Uncertainty quantification based on symbolic regression and probabilistic programming and its application

The joint roughness coefficient (JRC) is critical to evaluate the strength and deformation behavior of joint rock mass in rock engineering. Various methods have been developed to estimate JRC value based on the statistical parameter of rock joints. The JRC value is uncertain due to the complex, random rock joint. Uncertainty is an essential characteristic of rock joints. However, the traditional determinative method cannot deal with uncertainty during the analysis, evaluation, and characterization of the mechanism for the rock joint. This study developed a novel JRC determination framework to estimate the JRC value and evaluate the uncertainty of rock joints based on symbolic regression and probabilistic programming. The symbolic regression was utilized to generate the general empirical equation with the unknown coefficient for the JRC determination of rock joints. The probabilistic programming was used to quantify the uncertainty of the rock joint roughness. The ten standard rock joint profiles illustrated and investigated the developed framework. And then, the developed framework was applied to the collected rock joint profile from the literature. The predicted JRC value was compared with the traditional empirical equations. The results show that the generalization performance of the developed framework is better than the traditional determinative empirical equation. It provides a scientific, reliable, and helpful to estimate the JRC value and characterize the mechanical behavior of joint rock mass.