Simulation of discrete cracks driven by nearly incompressible fluid via 2D combined finite‐discrete element method

A. Munjiza, E. E. Knight, E. Rougier, H. Viswanathan, Z. Lei
International Journal for Numerical and Analytical Methods in Geomechanics
combined finite‐discrete element method, critical time step, explicit time integration, Hydraulic fracture, nearly incompressible fluid

In this work, we propose a novel hydraulic solver in order to simulate key mechanisms that control fluid‐driven cracks in the framework of the combined finite‐discrete element method (FDEM). The main innovative aspect of the present work is the independence of the fluid’s critical time step size with the fracture opening. This advantage is extremely important because it means that very fine meshes can be used around areas of interest, such as boreholes, without penalizing the computational cost as fractures propagate (ie, open) and the fluid flows through them. This is a great advantage over other recently introduced approaches that exhibit a dependency of the time step in the form of Δtcrit ∝ (l/a)2 where l is the element size and a is the fracture aperture. This paper presents a series of benchmark cases for the proposed solver. The rationale adopted by the authors was to benchmark and validate the implementation of the hydraulic solver in an incremental fashion, starting from the simplest cases and building in complexity. The results shown in this work clearly demonstrate that the proposed approach is able to reproduce analytical results for fluid flow through a single crack. The results presented in this paper also demonstrate that the new approach is robust enough to deal with complex fracture patterns and complex geometries; the obtained fluid‐driven fracture patterns in the vicinity of a borehole certainly stand to the scrutiny of human visual perception.

Keywords: combined finite‐discrete element method, critical time step, explicit time integration, hydraulic fracture, nearly incompressible fluid,

Access Full Text