Soil Liquefaction Calculator: CSR, CRR & Factor of Safety

simulator intermediate ~10 min
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FS = 0.82 — liquefaction likely at this site

For Mw 7.0, PGA = 0.25g, N₆₀ = 15, and 2 m water table depth, the factor of safety is 0.82 — indicating high liquefaction risk. Ground improvement or deep foundations are recommended.

Formula

CSR = 0.65 × (σ_v / σ'_v) × a_max × r_d / MSF
CRR₇.₅ = 1 / (34 - N₁₆₀) + N₁₆₀/135 + 50/(10×N₁₆₀+45)² - 1/200
FS = CRR / CSR (liquefy if FS < 1.0)

When Solid Ground Turns to Liquid

Soil liquefaction is one of the most dramatic and destructive consequences of earthquakes. During strong shaking, cyclic stresses in loose, saturated sand cause pore water pressure to rise progressively. When the pore pressure equals the total overburden stress, the effective stress drops to zero and the soil loses all shear strength, behaving like a dense fluid. Buildings tilt and sink, buried structures float upward, and the ground flows laterally on gentle slopes.

The Simplified Procedure

Engineers evaluate liquefaction risk using the Seed-Idriss simplified procedure, which compares seismic demand (CSR) to soil resistance (CRR). The cyclic stress ratio CSR = 0.65 × (σ_v/σ'_v) × a_max × r_d / MSF estimates the shear stress induced by the earthquake, where r_d is a depth reduction factor and MSF adjusts for magnitude (duration). The cyclic resistance ratio CRR is empirically correlated to field measurements — typically SPT blow count N₆₀ or CPT tip resistance.

Factor of Safety

The factor of safety FS = CRR/CSR is the key decision metric. FS < 1.0 indicates liquefaction is expected; FS between 1.0 and 1.2 is marginal; and FS > 1.2 is generally considered safe. The liquefaction potential index (LPI) integrates the factor of safety over the top 20 meters to provide a single-number hazard assessment for the entire site profile, accounting for the severity and depth extent of liquefiable layers.

Consequences and Mitigation

Liquefaction causes four main types of ground failure: sand boils (ejection of sand and water), loss of bearing capacity (foundation settlement and tilting), lateral spreading (horizontal displacement on gentle slopes), and flow failure (large-scale landslides on steeper slopes). The 1964 Niigata and 1995 Kobe earthquakes produced iconic examples. Modern mitigation strategies include densifying loose soils through vibro-compaction, installing stone columns for drainage, or using deep pile foundations that transfer loads to non-liquefiable strata.

FAQ

What is soil liquefaction?

Liquefaction occurs when loose, saturated soil loses its strength during earthquake shaking. Cyclic loading increases pore water pressure until it equals the overburden stress, eliminating effective stress and causing the soil to behave like a liquid. Sand boils, lateral spreading, and foundation failure are common consequences.

What is the simplified procedure for liquefaction evaluation?

The Seed-Idriss simplified procedure compares the cyclic stress ratio (CSR, the seismic demand) to the cyclic resistance ratio (CRR, the soil capacity). CSR depends on PGA, depth, and magnitude. CRR is estimated from SPT blow counts or CPT tip resistance. If CSR > CRR (FS < 1), liquefaction is predicted.

What factors increase liquefaction risk?

Five main factors: loose granular soil (low SPT N-value), shallow water table (full saturation), strong shaking (high PGA), long duration (high magnitude), and uniform fine sand grain size. Clays and gravels generally resist liquefaction, as do dense sands with N₆₀ > 30.

How can liquefaction be mitigated?

Common mitigation methods include: vibro-compaction to densify loose sand, stone columns to increase drainage and density, deep soil mixing with cement, surcharge loading to increase effective stress, and dewatering to lower the water table. Deep foundations (piles) can transfer loads through liquefiable layers to stable bearing strata.

Sources

Embed

<iframe src="https://homo-deus.com/lab/seismology/liquefaction/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub