Quantification of statistical uncertainties of rock strength parameters using Bayesian-based Markov Chain Monte Carlo method

Abstract

Although unconfined compressive strength (UCS) plays an important role in geotechnical design and analysis involving rock materials, how to quantify the statistical uncertainties underlying rock strength parameters is rarely reported. Based on a site investigation report in Bukit Timah Granite (BTG) formation in Singapore, this paper presents a set of database about UCS from four sites in BTG formation. Subsequently, Markov Chain Monte Carlo (MCMC) algorithm was applied to quantitatively evaluate the uncertainties of statistical parameters including the mean value, variance, and autocorrelation distance of UCS of BTG rocks making use of the available test data under the Bayesian framework. It was proven that the Bayesian-based MCMC method can effectively quantify the uncertainty of geo-mechanical parameters via a series of equivalent samples. The results indicate that the uncertainties of statistical parameters of UCS of BTG rocks are significant, and the magnitude to some extent relies on the selection of basic parameter in Bayesian framework. In terms of the basic parameters, the sensitive degree of uncertainties of three statistical parameters is different from each other.