Bayesian Multimodel Probabilistic Methodology for Stability Analysis of Rock Structures with Limited Data of Copula-Dependent Inputs

Abstract

Stability analysis of rock structures with limited data of uncertain rock properties possessing mutual dependencies currently is an unexplored domain. This study used a Bayesian multimodel inference-based probabilistic methodology to analyze the stability of rock structures with limited data of copula-dependent uncertain inputs. The methodology propagates the epistemic uncertainties in the model types and parameters of the marginals and copula of inputs emanating due to limited data to the outputs of interest. A stratified Bayesian multimodel inference is employed initially to characterize the uncertainties in the input marginals by preparing the model sets using a reweighting approach. These model sets are employed in the second stage to characterize the uncertainties in their copula dependence. These input uncertainties, represented via an ensemble of multivariate candidate densities, are propagated to estimate the uncertainties in the outputs. The proposed methodology was demonstrated for a tunnel under consideration in the Karnataka state of India. The methodology was found to be effective because it propagates the mutual dependencies and epistemic uncertainties of the inputs to the outputs (probability of failures) and estimates their confidence intervals instead of their fixed-point estimates. These interval estimates include the point estimates of the outputs along with their upper and lower bounds within which the point estimates may vary, making users more informed about the response of structures. Additional analyses showed that the epistemic uncertainties of inputs and their dependencies significantly affect the outputs with epistemic uncertainties playing the dominating role.