ni...
Figure 6.13 shows the subsoil profile at Kawagishi-cho in Niigata. Assume a level-ground site with the groundwater table at a depth of 1.5 m below ground surface; the medium sand and medium-fine sand have less than 5 percent fines; the total unit weight \gamma_{t} of the soil above the groundwater table is 18.3 kN/m³; and the buoyant unit weight \gamma_{b} of the soil below the groundwater table is 9.7 kN/m³.
The standard penetration data shown in Fig. 6.13 are uncorrected N values. Assume a hammer efficiency E_{m} of 0.6 and a boring diameter of 100 mm, and the length of drill rods is equal to the depth of the SPT test below ground surface. The earthquake conditions are a peak ground acceleration a_{\max } of 0.16g and a magnitude of 7.5. Using the standard penetration test data, determine the factor of safety against liquefaction versus depth.
See App. E for the solution and Fig. 6.14 for a plot of the factor of safety against liquefaction versus depth.
See page E.6.
| Cyclic stress ratio (CSR) | N value corrections | |||||||||||
| Depth, m |
\sigma_{v},, kPa |
\sigma_{v}^{\prime}, kPa |
\sigma_{v} / \sigma_{v}^{\prime} | r_{d} | CSR | N value | C_{r} | N_{60} | C_{N} | \left(N_{1}\right)_{60} | CRR | FS = CRR/CSR |
| 1.5 | 27.5 | 27.5 | 1.00 | 0.98 | 0.10 | 8 | 0.75 | 6.0 | 1.91 | 11 | 0.12 | 1.18 |
| 2.5 | 47.0 | 37.2 | 1.26 | 0.97 | 0.13 | 5 | 0.75 | 3.8 | 1.64 | 6.2 | 0.07 | 0.55 |
| 3.5 | 66.5 | 46.9 | 1.42 | 0.96 | 0.14 | 4 | 0.75 | 3.0 | 1.46 | 4.4 | 0.05 | 0.35 |
| 4.5 | 86.0 | 56.6 | 1.52 | 0.95 | 0.15 | 5 | 0.85 | 4.3 | 1.33 | 5.7 | 0.06 | 0.40 |
| 5.5 | 105 | 66.3 | 1.58 | 0.93 | 0.15 | 9 | 0.85 | 7.7 | 1.23 | 9.5 | 0.11 | 0.72 |
| 6.5 | 125 | 76.0 | 1.64 | 0.92 | 0.16 | 10 | 0.95 | 9.5 | 1.15 | 11 | 0.12 | 0.76 |
| 7.5 | 144 | 85.7 | 1.68 | 0.91 | 0.16 | 12 | 0.95 | 11 | 1.08 | 12 | 0.13 | 0.82 |
| 8.5 | 164 | 95.4 | 1.72 | 0.90 | 0.16 | 12 | 0.95 | 11 | 1.02 | 11 | 0.12 | 0.75 |
| 9.5 | 183 | 105 | 1.74 | 0.89 | 0.16 | 15 | 0.95 | 14 | 0.98 | 14 | 0.16 | 1.00 |
| 10.5 | 203 | 115 | 1.77 | 0.87 | 0.16 | 11 | 1.00 | 11 | 0.93 | 10 | 0.11 | 0.69 |
| 11.5 | 222 | 124 | 1.79 | 0.86 | 0.16 | 23 | 1.00 | 23 | 0.90 | 21 | 0.23 | 1.44 |
| 12.5 | 242 | 134 | 1.81 | 0.85 | 0.16 | 11 | 1.00 | 11 | 0.86 | 9.5 | 0.11 | 0.69 |
| 13.5 | 261 | 144 | 1.81 | 0.84 | 0.16 | 10 | 1.00 | 10 | 0.83 | 8.3 | 0.09 | 0.57 |
| 14.5 | 281 | 154 | 1.82 | 0.83 | 0.16 | 10 | 1.00 | 10 | 0.81 | 8.1 | 0.09 | 0.57 |
| 15.5 | 300 | 163 | 1.84 | 0.81 | 0.16 | 25 | 1.00 | 25 | 0.78 | 20 | 0.23 | 1.48 |
| 16.5 | 320 | 173 | 1.85 | 0.80 | 0.15 | 27 | 1.00 | 27 | 0.76 | 21 | 0.24 | 1.56 |
| 17.5 | 339 | 183 | 1.85 | 0.79 | 0.15 | 4 | 1.00 | 4 | 0.74 | 3.0 | 0.03 | 0.20 |
| 18.5 | 359 | 192 | 1.87 | 0.78 | 0.15 | 5 | 1.00 | 5 | 0.72 | 3.6 | 0.04 | 0.26 |
| 19.5 | 378 | 202 | 1.87 | 0.77 | 0.15 | 3 | 1.00 | 3 | 0.70 | 2.1 | 0.02 | 0.13 |
| 20.5 | 398 | 212 | 1.88 | 0.75 | 0.15 | 38 | 1.00 | 38 | 0.69 | 26 | 0.30 | 2.05 |
| Notes: Cyclic stress ratio: a_{\max }=0.16 g, r_{d} from Eq. (6.7). N value corrections: E_{m}=0.6, C_{b}=1.0, C_{N} from Eq. (5.2). CRR from Fig. 6.6. r_{d}=1-0.012 z (6.7) \left(N_{1}\right)_{60}=C_{N} N_{60}=\left(100 / \sigma_{v 0}^{\prime}\right)^{0.5} N_{60} (5.2) |
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