Elastoplastic model of damaged rock based on the strength theory

The one-dimensional damage variable was defined based on the elasto-brittle behavior of rock under uniaxial loading. To define the damage and its evolution in three-dimensional loading, the twln-shear theory was introduced to generalize the one-dimensional damage model into the three-dimensional model. The elastic behavior of the damaged material under loading can be expressed by reducing the elastic module, and the plastic flow can be represented by the slide on the plane between the two parts of the fractured rock. To establish the elastoplastic model of the damaged material, the concept of effective stress was used to contain the effects of damage in the yielding equation as well as in the function of plastic potential. The model was established in the frame of the classical plasticity theory in which the Mohr-Coulomb criterion was employed as the yielding criterion, and the friction law on the pre-sliding plane was taken as the hardening-softening rule to describe the change of the yielding surface with the progressive yielding. The comparison of the calculated results with tested results by a CT machine shows that the damage model presented in the paper can accurately describe the damage evolution of rock in Nanqiao Sandstone, and that the damage-elasto-plastic model is indeed feasible in describing the mechanical properties of the damaged material.