Statistical meso-damage model for quasi-brittle rocks to account for damage tolerance principle

Damage evolution in quasi-brittle rocks is a complicated procedure in which both the post-peak strain-softening behavior and the immobile residual strength play key roles. The post-peak behavior observed from existing experiments is critical for the determination of the complete constitutive relation of quasi-brittle rocks. Based on the test observation on the post-peak immobile residual strength of quasi-brittle rock specimens, a proper damage tolerance is defined in this study. Following this theme, a damage tolerance principle is presented by adopting an alternative methodology, which incorporates a loading function to represent the reaction to the stress state and a condition of damage tolerance based on the Mohr–Coulomb criterion without cohesive strength. Then, an iterative solution is proposed to identify the parameters of the proposed model. The identified constitutive law is employed to determine the load–deformation behavior of quasi-brittle rocks including sandstone and quartzite, and the calculated results are compared with the test results under different confinement stress levels. Results show that the developed constitutive law for quasi-brittle rocks with damage tolerance principle can be used to predict the post-peak behavior including the strain-softening behavior and the immobile residual strength with acceptable accuracy. Finally, a parametric study is conducted to essentially investigate the effect of parameters of the proposed model on the observed characteristics of quasi-brittle rocks.