Bayesian Approaches for Site-specific Model Selection and Probabilistic Characterization of Young's Modulus of Rock

摘要

The Young's modulus of rock (E) is a rock property that is used as an input parameter during design and construction of engineering projects of rock structures.Although, E can be determined directly in the laboratory, this is sometimes difficult because of high-quality cores required and other testing requirements.For this reason, many regression models have been reported in the literature for estimating E of rock based on uniaxial compressive strength (UCS).Selecting appropriate model out of the many models available in the literature for estimating values of E is difficult because of the site-specific nature of the models.This study presents Bayesian approach for selecting appropriate regression model for site-specific estimation of E based on UCS.The most appropriate model for a specific site is selected, using a limited number of UCS data obtained from such site.The most appropriate model for the specific site is the model with the highest occurrence probability for the given set of available UCS data.The selected model is integrated with engineering prior knowledge and site UCS data in a Bayesian framework, and Markov Chain Monte Carlo (MCMC) simulation is used to transform the integrated knowledge into large number of equivalent E samples, Conventional statistical analysis of the equivalent samples is performed to obtain its mean, standard deviation and full probability distribution.The Bayesian approaches use engineering prior knowledge in a rational and transparent way to select appropriate model and tackle the difficulty of obtaining E values and its probability distribution for site-specific engineering design and construction.