Statistical Damage Constitutive Model for Rocks Considering Residual Strength

Statistical damage constitutive models (SDCMs) have been widely employed to describe the mechanical response of strain-softening rock, especially in brittle failure under moderate confining pressure. The residual strength, referring to the strength of strain-softening rock in the postpeak region, has not been accurately considered in present works. In this study, an extended definition of damage was proposed based on the fact that the intact material gradually evolves into another damaged material, and these two parts are mixed together to carry external loads. Accordingly, a modified damage mechanical model was established. Then, the evolution equation of the damage variable was formulated based on the well-known Weibull distribution. Furthermore, a modified SDCM reflecting strain-softening and residual strength behavior for rocks loaded in conventional triaxial compression (CTC) was developed. The model parameters were estimated based on the extremum method. Finally, validation indicated that the calculated results from the modified SDCM had good agreement with the experimental observation and were much better than the calculated results from other models. Issues related to the lateral deformation of this model were also examined.