Bayesian prediction of elastic modulus of intact rocks using their uniaxial compressive strength

Abstract

The uniaxial compressive strength (UCS) and the Young's modulus (E) are two important aspects of intact rock behavior. Although they can be measured in the laboratory, testing requirements increase the difficulty and cost of such tests. For that reason, faster and less costly methods have been proposed to indirectly estimate UCS, and many models have been proposed to estimate E of intact rock based on UCS. We present a novel approach, based on the Bayesian framework for model assessment, to estimate the Young's moduli of intact rocks based on their uniaxial compressive strengths. We work with Deere's proportionality rule (E=MRUCS); and we develop an extensive database, available as “Supplementary material”, of testing data compiled from the literature. Our approach provides uncertainty estimates of parameters and predictions, and can differentiate among the sources of error. We develop ‘rock-specific’ models for common rock types. In some cases, our MR results are significantly different from Deere's traditional values. We also illustrate that such ‘initial’ models can be ‘updated’ to incorporate new project-specific information as it becomes available, reducing model uncertainties and improving their predictive capabilities.