A variational approach to analyze a natural fault with hydraulic fracture based on the strain energy density criterion

A simplified analytical model of the interaction between a hydraulic fracture and an existing natural fault is developed. The mechanical activation of the natural fault as a result of contact with a pressurized fracture is described for plane strain conditions and quasi-static fracture propagation approximation. Using a variational approach, the normal and shear stresses, as well as the boundaries of the open and sliding zones along the fault, are predicted for three stages of the fracturing process (fracture approaching, coalescence, and fluid penetration). An accumulated concentration of shear stress at the tip of the fault’s sliding zone is shown to create sufficient tensile stress to initiate a new tensile crack on the opposite side of the fault, provided either the differential in situ stress is low or the friction coefficient is sufficiently large. The results of direct numerical simulation of the fracture interaction fit the model predictions made from the strain energy density fracture criterion.