Probabilistic characterization of correlation between two rock properties: a data-driven approach

Abstract

Rock parameters are required during the design and stability analysis of mining and geotechnical structures. There is a correlation between some rock properties, especially those obtained from the same experimental set-up, and the proper estimation of such correlation is important for reliable mining engineering analysis. However, a limited quantity of rock property data often available for most mining project sites makes it difficult to estimate a reliable correlation between two rock properties. To overcome this challenge, a data-driven approach that is based on Bayesian framework is presented in this study. The approach utilizes limited data pairs of rock parameters from a site and characterizes the site-specific joint probability distribution of two correlated rock properties, without the use of an empirical model. Real data of rock properties obtained from uniaxial compression tests on migmatites at the Sanandaj-Sirjan zone in Iran is used to illustrate the approach. The results from the approach show that the marginal statistics, marginal and joint probability distributions, and correlation coefficient from the proposed approach are consistent with those of the measured data from the adopted site. This indicates that the approach is effective for characterizing the correlation between correlated rock properties and can be used when there is a need for such characterization at a site with limited data.