Cyclic Stress Ratio for Liquefaction Screening (Simplified)
Cyclic Stress Ratio for Liquefaction Screening (Simplified)
Liquefaction — the sudden loss of soil strength when a saturated, loose granular deposit is shaken by an earthquake — is one of the most damaging geotechnical earthquake hazards, having caused widespread building tilting and ground failure in major quakes. The simplified procedure developed by Seed and Idriss compares an earthquake-induced cyclic stress ratio (the demand) against a soil's cyclic resistance ratio (the capacity) to screen for liquefaction risk at a given depth. This screening-level formula for CSR is only the demand half of the comparison — a full liquefaction assessment also requires the site-specific cyclic resistance ratio from SPT, CPT, or shear-wave velocity correlations, and the two are compared to compute a factor of safety against liquefaction.
The simplified cyclic stress ratio is CSR = 0.65*(amax/g)*(sigma_v/sigma_v_eff)*rd. where amax_g is the peak ground acceleration expressed as a fraction of gravity, sigma_v is total vertical overburden stress, sigma_v_eff is effective (buoyant) vertical stress, and r_d is a depth-dependent stress reduction factor.
Inputs
amax_g := 0.3=0.3
sigma_v := 100 kPa=100000 Pa
sigma_v_eff := 60 kPa=60000 Pa
r_d := 0.95=0.95
The 0.65 factor converts a peak, one-time acceleration into an equivalent uniform cyclic stress, the sigma_v/sigma_v_eff ratio accounts for how pore pressure reduces the soil's effective confinement, and rd corrects for how shaking intensity attenuates with depth in a flexible soil column.
CSR_liq := 0.65·amax_g·(sigma_v/sigma_v_eff)·r_d=0.31
Results
A CSR around 0.3-0.35 at this depth and shaking level is a moderate-to-significant demand that would need to be checked against a site-specific cyclic resistance ratio before drawing conclusions. If CSR exceeds the soil's resistance ratio, the factor of safety against liquefaction falls below 1 and mitigation (densification, drainage, or foundation redesign) is typically warranted — this simplified CSR is only ever the first half of that comparison.
Assumptions & limitations
- Simplified Seed-Idriss procedure — only the demand (CSR) side, not resistance.
- rd is a depth-dependent factor that should be selected/verified for the actual depth of interest.
- Assumes level ground and free-field site conditions (no slope or structure effects).
- A full liquefaction assessment also requires comparison against a soil cyclic resistance ratio.