A new integral equation method for calculating interacting stress-intensity factors of multiple holed-cracked anisotropic rock under both far-field and arbitrary surface stresses

Abstract

Calculation of interacting stress-intensity factors (SIFs) of multiple holed-cracked anisotropic problem is of very importance not only for improving hydraulic fracturing technology in shale-gas exploitation, but also for optimizing crack-arrest holes in rock engineering. Current literatures are mainly focused on interacting SIFs of multiple holed-cracked anisotropic body under far-field stresses regardless of surface stresses on holes and cracks. In this paper, a new integral equation method, based on our derived exact fundamental stress solutions (with simple formulae and high-efficiency calculation process), is proposed to calculate interacting SIFs for multiple holed-cracked anisotropic rock under both far-field and arbitrary surface stresses, where the circular-holes and cracks are of any number, sizes, orientations, relative locations. The new method is proved to be valid by comparing our results of interacting SIFs with those obtained by Green function's method, hyper-singular integral equation method and finite element method. Several computational examples are given to investigate effect of loadings, holed-cracked geometries and orthotropic material properties of shale on interacting SIFs. Research results show that the far-field stress ratio (σx∞/σy∞) greatly affects the neutral crack orientation angle α0of KIA, KIIA and KIB (with null-effect of the circular-hole on the crack) but scarcely affects α0of KIIB (where A, B are inner, outer crack-tips). The surface compressive stresses acting alone on the hole (n) and alone on the crack (p) have little effect on α0. The circular-hole radius (r) is almost irrelative to α0, but relative to the amplifying or shielding degree of interacting SIFs. Young's modulus ratio (E2/E1) and bedding plane orientation angle (φ) of shale decide α0 of KIB but are nearly independent of α0 of KIA and KIIA. In addition, decreasing σx∞/σy∞ or increasing n, p can facilitate crack propagation, and decreasing E2/E1 and φ are helpful for crack arrest. The new method not only avoids the trouble in solving the singular integral equation (without any singularity), but also has high accuracy (exact fundamental stress solutions) and wider application (under both far-field uniform stresses and arbitrarily distributed surface stresses) than the common methods. It is proved to be effective for predicting the multi-crack initiation of rock under hydro-mechanical coupling stress in underground rock engineering for safety assessment and cracking-arrest design, and for optimizing the orientation angle of hydraulic-crack to form better fracturing network in shale-gas exploitation for improvement of shale-gas exploitation efficiency.