Liquefaction triggering: CSR, CRR and the factor of safety
The simplified procedure in plain terms: how earthquake demand (CSR) is compared with soil resistance (CRR) from SPT or CPT data, what MSF, Kσ and fines corrections do, and how LPI rolls a profile up into one number.
Loose saturated sand can lose almost all of its strength during shaking. Each cycle squeezes the grains a little closer, but the water cannot escape quickly enough, so pore pressure rises until effective stress drops towards zero. The simplified procedure (Seed and Idriss, updated by Boulanger and Idriss 2014) checks this layer by layer.
Demand: cyclic stress ratio
CSR = 0.65 · (amax/g) · (σv/σ′v) · rd. The 0.65 converts peak shaking into an equivalent uniform stress. The ratio σv/σ′v is large below the water table, and rd reduces the demand with depth because the soil column is not rigid. The result is then scaled to a magnitude 7.5 event with the magnitude scaling factor (MSF) and to 1 atmosphere overburden with Kσ.
Capacity: cyclic resistance ratio
CRR comes from case histories of sites that did and did not liquefy. For SPT it is a function of the clean-sand equivalent blow count (N1)60cs. For CPT it is a function of the normalised tip resistance qc1Ncs, with fines handled through the soil behaviour type index Ic.
The factor of safety is FS = CRR/CSR. Values below 1 indicate triggering. Many practitioners treat values between about 1.0 and 1.3 as marginal. Because the case-history curves carry uncertainty, a probabilistic version also exists, but the deterministic FS is still the most common screening output.
From layers to a site: LPI and settlement
One weak layer at 18 m matters less than a thick one at 3 m. The Liquefaction Potential Index (Iwasaki) integrates (1 − FS) with a depth weight of 10 − 0.5z over the top 20 m. Roughly, LPI above 15 is high and below 5 is low. Volumetric strain relationships (for example Ishihara & Yoshimine, or the Idriss & Boulanger form) turn the FS profile into a free-field reconsolidation settlement.
- Use the earthquake magnitude and PGA required by the project's design basis, not just a code default.
- Fines content and its measurement method strongly affect the SPT result. Record them carefully.
- Layers with Ic > 2.6 (CPT) are usually clay-like and need a different assessment (cyclic softening).