Soil Liquefaction Calculator: CSR, CRR & Factor of Safety

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FS = 0.87 — CSR = 0.198, CRR = 0.173 → Liquefaction likely

At 6 m depth with a_max = 0.25g and N₁₆₀ = 12, the cyclic stress ratio is 0.198 and the cyclic resistance ratio is 0.173, giving FS = 0.87 — liquefaction is likely under this earthquake scenario.

Formula

CSR = 0.65 · (a_max/g) · (σ_v/σ'_v) · r_d
r_d = 1 − 0.00765z (z ≤ 9.15 m)
FS_liq = CRR₇.₅ · MSF / CSR

When Solid Ground Turns Liquid

Liquefaction is one of the most destructive geotechnical hazards. During an earthquake, cyclic shear stresses cause loose saturated sand to contract, but because water is incompressible and cannot drain fast enough, pore pressure rises. When excess pore pressure equals the effective confining stress, the soil particles lose contact with each other and the ground behaves like a dense fluid. Buildings tilt and sink, bridge piles lose lateral support, buried tanks and manholes float upward, and lateral spreading can move entire slopes toward free faces.

The Simplified Procedure

The Seed-Idriss simplified procedure, the most widely used liquefaction evaluation method worldwide, compares seismic demand (CSR) with soil resistance (CRR). The cyclic stress ratio CSR = 0.65·(a_max/g)·(σ_v/σ'_v)·r_d represents the average shear stress induced by the earthquake, normalized by effective overburden. The depth reduction factor r_d accounts for soil column flexibility, reducing CSR with depth. The simulation plots CSR and CRR together, clearly showing whether the demand exceeds resistance.

Resistance from SPT Data

Cyclic resistance ratio CRR is determined from empirical correlations based on in-situ test results. The SPT-based curve, developed from case histories of sites that did and did not liquefy in past earthquakes, plots CRR against corrected blow count N₁₆₀. Below approximately N₁₆₀ = 30, CRR increases gradually with density; above 30, the soil is considered non-liquefiable. Fines content shifts the curve: silty sands require a correction to N₁₆₀ that increases apparent resistance, reflecting the stabilizing effect of fine particles in moderate amounts.

Ground Improvement

When analysis predicts liquefaction (FS < 1), engineers have several mitigation strategies. Vibro-compaction drives a vibrating probe into the ground, densifying sand within a 2-3 m radius. Stone columns replace liquefiable soil with compacted gravel, providing both densification and drainage paths for rapid pore pressure dissipation. Deep soil mixing creates cemented panels that resist shearing. The choice depends on soil type, site access, depth, and cost — but all share the goal of either densifying the soil above the liquefaction threshold or providing drainage to prevent pore pressure buildup.

FAQ

What is soil liquefaction?

Liquefaction occurs when saturated loose granular soil loses its strength and stiffness during earthquake shaking. Cyclic loading generates excess pore water pressure that equals the effective confining stress, causing the soil to behave like a liquid. Structures on liquefied ground can sink, tilt, or collapse, and buried utilities float to the surface. It was dramatically observed in the 1964 Niigata and 2011 Christchurch earthquakes.

What is the simplified procedure for liquefaction evaluation?

Developed by Seed and Idriss (1971) and updated by Youd et al. (2001), the simplified procedure compares earthquake demand (CSR) with soil resistance (CRR). CSR is calculated from peak ground acceleration, total and effective stresses, and a depth reduction factor. CRR is read from empirical curves based on corrected SPT blow count N₁₆₀ or CPT tip resistance. If CRR/CSR < 1, liquefaction is predicted.

What soils are susceptible to liquefaction?

Liquefaction primarily affects loose, saturated, clean to silty sands at shallow depth (typically < 20 m). Fine-grained soils with plasticity index > 18 and clay content > 15% are generally not susceptible. Well-graded gravels and very dense sands resist liquefaction. The water table must be high enough to saturate the soil — unsaturated soils cannot liquefy.

How can liquefaction be mitigated?

Ground improvement techniques densify or reinforce liquefiable soils: vibro-compaction and vibro-replacement (stone columns) increase density and provide drainage; deep soil mixing creates cemented columns; compaction grouting injects stiff grout to densify surrounding soil. Structural solutions include deep foundations bypassing liquefiable layers or reinforced mat foundations that bridge over liquefied zones.

Sources

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