Fracture mechanism simulation of inhomogeneous anisotropic rocks by extended finite element method

The vast majority of rock masses is anisotropic due to factors such as layering, unequal in-situ stresses, joint sets, and discontinuities. Meanwhile, given the frequently asymmetric distribution of pores, grain sizes or different mineralogical compounds in different locations, they are often classified as inhomogeneous materials. In such materials, stress intensity factors (SIFs) at the crack tip, which control the initiation of failure, strongly depend on mechanical properties of the material near that area. On the other hand, crack propagation trajectories highly depend on the orthotropic properties of the rock mass. In this study, the SIFs are calculated by means of anisotropic crack tip enrichments and an interaction integral are developed for inhomogeneous materials with the help of the extended finite element method (XFEM). We also use the T-stress within the crack tip fields to develop a new criterion to estimate the crack initiation angles and propagation in rock masses. To verify and validate the proposed approach, the results are compared with experimental test results and those reported in the literature. It is found that the ratio of elastic moduli, shear stiffnesses, and material orientation angles have a significant impact on the SIFs. However, the rate of change in material properties is found to have a moderate effect on these factors and a more pronounced effect on the failure force. The results highlight the potential of the proposed formulation in the estimation of SIFs and crack propagation paths in inhomogeneous anisotropic materials.