A statistical damage model for quasi-brittle rocks based on a modified Hoek-Brown criterion incorporating with the lognormal distribution

The failure behavior of rocks is complex due to the existence of random microscopic defects. This paper presents a new statistical damage model based on the modified Hoek-Brown criterion, i.e., the Pan-Hudson criterion, for predicting the mechanical characteristics of quasi-brittle rocks under compression, and demonstrated its predictive performance for medium-strong rocks. The lognormal distribution is incorporated to validate and reveal the statistical nature of internal microscopic defects. Its effectiveness in describing microscopic defects evolution is highlighted by comprehensive discussions on characteristic distribution parameters, which are rigorously derived. The degradation effects of microscopic defects on macroscopic mechanical responses are reflected by establishing the quantitative relation between damage variables and compressive strength. To validate the proposed model, a series of triaxial compression tests on sandstone are conducted. The peak strength and quasi-brittle post-peak behavior under various confining pressures are well captured. Sensitivity analyses on mechanical and characteristic distribution parameters are also carried out to develop an intuitive understanding of how the introduced modifications affect the mechanical responses. Finally, the deviatoric stress-axial strain curves were compared between our testing data of limestone and previous study. The advantages in capturing peak intensity and simulating the post-peak behavior of the proposed model is emphasized.