Theoretical and numerical models of rock wing crack subjected to hydraulic pressure and far-field stresses

The evolution laws of stress intensity factor (SIF) at the crack tip subjected to hydraulic pressure have still not elucidated clearly. This article attempts to study the evolution laws of SIF at the wing crack tip subjected to hydraulic pressure and far-field stresses, theoretically and numerically, based on the previous proposed wing crack models without considering hydraulic pressure. The numerical model of wing crack subjected to hydraulic pressure and far-field stresses is proposed by ANSYS based on finite element model (FEM). Research results show that the curves of the dimensionless SIF at the wing crack tip versus equivalent crack propagation length are in three major types: D type, DR type, and R type. The D type curve exhibits a steady propagation behavior of wing crack; however, the DR type and R type curves exhibit unsteady propagation behavior. The D type curve gradually transfers to the DR and R type curves with increasing hydraulic pressure. On the whole, the tendency of theoretical model curves is in agreement with that of numerical simulation curves. The average SSRs of HN, S, B, LK, W, and Z model solutions to SIF at the wing crack tip are 0.0079, 0.0348, 0.0099, 0.0127, 0.0077, and 0.0068, respectively. So the average SSRs of the Z and S model solutions are the lowest and highest among all theoretical model solutions. The Z model solution to SIF at the wing crack tip subjected to the combined action of hydraulic pressure and far-field stresses can be considered an optimal solution due to the lowest average SSR. The study further enhances the understanding of the mechanical behavior of hydraulic fracturing in rock mass engineering.