Coupled hydro-mechanical modelling of saturated fractured porous media with unified embedded finite element discretisations

Abstract

This paper presents the first unified finite element strategy for coupled hydro-mechanical (HM) analysis of fractured porous media where cracks arbitrarily intersect standard finite elements. This strategy is built by employing a discrete strong discontinuity approach and a coupling finite elements framework for the mechanical displacement and fluid pressure fields, respectively. The unified nature of the formulation means that both fracture network and bulk do not need to conform while relying only on standard finite element shape functions. The crack framework is directly embedded in the standard finite elements in both mechanical and fluid field approximations by applying two simple coupling statements. These establish the transmission of displacements due to crack openings accounted by shear and normal stiffness, as well as the internal compatibility of the longitudinal pressure field within the crack network and bulk. Uniquely, the coupling techniques presented here do not require additional degrees of freedom. In addition, the traction at discontinuities and its interaction with the fluid pressure within the discontinuity have a direct physical meaning, and are automatically accounted for in the coupled HM model. Since only standard shape functions are used, the implementation remains simple despite the complexity of the problem being simulated, and no special integration procedures within split domains are required. This is a novelty that contrasts with many existing formulations based on the partition of the unity method and non-matching meshes. Five numerical verification examples are used to assess the performance of the proposed method against existing reference solutions. A good agreement is found between the proposed method and reference solutions.