An X-FEM investigation of hydro-fracture evolution in naturally-layered domains

•X-FEM implementation of hydro-fracture growth in naturally layered domains.•Eigen-value based enrichment functions for bimaterial crack-tip singularities.•Penetration/deflection criterion for fracture evolution in layered formations.•Mode-mixity dependent interface toughness.•Hydraulic fracturing in stiff to soft/soft to stiff material configurations. In this paper, a computational model is developed for the simulation of hydro-fracture growth in naturally layered impervious media using the extended finite element method (X-FEM). The equilibrium equation of the bulk is solved in conjunction with the hydro-fracture inflow and continuity equations using the staggered Newton method. The hydro-fracture inflow is governed by the lubrication theory, where the permeability of the fracture is incorporated by taking advantage of the cubic law. The Eigen-function expansion method is utilised in order to develop enrichment functions suited for the asymptotic stress field in the vicinity of the singular points. An energy release rate-based criterion is used in order to study the competition between hydro-fracture penetration/deflection at the material interface. Finally, the robustness of the computational framework is explored by means of numerical simulation.