A statistical damage constitutive rock model based on elastic energy release rate

In order to truly reveal the mechanism of rock deformation and failure and the nature of rock material damage, based on the analysis of rock material deformation law and mechanical characteristics, a rock damage constitutive model based on elastic energy release rate is established using the energy principle. Taking the damage variable as an internal variable that affected the change of rock performance, a new type of statistical damage constitutive model for rock is established based on the effective stress principle and statistical damage theory. It further improves the theoretical system of rock damage constitutive model and mades up for the shortcomings that traditional damage models cannot reasonably explain the causes of rock failure. The parameters of the damage model are determined using the rock test data, and the feasibility and applicability of the damage model are verified through a comparative analysis of the model curve and the test curve. The damage evolution model is substituted into the elastic energy-strain model to analyze the law of rock elastic energy change during loading. The results show that the model curve and the test curve almost coincide in the deformation phase before the peak, indicating that the damage model perfectly reflects the linear elastic deformation characteristics of the rock. The model curve and the test curve do not agree well at the post-peak stage, but they also have a good description of the nonlinear deformation law of the rock. The damage model also better reflectes the relationship between the accumulation and release of elastic energy and the damage and destruction of rocks, and the characteristics of the degree of rock damage increases with the increasing confining pressure. At the same time, in the initial loading stage, the damage variable of the rock increases with the increasing axial strain. This shows that under the load, the internal cracks in the rock gradually develop, so that the damage of the rock material is gradually accumulated. When the confining pressure reaches above 10 MPa, the damage-strain curves basically coincide. The growth rate of the damage-strain curve rises sharply at the moment of initial loading. When the strain of the rock is about 0.01%, the damage-strain curve changes from rapid growth to steady growth. Because the damage quickly accumulates near the peak stress point of the rock, the damage variable rapidly increases to 1 in value.