Wing-crack initiation angle: A new maximum tangential stress criterion by considering T-stress

Abstract

Fracture mechanism of a rock under compression is a key issue for the practicing rock engineering. Because of ignoring the effect of the non-singular term (T-stress) of the elastic stress state near a crack tip in Williams’ series expression, the theoretical predictions obtained from the classic Maximum Tangential Stress (MTS) criterion in the classic fracture mechanics is not consistent with the experimental results. On basis of analyzing the crack mechanical behavior under compression, T-stress is introduced into the classic MTS criterion, and accordingly the new MTS criterion is proposed by considering T-stress. Meanwhile, by considering the effect of the crack on the stress transfer under compression, the crack deformation parameters (e.g., the crack normal and shear stiffness) are introduced into the new MTS criterion. Accordingly, the new MTS criterion can characterize the initiation mechanism of the crack under the compression, which considers the co-effect of the rock property, crack geometry parameters (e.g., the crack dip angle and length), strength parameters (e.g., the crack friction coefficient) and deformation parameters (e.g., the crack normal and shear stiffness) on the wing-crack initiation angle at the same time. The calculation example indicates that the wing-crack initiation angle obtained with the proposed method agrees well with that of the experiment. I also find that α (=2rc/a, rc is the critical radius from the crack tip, and a is the crack half-length) affects significantly the wing-crack initiation angle with the parametric sensitivity analysis.