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

• Bayesian approach is developed to characterize site-specific correlation between UCS and E.
• The approach combines regression model with the prior knowledge and limited site-specific data pair of UCS and E.
• Implementation procedures are illustrated through real examples.

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.