Incorporating region-variability of model bias into liquefaction-triggering procedures for sandy and gravelly soils through BUS-powered hierarchical Bayesian updating

The accuracy of semi-empirical liquefaction-triggering procedures can vary systematically from region to region, but it is challenging to regionalize models due to the lack of region-specific data. This paper presents a hierarchical Bayesian modeling (HBM)-based framework for incorporation of inter-region and intra-region variabilities of the bias factor in liquefaction-triggering procedures. A key feature of the framework is that the BUS approach (Bayesian Updating with Structural reliability methods) is combined with subset simulation to efficiently update high-dimensional statistics of bias factors. Another feature is the quantification of evidence for model plausibility evaluation using Gaussian copula. This framework is utilized to develop three sets of region-specific liquefaction probability models, covering liquefaction-susceptible sandy and gravelly soils. The results show that HBM considering both region-specific means and variances of bias factor matches better with liquefaction observations and produces larger total variance, compared to the existing lumped-region modeling and HBM with only region-specific means. Meanwhile, the population-level distribution and the weighting factor of liquefaction/non-liquefaction occurrence can considerably affect modeling performance. Furthermore, a discrete integration-based probabilistic method is suggested for liquefaction-triggering hazard assessment. Illustrative examples show that different HBM configurations can yield notably different liquefaction hazard results, while neglecting the region-variability is likely to be unconservative.