Liquefaction triggering
The simplified liquefaction triggering procedure layer by layer from SPT or CPT data, with the earthquake demand from the ASCE 7-22 11.8.3 peak ground acceleration PGA_M: the cyclic stress ratio, the cyclic resistance by Boulanger and Idriss (2014) or, for SPT, Youd et al. (2001), the factor of safety of each layer, and an estimate of the free-field post-liquefaction settlement (Idriss and Boulanger 2008, after Yoshimine et al. 2006).
Inputs of the liquefaction check #
- Earthquake: PGA_M = FPGA·PGA for the site class (ASCE 7-22 11.8.3; the USGS values) and the moment magnitude M (from the USGS deaggregation: mean or modal, the engineer's choice).
- Site: SPT or CPT; the procedure (Youd et al. 2001 is offered for SPT only); the water table during the earthquake; the layers top down, each evaluated at its mid-depth: thickness, total unit weight (saturated below water), N60 (corrected for energy, rod length, sampler and borehole) or qc, fines content FC, and whether the layer is susceptible (plastic or clayey soils by the engineer's judgment).
- Criteria: the required factor of safety (1.0 marks triggering; 1.1 to 1.3 is common for design), the Kσ exponent f of Youd et al., and the settlement limit set by the structure.
Checks performed #
| Check | Basis |
|---|---|
| Lowest factor of safety ≥ the required value | FS = CRR·MSF·Kσ / CSR, CSR = 0.65·PGA_M·(σv/σ'v)·rd |
| B&I 2014, SPT | (N1)60cs = CN·N60 + ΔN(FC), CN = (pa/σ'v)^m ≤ 1.7, m = 0.784 − 0.0768√(N1)60cs (iterated); CRR = exp(N/14.1 + (N/126)² − (N/23.6)³ + (N/25.4)⁴ − 2.8); MSFmax = 1.09 + (N/31.5)² ≤ 2.2; Cσ = 1/(18.9 − 2.55√N) ≤ 0.3 |
| B&I 2014, CPT | qc1Ncs = CN·qc/pa + Δqc1N(FC), m = 1.338 − 0.249·qc1Ncs^0.264; CRR = exp(q/113 + (q/1000)² − (q/140)³ + (q/137)⁴ − 2.80); MSFmax = 1.09 + (q/180)³ ≤ 2.2; Cσ = 1/(37.3 − 8.27q^0.264) ≤ 0.3 |
| B&I 2014 common | rd = exp(α(z) + β(z)·M) (Idriss 1999) to 34 m; MSF = 1 + (MSFmax − 1)(8.64·e^(−M/4) − 1.325); Kσ = 1 − Cσ·ln(σ'v/pa) ≤ 1.1 |
| Youd et al. 2001, SPT | CN = (pa/σ'v)^0.5 ≤ 1.7; (N1)60cs = α + β(N1)60; CRR = 1/(34 − N) + N/135 + 50/(10N + 45)² − 1/200 for N < 30 (too dense to liquefy above); rd by Liao and Whitman; MSF = 10^2.24/M^2.56; Kσ = (σ'v/pa)^(f−1) ≤ 1 |
| Settlement estimate | εv = 1.5·exp(−2.5Dr)·min(0.08, γmax), γmax from FS and Dr (Yoshimine et al. 2006), Dr from the penetration resistance; Σ εv·t against the limit |
The drawings show the soil column with each layer's factor of safety and the CSR, CRR·MSF·Kσ and FS by depth.
Limitations #
- The equations of Boulanger and Idriss (2014), Youd et al. (2001) and Idriss and Boulanger (2008) are written from knowledge; the reports are not on disk (to confirm against the published text).
- Fines content is entered (no Ic-based estimate from the CPT); qc is used as entered (enter qt where the pore pressure correction matters); no thin-layer or transition corrections.
- No lateral spreading, residual strength or flow failure, and no effect on foundations (downdrag, loss of bearing); the settlement is free-field volumetric settlement only.
Verification examples #
Verification status: 10 values compared in 3 examples (0 published, 3 hand calculations from the cited equations): 10 within tolerance, 0 recorded deviations. No published example: every value is a hand calculation. That checks the program against this reading of the code, not the reading itself. Code basis: written without the code document on hand, and confirmed only in part through published examples.
Hand calculations from the equations (backend/tests/test_verify_liquefaction.py), with a layer at one atmosphere of effective stress so that CN and Kσ are 1:
| Source | What it checks | Published | ILX Calcs |
|---|---|---|---|
| Hand, B&I 2014 SPT N60 = 20, PGA_M 0.2 g, M 7.5, z = 10.34 m | rd, CSR, CRR, MSF, FS, settlement | 0.8913, 0.2317, 0.2059, 1.000, 0.888, 10.43 in. | (test run) |
| Hand, B&I 2014 CPT qc1Ncs = 100 | CRR | 0.1373 | (test run) |
| Hand, Youd et al. 2001 SPT N = 20, M 6.5 | rd, CRR, MSF | 0.898, 0.2154, 1.442 | (test run) |