Predicting liquefaction probability based on shear wave velocity: an update

Abstract

The simplified methods based on the cone penetration test (CPT), standard penetration test (SPT), and shear wave velocity (V _s ) test are prevalent in liquefaction potential evaluation. In this study, new case histories with the shear wave velocity measurements and the liquefaction phenomenon observations are compiled from the 22 February 2011 Canterbury earthquakes in New Zealand. The new case histories are combined with the existing V _s database for assessing and updating probabilistic models. The widely used logistic regression models, as well as other probabilistic models, are examined in the framework of generalized linear models (GLMs). To this end, the maximum likelihood estimation (MLE) principle is used to determine the model parameters. Then, the developed generalized linear models are ranked using three model assessment criteria. Based on the assessment criteria adopted, the log–log and logistic models are recommended for both the existing and the combined database. The updated log–log model and logistic model are recommended for shear wave velocity based liquefaction potential evaluation.

Appendix: Summary of the Andrus and Stokoe (2000) method

Factor of safety F _s is computed as:

$$ F_{s} = \frac{{{\text{CRR}}_{7.5} }}{{{\text{CSR}}_{7.5} }} $$

(25)

Cyclic stress ratio CSR _7.5 is computed as:

$$ {\text{CSR}}_{7.5} = \frac{{\tau_{av} }}{{\sigma^{\prime}_{v} }} = 0.65\left(\frac{{a_{\hbox{max} } }}{g}\right)\left(\frac{{\sigma_{v} }}{{\sigma^{\prime}_{v} }}\right)\gamma_{d} /{\text{MSF}} $$

(26)

where τ _av is the average equivalent uniform cyclic shear stress caused by the earthquake and assumed to be 0.65 of the maximum induced stress; a _max is the peak horizontal ground surface acceleration; g is the acceleration of gravity; σ _v is the total overburden stress in kPa; σ′ _v is the initial effective overburden stress in kPa, and γ _d is a shear stress-reduction coefficient given as

$$ \gamma_{d} = \left\{ \begin{array}{ll} 1.0 - 0.00765z & {\text{for}}\ z \le 9.1 5\;{\text{m}} \\ 1.174 - 0.0267z & {\text{for}}\ 9.1 5\;{\text{m}} < z \le 23\;{\text{m}} \\ 0.744 - 0.008z & {\text{for}}\ 23\;{\text{m}} < z \le \; 30 {\text{m}} \end{array} \right. $$

(27)

where z is the depth below the ground surface.

MSF is the magnitude scaling factor, defined as:

$$ {\text{MSF}}\;{ = }\;({{M_{w} } \mathord{\left/ {\vphantom {{M_{w} } {7.5}}} \right. \kern-0pt} {7.5}})^{{{ - }2.56}} $$

(28)

Cyclic resistance ratio CRR_7.5 is computed as:

$$ {\text{CRR}}_{7.5} = 0.022\,\left( {\frac{{V_{s1,cs} }}{100}} \right)^{2} + 2.8\left( {\frac{1}{{215 - V_{s1,cs} }} - \frac{1}{215}} \right) $$

(29)

where V _s1,cs is the clean sand equivalence of stress-corrected shear wave velocity designated as modified shear wave velocity here.

$$ V_{s1,cs} = K_{fc} V_{s1} = K_{fc} V_{s} C_{vs} = K_{fc} V_{s} \left( {\frac{{P_{a} }}{{\sigma^{\prime}_{v} }}} \right)^{0.25} $$

(30)

where

K _fc is a fines content correction to adjust values to a clean soil equivalent.

$$ K_{\text{fc}} = \left\{ {\begin{array}{*{20}l} {1\quad {\text{for FC}} \le 5\,\% } \\ {1 + (FC - 5)f(V_{s1} )\quad {\text{for 5}}\,{\text{\% < FC}} < 35\,\% } \\ {1 + 30f(V_{s1} )\quad {\text{for FC}} \ge 35\,\% } \\ \end{array} } \right. $$

(31)

$$ f(V_{s1} ) = 0.009 - 0.0109({{V_{s1} } \mathord{\left/ {\vphantom {{V_{s1} } {100}}} \right. \kern-0pt} {100}}) + 0.0038({{V_{s1} } \mathord{\left/ {\vphantom {{V_{s1} } {100}}} \right. \kern-0pt} {100}})^{2} $$

(32)

V _s1 is the stress-corrected shear wave velocity

C _vs is a factor to correct measured V _s for overburden pressure.

P _a is a reference stress of 100 kPa.