Numerical Study of Slip Distribution at Pre-existing Crack in Rock Mass using Extended Finite Element Method (XFEM)

Materials’ fracture mechanics are crucial because they can predict how a material will break before it really happens. An extended finite element 2D numerical model implemented in the finite element ABAQUS software was used to investigate the initiation and propagation of pre-existing frictional cracks in rock material. The material used in this study was Coconino sandstone. First, a single pre-existing crack in a rock medium was modeled using a displacement method to determine the Stress Intensity Factor (SIF) at the tips of the crack. To validate the modeling methodology, the SIF derived using this approach was compared to a closed-form solution. Then, the size effect of a single flaw was studied. Results of the verification show that the relative error between the numerical and theoretical solutions decreases and eventually approaches a constant value as the plate size ratio to the flaw length increases. Hence, the effects of the boundary condition on SIF are negligible, and the medium can be assumed as infinite. Then, two pre-existing frictional cracks were modeled. The slip distribution along flaw length was obtained for these pre-existing cracks. The results show that slip distribution is zero at the flaw tips and maximum at the middle part of the flaw length. Additionally, increasing the pre-existing crack's friction coefficient causes an increase in the flaw's surface strength and a decrease in the slip distribution along the flaw's length. Finally, it was examined how the size of the rock mass model affected the uniaxial compressive load and SIF. The findings reveal that increasing the flaw length to model dimension leads to a decrease in uniaxial compressive strength on the rock mass model, but there is no significant change in SIF until the ratio is greater than 0.33, however after the ratio of 0.33 significant variation occurs.