Numerical analysis of multiple hydro-fracture growth in layered media based on a non-differentiable energy minimization approach

•A non-differentiable energy-based formulation is extended for multiple hydraulic fracturing in layered media.•The graph theory is applied to identify the interconnected network of pressurized cracks in heavily fractured rock mass.•Several numerical simulation results are presented for multiple hydro-fracture growth in layered media for a range of contrasts in material stiffness. In this study, the evolution of hydraulically driven fractures in naturally layered and fractured media is investigated. The non-differentiable energy minimization approach to cohesive fracture is employed with a Discontinuous Galerkin (DG) discretization in which every element edge in the mesh is a potential site of cracks. The coupled hydro-mechanical model accounts for the flow continuity equation governing the hydro-fractures inflow in which the opening-dependent permeability of the hydro-fractures is modelled based upon the well-known cubic law. The proposed framework provides great flexibility in modeling multiple fractures and is applied to study the interaction between hydro-fractures and material interfaces in naturally fractured layered domains. Results indicate robustness and versatility of the algorithm and exemplify several simulation aspects there were eluded in many of the works in previous literature.