Civil, Structural & Geotechnical Engineering
Seed-Idriss Soil Liquefaction Formula: Cyclic Stress Ratio CSR & Factor of Safety
Evaluate earthquake-induced sand liquefaction using H. Bolton Seed and I. M. Idriss’s (1971 / NCEER) Simplified Procedure: compute depth stress-reduction r_d, Cyclic Stress Ratio CSR, and Liquefaction Factor of Safety FS_liq = (CRR_7.5 * MSF) / CSR.
Compare earthquake Cyclic Stress Demand (CSR) against soil Cyclic Resistance (CRR)!
Formulated by H. Bolton Seed and I. M. Idriss (1971) and standardized by the 1996/1998 NCEER/NSF workshops (Youd et al., 2001), the Simplified Liquefaction Triggering Procedure converts peak ground surface acceleration a_max / g into an equivalent uniform cyclic shear-stress ratio at depth z (using the 0.65 peak-to-equivalent harmonic factor): CSR = 0.65 * (a_max / g) * (sigma_v0 / sigma'_v0) * r_d!
Here sigma_v0 / sigma'_v0 amplifies demand below shallow water tables, and Liao & Whitman’s piecewise depth-flexibility factor r_d equals 1.0 - 0.00765 * z for z <= 9.15 m and 1.174 - 0.0267 * z for 9.15 < z <= 23 m. Dividing magnitude-scaled cyclic resistance CRR_7.5 * MSF by CSR yields Liquefaction Factor of Safety FS_liq (where FS_liq < 1.0 predicts liquefaction triggering and design codes typically target FS_liq >= 1.20–1.30).
| Liquefaction Quantity (PGA = 0.28g, z = 8 m, sigma_v0 = 160 kPa, sigma'_v0 = 95 kPa) | Formula | Evaluated Value |
|---|---|---|
| Depth Stress-Reduction Factor r_d | 1 - 0.00765 * z | 0.9388 |
| Seismic Cyclic Stress Ratio CSR | 0.65 * (a_max/g) * (sigma_v0 / sigma'_v0) * r_d | 0.2878 |
| Liquefaction Factor of Safety (Loose Sand CRR = 0.26) | (CRR_7.5 * MSF) / CSR | 0.904 (Liquefaction!) |
| Liquefaction Factor of Safety (Vibro-Compacted CRR = 0.36) | (CRR_7.5 * MSF) / CSR | 1.251 (Safe) |
Seed-Idriss Seismic Cyclic Stress Ratio CSR at Depth z <= 23 m
Evaluates 0.65 * PGA_g * (sigma_v0 / sigma'_v0) * r_d(z) with NCEER piecewise depth reduction r_d.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B4 > B3, B5 <= 0, B5 > 23), "Invalid Seismic or Overburden Inputs", ROUND(0.65 * B2 * (B3 / B4) * IF(B5 <= 9.15, 1 - 0.00765 * B5, 1.174 - 0.0267 * B5), 4))Liquefaction Triggering Factor of Safety FS_liq = (CRR_7.5 * MSF) / CSR
Compares magnitude-scaled cyclic resistance B6 * B7 against seismic demand CSR.
=IF(OR(B2 <= 0, B3 <= 0, B4 <= 0, B4 > B3, B5 <= 0, B5 > 23, B6 <= 0, B7 <= 0), "Invalid Seismic or Overburden Inputs", ROUND((B6 * B7) / (0.65 * B2 * (B3 / B4) * IF(B5 <= 9.15, 1 - 0.00765 * B5, 1.174 - 0.0267 * B5)), 3))Try the example
Use the original values or change them to test your understanding.