A Study on the Mechanical Behavior and Statistical Damage Constitutive Model of Sandstone

Triaxial compression test results of sandstone indicate that the peak point strain, elastic modulus, peak deviatoric stress and residual deviatoric stress of the tested sandstone increase with increasing confining pressure, and the variations in them with the confining pressure can be described with a linear function, a logistic function, the generalized Hoek–Brown criterion and the linear Mohr–Coulomb criterion, respectively. Supposing that the rock material can be divided into an elastic part and a damaged part in the rock failure process, the deviatoric stress–strain relationship of the elastic part satisfies Hooke’s law, while the damaged part provides residual deviatoric stress. On this basis, it was assumed the rock meso-element strength follows a composite power function distribution. Then, the damage evolution equation was deduced using a statistical method, and a new damage model, which can reflect the rock residual deviatoric stress, was proposed. The reasonability of the new model was verified using the test results of the sandstone. A comparison of the predicted and test results shows that this damage model can well simulate the deviatoric stress–strain response in the failure process of the tested sandstone. In particular, it can reflect the residual deviatoric stress after rock failure.