First-Order Reliability Method for Probabilistic Liquefaction Triggering Analysis Using CPT

The potential for liquefaction triggering of a soil under a given seismic loading is measured herein by probability of liquefaction. The first order reliability method (FORM) is used to calculate reliability index, from which the probability of liquefaction is obtained. This approach requires the knowledge of parameter and model uncertainties; the latter is the focus of this paper. An empirical model for determining liquefaction resistance based on cone penetration test (CPT) is established through “neural network learning” of case histories. This resistance model along with a reference seismic loading model forms a performance function or limit state for liquefaction triggering analysis. Within the framework of the FORM, the uncertainty of this limit state model is characterized through an extensive series of sensitivity studies using Bayesian mapping functions that have been calibrated with a set of quality case histories. In addition, a deterministic model for assessing liquefaction potential in terms of factor of safety is presented, and the probability-safety factor mapping functions for estimating the probability of liquefaction for a given factor of safety in the absence of the knowledge of parameter uncertainty are also established. Examples are presented to illustrate the proposed methods.