An extended J-integral for evaluating fluid-driven cracks in hydraulic fracturing

J-integral has served as a powerful tool in characterizing crack tip status. The main feature, i.e. path-independence, makes it one of the foremost fracture parameters. In order to remain the path-independence for fluid-driven cracks, J-integral is revised. In this paper, we present an extended J-integral explicitly for fluid-driven cracks, e.g. hydraulically induced fractures in petroleum reservoirs, for three-dimensional (3D) problems. Particularly, point-wise 3D extended J-integral is proposed to characterize the state of a point along crack front. Besides, applications of the extended J-integral to porous media and thermally induced stress conditions are explored. Numerical results show that the extended J-integral is indeed path-independent, and they are in good agreement with those of equivalent domain integral under linear elastic and elastoplastic conditions. In addition, two distance-independent circular integrals in the K-dominance zone are established, which can be used to calculate the stress intensity factor (SIF).