About Soil Liquefaction Triggering Calculator
This soil liquefaction calculator evaluates the triggering of liquefaction in saturated cohesionless soils using the simplified Seed-Idriss procedure as updated by the 1997 NCEER workshop. It compares the cyclic stress ratio (CSR) imposed by an earthquake with the cyclic resistance ratio (CRR) of the soil to return a factor of safety.
Enter the depth of the layer, the peak ground acceleration as a fraction of g, the earthquake moment magnitude, and the corrected SPT blow count (N1)60. Vertical stresses may be supplied directly or computed from a uniform soil unit weight and the depth to the water table. The tool reports CSR, CRR7.5, the magnitude scaling factor, and the factor of safety, with a verdict of liquefaction, marginal, or no liquefaction.
How It Works
- Compute the total and effective vertical stress at the analysis depth, either from your direct inputs or from unit weight and the water-table depth.
- Evaluate the stress reduction coefficient rd and the cyclic stress ratio CSR = 0.65 (amax/g)(sigma_v/sigma_v_eff) rd, which represents the seismic demand.
- Evaluate the cyclic resistance ratio CRR7.5 from the corrected SPT (N1)60 using the NCEER 1997 clean-sand relationship, and the magnitude scaling factor MSF.
- Combine these into the factor of safety FS = (CRR7.5 × MSF) / CSR and classify the result against the usual screening thresholds.
Worked Example
A saturated sand layer at z = 6 m has a total vertical stress sigma_v = 108 kPa and effective vertical stress sigma_v_eff = 68.76 kPa (gamma = 18 kN/m^3, water table at 2 m). For amax = 0.25 g and an Mw 7.5 earthquake, the stress reduction factor is rd = 1 - 0.00765 × 6 = 0.954, so CSR = 0.65 × 0.25 × (108 / 68.76) × 0.954 = 0.243. With a corrected SPT (N1)60 = 15, the NCEER cyclic resistance ratio is CRR7.5 = 1/(34-15) + 15/135 + 50/(150+45)^2 - 1/200 = 0.160. The magnitude scaling factor at Mw 7.5 is MSF = 1.0, so the factor of safety is FS = (0.160 × 1.0) / 0.243 = 0.66, which is below 1.0 and indicates that liquefaction is likely to be triggered.
Formulas
- Cyclic stress ratio (seismic demand)
CSR = 0.65 (amax/g) (sigma_v / sigma_v_eff) rd- Stress reduction coefficient (Liao & Whitman)
z < 9.15 m: rd = 1 - 0.00765 z; 9.15 <= z < 23 m: rd = 1.174 - 0.0267 z- Cyclic resistance ratio (NCEER 1997, clean sand)
CRR7.5 = 1/(34 - (N1)60) + (N1)60/135 + 50/(10 (N1)60 + 45)^2 - 1/200- Magnitude scaling factor and factor of safety
MSF = 10^2.24 / Mw^2.56; FS = (CRR7.5 * MSF) / CSR
Standards & References
- Seed & Idriss (1971) simplified procedure
- NCEER 1997 Workshop (Youd et al., 2001)
- Idriss & Boulanger, Soil Liquefaction During Earthquakes
- ASCE 7 / Eurocode 8 seismic site evaluation
Frequently Asked Questions
What factor of safety against liquefaction is considered safe?
A factor of safety FS = (CRR × MSF) / CSR below 1.0 means liquefaction is expected to be triggered. Values between about 1.0 and 1.2-1.3 are marginal and usually warrant further study, while values above 1.2-1.3 are generally taken as not liquefiable. The exact screening threshold depends on the importance of the structure and local practice.
What is the corrected SPT (N1)60 and why is it used?
The (N1)60 is the standard penetration test blow count corrected to a 60 percent hammer energy and normalised to an effective overburden of one atmosphere. Normalising removes the influence of depth and equipment so that a single resistance curve (the CRR relationship) can be used across sites. You must enter the already-corrected value.
What does the magnitude scaling factor account for?
The CRR relationship is calibrated for a magnitude 7.5 earthquake. The magnitude scaling factor MSF adjusts the resistance for the number of equivalent stress cycles produced by other magnitudes: smaller earthquakes give MSF greater than 1 (more resistance) and larger earthquakes give MSF less than 1 (less resistance).
Does this calculator account for fines content or cohesive soils?
No. It uses the clean-sand NCEER relationship and does not apply a fines-content correction to (N1)60, nor does it assess clays or silts that may behave as cyclically softening rather than liquefying. Apply the appropriate fines correction to (N1)60 before entering it, and use a separate procedure for fine-grained soils.