Prediction of Young's Modulus of Intact Rock Using Bayesian Approach

Abstract

Many models have been proposed to estimate the Young’s modulus, E, of intact rock based on its uniaxial compressive strength, UCS. Deere’s model, i.e., E = MR · UCS (where MR is the modulus ratio), is the most accepted one. However, traditional models cannot provide uncertainty estimates of parameters and predictions. We present a novel approach, based on Bayesian theory, to estimate E of intact rock based on UCS. We develop three ‘rock specific’ models, i.e., for basalt, limestone, and chalk, that account for the different sources of uncertainty and we also provide parameters to analytically approximate the posterior joint distribution of model parameters for the three rock types. An example illustrates that such ‘rock specific’ models can be updated to incorporate new project-specific information, showing that the model uncertainty is reduced and that the predictive capability is improved through the updating process.