Behnia, Mahmoud, et al. "Numerical simulation of interaction between hydraulic and natural fractures in discontinuous media." Acta Geotechnica 10.4 (2015): 533-546.

In this study, the displacement discontinuity formulation is used to solve the problem of interaction between hydraulic fractures (HF) and natural fractures (NF). Furthermore, a numerical program (2DFPM) is developed to study the mechanical activation of a NF because of the propagation of the HF. The accuracy of the numerical method is enhanced using the higher-order displacement variation along the HF and the special crack tip element near its ends. The maximum tangential stress criterion is implemented to predict the HF propagation path, and the stages of hydraulic fracturing tip approaching, coalescence and fluid penetration along the NF are modeled. The tangential stress around the NF with different contact modes (bonded, sliding and opening) is calculated by coupling the finite difference and boundary element methods. The location of secondary tensile fracture that re-initiates along the opposite …