A novel constitutive model with plastic internal and damage variables for brittle rocks

The damage evolution and plastic flow are usually coupled for rocks due to heterogeneity, which is significant for the design and construction of underground structures. In this paper, a novel damage model considering the plastic strain is proposed for rocks. The novelty of the model lies in the damage evolution associated with the plastic flow, which incorporates double variables (damage and plastic internal variables). The damage model consists of three parts, i.e., the stressstrain, cohesive force and dilation angle functions. In these functions, the plastic strain and plastic internal variable follow the Weibull distribution. In the cohesive force and dilation functions, the damage variable can be modified by the plastic internal variable, since the plastic strain is defined as the plastic internal variable. This is a key point in this paper. To validate this model, tri-axial experimental data of different types of rocks under different confining pressures are reported. It was found that the results obtained by the proposed model yield good agreements with the experimental data in most cases, except for a situation of a long stress platform in the strainsoftening stage. Characteristics of deformation, strain-hardening/softening, and dilation are controlled by model parameters, which can be determined using the experimental data of yield strength, peak strength and residual strength points. As these parameters are not difficult to obtain, the proposed model can be widely used in underground engineering.