Stress intensity factor calculation of the cracks interacted by the oval-holes in anisotropic elastic solids under remote and non-uniform surface stresses

Abstract

In underground rock engineering, natural defects (such as cracks, joints, cavities of arbitrary shape) and anisotropy of rock mass are main factors influencing the engineering strength. Calculating stress intensity factors (SIFs) of anisotropic elastic solids with multiple oval-holes and cracks is of great significance not only for designing the stop-holes to improve the stability of mining exploitation, but also for optimizing the hydraulic fracturing parameters to improve the productivity of geothermal/shale-gas utilization. Current studies are mainly focused on the loading case of remote stresses, regardless of the surface stresses applied onto the holes and cracks. In this paper, both remote uniform stresses and non-uniform surface stresses are taken into account to calculate the multi-crack SIFs interacted by the multiple oval-holes in anisotropic elastic solids. Two elementary solutions for traction components of single oval-hole and single crack subjected to the surface point-forces in the anisotropic solids are analytically deduced based on Cauchy integral approach in complex variable theory. A new integral equation approach is established to solve the interacting SIFs of multiple oval holes and cracks in the two-dimensional anisotropic elastic solids, without any limitation of the number, sizes, orientations and locations for oval-holes and cracks. Its accuracy and feasibility are validated by comparing our SIF solutions against the available exact solutions, approximated solutions and finite element solutions. The new method has high accuracy (with almost the same SIF solutions as the exact ones), simple formulation (without any singularity) and wide applicability (under both remote uniform stresses and non-uniform surface stresses). It can be further developed for three-dimensional anisotropic hole-crack problem under the same complex stress states.