By considering the effect of hydraulic pressure filled in wing crack and the connected part of main crack on the stress intensity factor at wing crack tip, a new wing crack model exerted by hydraulic pressure and far field stresses was proposed. By introducing the equivalent crack length lcq of wing crack, two terms make up the stress intensity factor K1 at wing crack tip： one is the component K（1） for a single isolated straight wing crack of length 2l subjected to hydraulic pressure in wing crack and far field stresses, and the other is the component K1^（2） due to the effective shear stress induced by the presence of the equivalent main crack. The FEM model of wing crack propagation subjected to hydraulic pressure and far field stresses was also established according to different side pressure coefficients and hydraulic pressures in crack. The result shows that a good agreement is found between theoretical model of wing crack proposed and finite element method （FEM）. In theory, an unstable crack propagation is shown if there is high hydraulic pressure and lateral tension. The wing crack model proposed can provide references for studying on hydraulic fracturing in rock masses.
A new wing crack model subjected to hydraulic pressure and far-field stresses was proposed considering the effect of hydraulic pressure in wing crack and the connected part of the main crack on the stress intensity factor at the wing crack tip. With the equivalent crack length Ieq of the wing crack introduced, the stress intensity factor Kl at the wing crack tip was as- sumed to the sum of two terms： on one hand a component K1^（1） for a single isolated straight wing crack of length 21, and subjected to hydraulic pressure in the wing crack and far-field stresses; on the other hand a component K1（2） due to the effective shear stress induced by the presence of the equivalent main crack. The lateral tensile stress and hydraulic high pressure are the key factors that induce crack propagation unsteadily. The new wing crack theoretical model proposed can supply references for the study on hydraulic fracture in fractured masses, hydraulic fracturing in rock masses.
