Evaluation of generalized linear models for soil liquefaction probability prediction

A soil deposit subjected to seismic loading can be viewed as a binary system: it will either liquefy or not liquefy. Generalized linear models are versatile tools for predicting the response of a binary system and hence potentially applicable to liquefaction prediction. In this study, the applicability of four generalized linear models (i.e., logistic, probit, log–log, and c-log–log) for liquefaction potential evaluation is assessed and compared. Eight liquefaction models based on the four generalized linear models and two sets of explanatory variables are evaluated. These models are first calibrated with past liquefaction performance data. A weighted-likelihood function method is used to consider the sampling bias in the calibration database. The predicted liquefaction probabilities from various models are then compared. When liquefaction probability is small, the predicted liquefaction probability is sensitive to the regression models used. The effect of sampling bias is more marked in the high cyclic stress ratio region. The eight models are finally ranked using a Bayesian model comparison method. For the generalized linear models examined, the logistic and c-log–log regression models are most supported by the past performance data. On the other hand, the probit and c-log–log regression models are much less applicable to liquefaction prediction.