Uncertainty quantification for characterization of rock elastic modulus based on P-velocity

The elastic modulus of rock is an important parameter in rock engineering, but the common methods based on laboratory tests are laborious, especially for obtaining the probability distribution of the elastic modulus that is required in reliability-based design. Many scholars have studied the regression model between the elastic modulus and P-wave velocity; however, most previous reports have ignored the characterization of parameter variability and model uncertainty. To address this problem, a large number of granite samples are collected from the Yingliangbao hydropower station (YLB), compressive wave velocity (P-wave velocity) and uniaxial compression tests are carried out in the laboratory. Then, four different regression models based on the frequentist method and Bayesian method are established to estimate the elastic modulus, the normal priors are adopted by prior analysis and the widely applicable information criterion (WAIC) is used to select the most appropriate Bayesian regression model. Finally, the effects of sample size and sample selection on different methods are studied, the results obtained from different priors are compared. The results show that the Bayesian method provides estimations that are more consistent with the test data and has better robustness in given sets of different sample selections, especially in small sample size.