Abstract: The conventional triaxial tests were carried out on sandstone to study the stress-strain relationship of rock during the loading-unloading process. The nonlinear characteristics of rock in the post-peak unloading process were analyzed, and the damage variable of rock was defined. Meanwhile, the elastic modulus model was established to describe the stress-strain relationship in the post-peak unloading process. The Poisson's ratio model under unloading was obtained by analyzing the relationship between the axial strain and radial strain in the loading-unloading process. The D-P plasticity model was introduced to modify the hardening function according to the plastic-hardening characteristics of sandstone, and a damage model associated with the equivalent plastic strain was established. At last, the established model was matrixed and numerically calculated. In this study, the following conclusions are obtained. During the loading process, the porous rock exhibits obviously nonlinear characteristics, and the elastic modulus of the rock increases with the increase of the body stress. During the post-peak unloading process, when the axial stress is greater than the confining pressure, the stress-strain can be described by the elastic modulus in the pre-peak elastic phase multiplying by the continuity factor. With the increase of equivalent plastic strain, Poisson's ratio increases first and then decreases until reaching a stable value. During the unloading process, the equivalent plastic strain maintains stable, and Poisson's ratio remains constant. The numerical calculation is conducted by the proposed constitutive model. Compared the numerical results with the experimental results, the proposed model can reflect the stress-strain relationship of rock in the post-peak unloading process.

Key words: rock mechanics, nonlinearity, damage, stress-strain relationship, Poisson’s ratio, elastic modulus