Methodology for Global Sensitivity Analysis of Flexible Pavements in a Bayesian Back-Analysis Framework

Abstract

Probabilistic sensitivity analysis is a crucial tool in the uncertainty analysis of systems, which allows the understanding of how the uncertainty in the output response can be apportioned to different sources of uncertainty in the input parameters. Sobol’s method is a widely accepted global sensitivity analysis (GSA) technique that has been applied to rank the input design parameters, based on their respective impact on the response randomness. Although this variance-based technique is highly efficient when the design parameters are independent, the estimation of Sobol indices in the presence of correlation has not been sufficiently documented. This paper addresses this shortcoming through the development of a generalized method for GSA in the Bayesian back-analysis framework, in which the Kullback-Leibler (K-L) entropy measure serves as the measure of sensitivity. The methodology has been explored in the context of design of flexible pavements in the mechanistic-empirical (M-E) framework, in which considerable correlation among the design parameters has been reported. The probabilistic back-analysis method has been solved using the Markov chain Monte Carlo (MCMC) simulation method to identify the critical parameters contributing to the failure of a flexible pavement section by fatigue cracking and rutting. The study shows that the sensitivity estimates for the two modes of failure are impacted by the presence of design parameter correlation. The advantage of this method over other techniques of GSA, in addition to the incorporation of correlation, is that the flexibility of the Bayesian methodology allows the incorporation of model uncertainty. The probabilistic back-analysis approach based on Bayes’ theorem thus presents a generalized method that can be efficiently used for the estimation of the critical parameters that contribute to the failure of any system.

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