End friction and its effect on crack propagation in fractured rock specimens

Crack propagation of the rock specimen containing a central closed flaw at different end friction coefficients (µ) under uniaxial compression and biaxial unloading confining pressure has been modeled under different loading conditions in this study employing a strength-based localized maximum stress (SLMS) criterion. The contact problem at the ends of specimens is solved via an augmented Lagrangian method. The effects of µ on tensile and shear crack propagation paths and lateral deformation of specimen ends are evaluated. Based on the variation of contact state at specimen ends under different loading and end conditions, the evolution of kinetic and static friction distribution at the specimen ends during crack propagation and the influence of µ on the kinetic and static friction distribution is investigated. The results show that the contact state at the specimen ends varies with different µ and can be classified into three types: complete sliding (µ = 0), sliding-sticking mixed (0 < µ < 0.3), and complete sticking (µ ≥ 0.3). The contact state of the end surfaces varies dynamically as the crack propagates when 0 < µ < 0.3. The friction on the end surfaces is kinetic-static mixed when 0 < µ < 0.3, while it is complete static friction when µ ≥ 0.3. For 0 < µ < 0.3, the static friction section in the end surfaces gradually increases with the crack propagation, which is more significant under biaxial unloading confining pressure due to the propagation of shear cracks.