Hierarchical Bayesian Approach to Estimating Variability of Liquefaction Resistance of Sandy Soils Considering Individual Differences in Laboratory Tests

Cyclic undrained triaxial tests are commonly used in research and practical design to evaluate the liquefaction resistance of sandy soils. This paper aims to propose a methodology to evaluate liquefaction resistance by considering the variability or uncertainty associated with experimentation, using Bayesian statistics with a Markov chain Monte Carlo technique. In addition to conventional nonhierarchical Bayesian modeling, hierarchical Bayesian modeling is adopted to properly incorporate the factor of variability caused by individual differences (e.g., difference between experimenters) into the liquefaction resistance evaluation. Findings show that the regression curves of the cyclic resistance ratio estimated by a nonhierarchical model for all experimenters' results in a cooperative triaxial test program are too generic and poorly applicable. In contrast, the curves estimated by a nonhierarchical model for each experimenter's results sometimes deviate from the overall trend, dragged by the individual characteristics. The hierarchical Bayesian modeling demonstrates that both the overall trend and each experimenter's individuality can be rationally considered in the regression results (e.g., posterior distributions of model input parameters) by referring to the other experimenters' results, even though the number of test cases is limited for the focal experimenter. Another advantage of the modeling is that, when a different experimenter newly performs similar laboratory tests, the posterior distribution based on the existing dataset can be used as a prior distribution to estimate model input parameters specific to the experimenter. The proposed methodology may also be used to estimate the variability of liquefaction resistance considering individual differences in laboratory tests that are difficult to quantify, e.g., differences in testing apparatus and specimen size.