A statistical damage constitutive model for softening behavior of rocks

A basic theory of damage mechanics was introduced to deal with the deformation of strain softening for rocks. In this theory, a statistical method was used to describe rock properties on a mesoscopic scale in order to generate realistic behavior at a macroscopic scale. First, some relevant concepts of damage mechanics theory were summarized. This summary was followed by the concise presentation of a damage model established for rocks. Subsequently, the effect of the damage threshold on the evolution of rock damage was analyzed based on this damage model. An evolution equation of the damage for rocks was then formulated by incorporating statistical considerations, as it underlies a corresponding method of measuring the mesoscopic element strength in characterizing the influence of the damage threshold. A statistical damage constitutive model for rocks was further proposed whereby the phenomenon of strain softening can be reflected. A simple, yet practical procedure for identifying the model parameters was provided and an associated flow for solving this constitutive model was also presented. In order to demonstrate the effectiveness of the proposed constitutive model, comparative analyses between experimental data and theoretical results were offered using the illustrative examples, and the discussions on several issues related to the rock behavior of this model were eventually performed.