Application of extended finite element method to study crack propagation problems of orthotropic rock mass

Sedimentary rocks such as shale and sandstone are very common in the fields of oil and unconventional gas drilling; and they are often characterized by orthotropy. The extended finite element method is used for crack propagation analysis of orthotropic rock mass and a Matlab program Betaxfem2D has been developed. Asymptotic crack tip displacement fields deduced by function of complex variable method are adopted as the crack tip displacement enrichment function; and mixed mode stress intensity factors are calculated by the interaction integral (M-integral) method. Besides, a modified maximum circumferential tensile stress criterion is adopted to determine crack propagation direction. Compared with conventional finite element method (FEM), the results show that the extended finite element method needs less DOFs and less computer resources to achieve the same calculation accuracy. The extended finite element method program developed by this paper and the conventional FEM program are used to simulate the 4-point bending test of rock sample, and both of them show the same results. Numerical experiments show that crack propagation direction angle γ varies according to an approximate sine function with a period of π with the increase of α, i.e. the angle between the orthotropic material coordinate and the space coordinate. Besides, when shear modulus and Poisson ratio remain constant; the range of the sine function shrinks with the decrease of the ratio of the elasticity moduli E1 /E2, but the phase basically remains unchanged. So, the orthotropy of rock cannot be neglected when dealing with the fracture mechanics problems of sedimentary rock.