Calculation methods

LiquiTer NX implements 4 semi-empirical methods to compute CRR (Cyclic Resistance Ratio), and hence the liquefaction safety factor. The choice depends on the in-situ test available:

In-situ test	Recommended method
SPT (Standard Penetration Test)	Seed (1971), Tokimatsu (1983)
CPT (Cone Penetration Test)	Boulanger-Idriss (2014)
Cross-hole / Down-hole (Vs)	Andrus-Stokoe (2000)

All methods compute CSR in the same way (Seed-Idriss 1971); only the way CRR is estimated changes.

CSR — Cyclic Stress Ratio

Common to all methods:

\[ \text{CSR} = 0{,}65 \cdot \frac{a_{\max}}{g} \cdot \frac{\sigma_v}{\sigma'_v} \cdot r_d \]

where:

• a_max = peak ground acceleration
• σ_v / σ'_v = total / effective stress at depth z
• r_d = depth reduction coefficient (Liao-Whitman 1986 or Idriss-Boulanger 2008 depending on the method)

1. Seed (1971)

On SPT — the classic method, still the most used in Italy.

CRR is estimated from N1,60,cs (SPT number corrected for: energy, confining pressure, fines content "clean-sand equivalent") using the original Seed et al. (1985) semi-empirical curve.

When to use it

• You have SPT as the main in-situ test
• The site contains sands / silty sands
• You want a result comparable with historical Italian literature

Limitations

• Does not clearly distinguish clean and silty sands (the clean-sand correction is approximate)
• Base curve derived from M = 7.5 earthquakes — apply the MSF scaling factor for other magnitudes

References

• Seed H.B., Idriss I.M. (1971) — Simplified procedure for evaluating soil liquefaction potential. JGED, ASCE
• Seed H.B., Tokimatsu K., Harder L.F., Chung R.M. (1985) — Influence of SPT procedures in soil liquefaction resistance evaluations. JGED

2. Tokimatsu (1983)

On SPT — variant that distinguishes clean/silty sands with dedicated curves.

Same logic as Seed but uses:

• Separate CRR(N1) curves for clean and silty sands
• A different correction for confining pressure

When to use it

• You have SPT + good grain-size characterisation (you know well whether the sand is clean or silty)
• You want to compare with Seed for verification

References

• Tokimatsu K., Yoshimi Y. (1983) — Empirical correlation of soil liquefaction based on SPT N-value and fines content. Soils and Foundations

3. Boulanger-Idriss (2014)

On CPT — the most recent method, recommended when you have continuous CPT.

CRR is estimated from qc1N,cs (normalised, clean-sand equivalent CPT resistance) using the Boulanger-Idriss (2014) curve.

Advantages over SPT:

• Continuous profile along the vertical (every 1-2 cm), not in 1-m steps
• More repeatable measurement (operator-independent)
• Fines-content corrections based on Ic (soil-behaviour type index) — more robust

When to use it

• You have CPT (CPTU if possible)
• You want a "continuous" calculation along the vertical
• International state of the art

References

• Boulanger R.W., Idriss I.M. (2014) — CPT and SPT based liquefaction triggering procedures. UC Davis Report UCD/CGM-14/01
• Idriss I.M., Boulanger R.W. (2008) — Soil liquefaction during earthquakes. EERI Monograph

4. Andrus-Stokoe (2000)

On Vs — useful when you have cross-hole/down-hole or passive seismic data.

CRR is estimated from Vs1,cs (normalised, clean-sand equivalent Vs) using the Andrus-Stokoe (2000) curve.

When to use it

• You have shear-wave velocity Vs (cross-hole, down-hole, passive seismic, MASW)
• The layer is gravelly or contains cobbles (problematic for SPT/CPT)
• The site is on a slope where SPT/CPT are difficult

Limitations

• Vs is less sensitive to small density variations than SPT/CPT
• Lower reliability in very loose sands

References

• Andrus R.D., Stokoe K.H. (2000) — Liquefaction resistance of soils from shear-wave velocity. JGGE, ASCE

Scaling factors

All methods apply correction factors to the raw FSL:

MSF — Magnitude Scaling Factor

Corrects for shaking duration, since the base CRR curves are for M = 7.5. For smaller M the earthquake is shorter → fewer cycles → higher CRR:

\[ \text{MSF} = \left(\frac{M_w}{7{,}5}\right)^{-2{,}56} \]

(Idriss 1999 formulation, accepted by NTC 2018)

K_σ — Overburden Correction

Corrects for confining pressure. For σ'_v > 100 kPa CRR decreases (loose sands) or slightly increases (dense sands):

\[ K_\sigma = 1 - C_\sigma \cdot \ln\left(\frac{\sigma'_v}{p_a}\right) \]

with C_σ a function of DR (relative density).

K_α — Static Shear Stress Correction

For slopes (in LiquiTer not implemented — horizontal ground assumed).

FSL — Safety factor

\[ \text{FSL} = \frac{\text{CRR} \cdot \text{MSF} \cdot K_\sigma}{\text{CSR}} \]

Liquefaction threshold: FSL < FSL_limit (default 1.25 for NTC 2018, 1.0 for EC8).

LPI — Liquefaction Potential Index

Iwasaki et al. (1982) — integrates the "deficit" FSL < 1 over the top 20 m:

\[ \text{IPL} = \int_0^{20} F(z) \cdot w(z) \, dz \]

with:

• F(z) = 1 - FSL(z) if FSL < 1, otherwise 0
• w(z) = 10 - 0.5 z (weight linearly decreasing with depth)

LPI	Liquefaction risk
0	Negligible
0–5	Low
5–15	Medium
> 15	High

Post-seismic settlements (Ishihara-Yoshimine 1992)

For each liquefiable layer, the volumetric settlement ε_v is a function of:

• FSL of the layer
• Relative density DR (estimated from N1,60 or qc1N)

The total settlement is the sum of the contributions of each liquefiable layer, integrated along the vertical.

LiquiTer shows:

• Per-layer settlement (cm)
• Total settlement at ground level (cm)
• Differential settlement (if relevant)

References

• Ishihara K., Yoshimine M. (1992) — Evaluation of settlements in sand deposits following liquefaction during earthquakes. Soils and Foundations

---

Which method to choose — summary

Situation	Method
SPT as the only in-situ test (most common case in Italy)	Seed or Tokimatsu
You have continuous CPT/CPTU	Boulanger-Idriss (state of the art)
You have Vs (cross-hole, down-hole, MASW)	Andrus-Stokoe
You want a multi-method comparison	Run all of them, compare LPI
Gravelly site or with cobbles	Andrus-Stokoe (Vs little affected by grain size)

---

Page useful? Contact us.