Ground engineering · Earthquake geotechnics
CPT liquefaction: FS profile, settlement and lateral spreading calculator
Runs the full Boulanger & Idriss (2014) CPT procedure on every reading: Ic and fines content from Robertson's normalised cone resistance, clean-sand qc1Ncs, CRR, stress reduction rd, MSF and Kσ, CSR and the factor of safety. Then post-liquefaction volumetric strain and settlement (Zhang 2002), maximum shear strain (Yoshimine 2006) and lateral displacement (Zhang 2004), with LPI and LSN.
Standard: Boulanger & Idriss (2014) · Robertson (2009) Ic · Zhang et al. (2002, 2004) · Yoshimine et al. (2006) · Iwasaki LPI · LSN (van Ballegooy 2014) · AS 1170.4
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Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| CPT readings (depth m, qc MPa, fs kPa) | 0.5, 4.25, 30 1.0, 4.50, 30 1.5, 4.75, 30 2.0, 5.00, 30 2.5, 5.25, 30 3.0, 5.50, 30 3.5, 5.75, 30 4.0, 6.00, 30 4.5, 6.25, 30 5.0, 6.50, 30 5.5, 6.75, 30 6.0, 9.80, 60 6.5, 9.95, 60 7.0, 10.10, 60 7.5, 10.25, 60 8.0, 10.40, 60 8.5, 10.55, 60 9.0, 10.70, 60 9.5, 10.85, 60 10.0, 11.00, 60 10.5, 11.15, 60 11.0, 11.30, 60 11.5, 11.45, 60 12.0, 11.60, 60 12.5, 11.75, 60 13.0, 11.90, 60 13.5, 12.05, 60 14.0, 12.20, 60 14.5, 12.35, 60 15.0, 12.50, 60 | |
| Groundwater depth | 1.5 | m |
| Average unit weight | 18.5 | kN/m³ |
| Earthquake magnitude Mw | 6.5 | |
| Peak ground acceleration amax | 0.15 | g |
| Fines-content fitting parameter CFC | 0 | |
| Ground slope (0 = free face case) | 1 | % |
| Free face L/H (when slope = 0) | 10 | |
| Tolerable liquefaction settlement | 50 | mm |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Layers with FS < 1 | 0 of 30 | |
| Minimum FS | 1.14 | |
| Liquefaction settlement | 36 | mm |
| Lateral displacement index LDI | 0.107 | m |
| Lateral displacement LD | 0.13 | m |
| Liquefaction potential index LPI | 0.0 | |
| Liquefaction severity number LSN | 6 |
- ✓ Settlement ≤ tolerable — 36 mm
- ✓ LPI ≤ 5 (low severity, Iwasaki) — 0.0
- ✓ LSN < 16 (minor expression, van Ballegooy) — 6
Method, formulas and assumptions
- Ic by Robertson (2009) with the stress exponent n iterated; FC = 80(Ic + CFC) − 137. qc1Ncs = CN·qc/pa + Δqc1N with CN = (pa/σ′v)^m, m = 1.338 − 0.249 qc1Ncs^0.264.
- CRR7.5 = exp(q/113 + (q/1000)² − (q/140)³ + (q/137)⁴ − 2.6); rd = exp[α(z) + β(z)M]; MSF from MSFmax = 1.09 + (q/180)³; Kσ = 1 − Cσ ln(σ′v/pa) ≤ 1.1; CSR = 0.65 amax σv/σ′v rd. Layers above the water table or with Ic ≥ 2.6 are taken as non-liquefiable.
- εv from Zhang et al. (2002) by qc1Ncs and FS; γmax (Yoshimine 2006) with Dr = 0.478 qc1Ncs^0.264 − 1.063; LD = (S + 0.2)·LDI for a slope or 6(L/H)^−0.8·LDI for a free face (Zhang 2004).
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.