Adaptive phase-field modelling of fracture propagation in poroelastic media using the scaled boundary finite element method

A scaled boundary finite element-based phase field formulation is proposed to model two-dimensional fracture in saturated poroelastic media. The mechanical response of the poroelastic media is simulated following Biot’s theory, and the fracture surface evolution is modelled according to the phase field formulation. To avoid the application of fine uniform meshes that are constrained by the element size requirement when adopting phase field models, an adaptive refinement strategy based on quadtree meshes is adopted. The unique advantage of the scaled boundary finite element method is conducive to the application of quadtree adaptivity, as it can be directly formulated on quadtree meshes without the need for any special treatment of hanging nodes. Efficient computation is achieved by exploiting the unique patterns of the quadtree cells. An appropriate scaling is applied to the relevant matrices and vectors according the physical size of the cells in the mesh during the simulations. This avoids repetitive calculations of cells with the same configurations. The proposed model is validated using a benchmark with a known analytical solution. Numerical examples of hydraulic fractures driven by the injected fluid in cracks are modelled to illustrate the capabilities of the proposed model in handling crack propagation problems involving complex geometries.