Improved damage constitutive modeling of post-peak random failure behavior in quasi-brittle rocks

Abstract This paper captures the frequently encountered post-peak random failure behaviour of quasi-brittle rocks in conventional triaxial compression. The post-peak theoretical curve of the classic statistical damage constitutive model is essentially regulated by the Weibull distribution parameters m and F0. There exists a one-to-one mapping relationship between the array sets of parameters m and F0 and the confining pressure. However, the peak point method is unable to effectively constrain the post-peak theoretical curve of the model, resulting in the situation that under specific confining pressure, the post-peak theoretical curve of the classic model is unique and stochastic. In order to address this issue, this paper considers the influence of the degradation effect of damaged micro-elements on heterogeneity and proposes a modified damage model based on the classic damage model. A functional hypothesis expression integrating the effects of heterogeneity and stress level is constructed, and an improved statistical damage constitutive model considering the influence of damage threshold is derived. Through case verification and sensitivity analysis of model parameters, the results indicate that compared with the classic model, the model proposed in this paper, with only one additional parameter, can effectively simulate the post-peak random failure behaviour of heterogeneous quasi-brittle rocks under specific confining pressure. A comparison between predictions and published experimental data is claimed to be satisfactory, and it is revealed that the stress drop in the post-peak region of rocks is not completely random but exhibits stochastic characteristics within a certain range.