2D-lattice modelling of crack propagation induced by fluid injection in heterogeneous quasi-brittle materials

Abstract Characterizing the path of a hydraulic fracture in a heterogeneous medium is one of the challenges of current research on hydraulic fracturing. We present here a 2D lattice hydro-mechanical model for this purpose. Natural joints are represented introducing elements with a plastic-damage behaviour. The action of fluid pressure on skeleton is represented using Biot’s theory. The interactions of cracks on fluid flow are represented considering a Poisueille’s flow between two parallel plates. The model is simplified by neglecting the effect of deformation in the equation governing fluid flow. Numerical coupling is achieved with a staggered coupling scheme. We consider first the propagation of fracture restricted to the homogeneous case. The numerical model is compared to analytical solutions. It is found that the model is consistent with LEFM in the pure mechanical case, and with analytical solutions from the literature in the case where the leak off is dominant. In very tight formations, deviations are observed, as expected, because of the assumption in the flow model. Finally, the influence of a natural joint of finite length crossed by the fracture is shown. Two cases are considered, the case of a joint perpendicular to the crack and the case of an inclined joint. In the first case, the crack passes through the joint, which is damaged due to the intrusion of the fluid. In the second case, the crack follows the joint and propagation starts again from the tip.