Efficient Bayesian characterization of cohesion and friction angle of soil using parametric bootstrap method

Abstract

This study develops an efficient Bayesian approach using the parametric bootstrap method for characterizing the joint probability density function (PDF) of c′ and ϕ′ based on limited site-specific test data and prior knowledge. An example using real data of c′ and ϕ′ obtained from direct shear tests on alluvial fine-grained soils at the Paglia River alluvial plain in Central Italy is presented to illustrate and demonstrate the parametric bootstrap method. A sensitivity study is performed to investigate the impact of the amount of site-specific test data and prior knowledge on the posterior statistics of c′ and ϕ′. The results indicate that the parametric bootstrap method has a good accuracy and efficiency in characterizing the joint PDF of c′ and ϕ′. By reconstructing the likelihood function and rewriting the joint PDF of c′ and ϕ′ based on a large number of parametric bootstrap samples, the parametric bootstrap method significantly improves the efficiency of the conventional Bayesian approach while retaining the same accuracy as the conventional Bayesian approach. The equivalent sample pairs of c′ and ϕ′ generated using the Markov chain Monte Carlo simulation represent the joint PDF of c′ and ϕ′ well. The amount of site-specific test data and prior knowledge have a significant impact on the posterior statistics of c′ and ϕ′. Increasing the amount of the site-specific data and informativeness of the prior knowledge can reduce the statistical uncertainty in the posterior statistics. In addition, the role of prior knowledge decreases as the amount of the site-specific data increases.