Bayesian characterization of correlation between uniaxial compressive strength and Young's modulus of rock

Abstract

The uniaxial compressive strength (UCS) and Young’s modulus (E) of rock are important mechanical parameters in rock engineering design and construction. UCS and E are also correlated and the correlation has important effect on reliability analysis in rock engineering. However, the UCS and E data obtained for a project site is generally limited, and the sparse number of UCS and E data often obtained is not sufficient to provide joint probability distribution of UCS and E and to estimate their correlation coefficient. This poses a challenge in many rock engineering reliability analyses. This paper aims to address this challenge by developing Bayesian approach for obtaining site-specific joint probability distribution of the uniaxial compressive strength (UCS) and the Young's modulus (E), and for quantifying the site-specific correlation between UCS and E for a project site. The Bayesian approach characterizes the joint probability distribution of UCS and E, using the available limited amount of site-specific UCS and E data and a regression model. The proposed approach integrates the limited site-specific UCS and E data with regression model and prior knowledge, and it transforms the integrated knowledge into a large number of UCS and E sample pairs using Markov Chain Monte Carlo (MCMC) simulation. Then, the correlation coefficient of the UCS and E sample pairs is obtained, together with marginal distributions of UCS and E, and their mean and standard deviation. The proposed approach effectively tackles the difficulty of estimating site-specific correlation coefficient and joint probability distribution from usually sparse test data of UCS and E obtained during investigation of a project site.