A statistical damage-based constitutive model for shearing of rock joints in brittle drop mode

Some rock joints exhibit significant brittleness, characterized by a sharp decrease in shear stress upon reaching the peak strength. However, existing models often fail to accurately represent this behavior and are encumbered by numerous parameters lacking clear mechanical significance. This study presents a new statistical damage constitutive model rooted in both damage mechanics and statistics, containing only three model parameters. The proposed model encompasses all stages of joint shearing, including the compaction stage, linear stage, plastic yielding stage, drop stage, strain softening stage, and residual strength stage. To derive the analytical expression of the constitutive model, three boundary conditions are introduced. Experimental data from both natural and artificial rock joints is utilized to validate the model, resulting in average absolute relative errors ranging from 3% to 8%. Moreover, a comparative analysis with established models illustrates that the proposed model captures stress drop and post-peak strain softening more effectively, with model parameters possessing clearer mechanical interpretations. Furthermore, parameter analysis is conducted to investigate the impacts of model parameters on the curves and unveil the relationship between these parameters and the mechanical properties of rock joints. Importantly, the proposed model is straightforward in form, and all model parameters can be obtained from direct shear tests, thus facilitating the utilization in numerical simulations.