Quasi-Static Crack Growth Under Symmetrical Loads in Hydraulic Fracturing

Symmetrical load on the crack surfaces is found in many fluid-solid problems. The combined effect of symmetrical normal and shear stresses is investigated, which impacts on the displacement and stress fields and the predictions of crack initiation and deflection. The boundary integral equations of displacement and stress fields are formulated using the integral-transform method. The equations of the displacement and stress are reduced using the Abel integral equations. The analytical solution of the full space for uniform normal and shear stresses is obtained. The asymptotic solution of the displacement of the crack surface is obtained near the crack tip under specific normal and shear stresses. Results show that shear stress tends to inhibit the crack, and the predictions of crack initiation and deflection could be inappropriate for a slit crack under a singular shear stress. This study may be useful for future investigations of the fluid-solid problems and help to understand the hydraulic fracturing.