Hierarchical Bayesian model for predicting small-strain stiffness of sand

Abstract

This paper develops a hierarchical Bayesian model (HBM) that integrates the physical knowledge and the test data to predict the small-strain shear modulus Gmax for a target sand type. The limited target-specific data is combined with the abundant generic data through a hierarchical structure so that the variability of Gmax within one sand type and across different sand types can be captured. The hyperparameters that characterize the same underlying distribution of physical model parameters across all the sand types are first estimated from the abundant generic data. The model parameters for the new sand type are then updated as the limited site-specific data become available. The approach is illustrated using a generic database and two real examples not covered by the generic database. Multiple possible hierarchical models are compared in terms of model complexity and goodness-of-fit. The results show that the hierarchical modeling of small-strain shear modulus data is reasonable and necessary. The hierarchical model can provide less biased and more accurate predictions of Gmax compared to the commonly used complete pooling model, especially for cases where the site-specific data is quite different from the overall average of the generic database.