Statistical damage model of rocks reflecting strain softening considering the influences of both damage threshold and residual strength

The damage threshold of rocks is used as a criterion to determine whether the rock is damaged or not. The damage threshold is related to the deformation characteristics in the pre-peak elastic stage at a low-stress level. In addition, after the damage, the rock still has residual strength, which is the main factor affecting the stress-strain curve in the post-peak stage. Therefore, in the development of a statistical damage model for investigating the whole process of deformation and damage of the rock, the damage threshold, and the residual strength of the rock should be considered. Based on the existing studies on the statistical damage model of rocks, we have modified the Drucker-Prager criterion for the measurement of the micro-unit strength of rocks and considered the influence of the damage threshold in the analysis. At the same time, the damage variables were redefined and the post-peak residual strength was considered. Over the basis, a statistical model on the rock damage and the strain softening was established, in which the influences of both the damage threshold and the residual strength were comprehensively considered. The parameters in the model were determined according to the geometric characteristics of the measured stress-strain curve of the rock. The results from the theoretical model agreed well with that from the experimental measurement and can comprehensively illustrate the whole stress-strain process of rocks.