Bayesian Uncertainty Quantification for Geomechanical Models at Micro and Macro Scales

Abstract

Uncertainty exists in geomaterials at contact, microstructural, and continuum scales. To develop predictive, robust multi-scale models for geotechnical problems, the new challenge is to allow for the propagation of model/parameter uncertainty (conditioned on laboratory/field measurements) between micro and macro scales. We aim to first quantify these uncertainties using an iterative Bayesian filtering framework. The framework utilizes the recursive Bayes’ rule to quantify the evolution of parameter uncertainties over time, and the nonparametric Gaussian mixture model to iteratively resample parameter space. Using the iteratively trained mixture to guide resampling, model evaluations are allocated asymptotically close to posterior modes, thus greatly reducing the computation cost. In this paper, we first respectively quantify the parameter uncertainty of models that are discrete and continuum in nature, namely a discrete particle and an elasto-plastic model. We then link the two models by conditioning their uncertainties on the same stress-strain response, thereby revealing micro-macro parameter correlations and their uncertainties. The micro-macro correlations obtained can be either general for any granular materials that share similar polydispersity or conditioned on the laboratory data of specific ones.