An analytical model for predicting the shear fracture behavior of discontinuities with multi-scale asperities incorporating the damage element method

Abstract

Asperities within discontinuities play a critical role in contributing to shear resistance. However, their influence on the shear fracture behavior of discontinuities is constrained by size effects. Revealing and predicting the fracture process of discontinuities with multi-scale asperities is crucial for guiding engineering stability assessment. In this study, PFC^2D was employed to simulate the microscopic fracture process of discontinuities with multi-scale asperities under shear loading conditions. The simulation revealed that first-order asperities predominantly experience wear failure, whereas second-order asperities primarily undergo shear failure. Based on these findings, the damage evolution equation for the microscopic elements of first-order asperities was formulated using classical wear theory, while the equation for second-order asperities employed Weibull distribution statistical theory. Consequently, an analytical model was developed that considers the influence of multi-scale asperities on the shear behavior of discontinuities incorporating the damage element method. Subsequently, this analytical model was validated against experimental data and numerical results, demonstrating its capability to accurately predict the rapid stress decrease following the peak point. Finally, the sensitivity of the model parameters was discussed.