A Plastic Strain-Induced Damage Model of Porous Rock Suitable for Different Stress Paths

It is extremely difficult to accurately predict the rock damage evolution during the underground space development or the deep excavation activity. In this paper, based on the statistical damage mechanics, a plastic strain-induced damage model of porous rock was established to describe the damage evolution and the constitutive behavior of porous rock under different stress paths. In the proposed model, the modified porosity was introduced which considered the effect of the generalized plastic shear strain. Besides, the proposed damage evolution function was also controlled by the generalized plastic shear strain. To validate the proposed damage model, the sandstone is selected as the experimental specimen due to it is a typical porous rock, and a series of conventional tri-axial compressive experiments (CTC) and confining pressure unloading experiments under constant deviatoric stress (UCP-CDS) were carried out. Furthermore, the confining pressure unloading experimental data under increscent deviatoric stress (UCP-IDS) was referenced to further validate the applicability of the proposed model. The results showed that the deviatoric strain-damage curves were an “S” shape, moreover, the relationship between the damage variable with the unloading ratio was exponential function. The proposed damage model could better reflect the void volume change and the radial dilation during the unloading process. Moreover, the model could successfully capture the damage evolution law and the mechanical behavior of sandstone by matching a set of tri-axial compressive experiments under different stress paths. Finally, it is found that the strength, strain-hardening and strain-softening characteristics were controlled by the Weibull distributed parameters m₀ and F₀.