Data-driven characterization of the correlation between uniaxial compressive strength and Youngs’ modulus of rock without regression models

Abstract The uniaxial compressive strength (UCS) and Youngs’ modulus (E) of rock are important parameters required during design and stability analysis of mining and geotechnical structures. There is correlation between UCS and E of rock, and the proper estimation of such correlation is important for reliable mining engineering analysis. However, limited quantity of UCS and E data pairs often available for most mining project sites makes it difficult to estimate reliable correlation between UCS and E. This study addresses the difficulty by developing Bayesian approach for characterizing the site-specific joint probability distribution of UCS and E that is data-driven, without the use of an empirical model. A major novelty of the proposed approach over previous studies is that it does not require selection or integration of a regression model as input to characterize the correlation between UCS and E. The likelihood function in the proposed approach is directly constructed from only limited UCS and E data pairs and their prior information as inputs. The Bayesian approach is incorporated into Markov Chain Monte Carlo (MCMC) simulation to generate samples pairs of UCS and E, which are then analysed for marginal statistics, marginal probability distribution, joint probability distribution and correlation. Real data of UCS and E obtained from uniaxial compression tests on migmatites at the Sanandaj-Sirjan zone in Iran is used to demonstrate the approach. The marginal statistics, distributions and correlation coefficient from the proposed approach is consistent with those of the measured data from the adopted site. This indicates that the approach is effective in characterizing the correlation between UCS and E, and can be used when there is need for such characterization at a site with limited data. Simulated data are also used in the approach and the results show that the quality and quantity of information available as inputs play an important role in the efficiency of the characterization by the approach. The hallmark of the proposed approach is that it is data-driven, and practitioners do not need to determine and select an appropriate site-specific regression model to evaluate the correlation between UCS and E of rock