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

Abstract

Summary 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.

HOSS: an implementation of the combined finite-discrete element method

“…3 Comparison of 2nd Generation algorithms and the Next Generation as seen in HOSS. Figure modified from Lei et al [31] essence, an extrinsic CZM can be retrieved from UCZM if α = 1.0; while an intrinsic CZM is obtained when α = 0.0. For an α between 0.0 and 1.0, a combined intrinsic-extrinsic UCZM is formulated.…”

“…This eliminates the need of continuously mapping variables between the fluid and solid domains. Most importantly, the HOSS-ISF features an explicit time integration solver with an apertureindependent critical time step size [31]. Previous solutions have applied a similar approach but with the great shortcoming of having time step sizes that are aperture-dependent, thereby highly restricting the simulation's efficiency as aperture dimensions increase.…”

“…4). The pressure nodes are used to calculate the fluid pressure according to an appropriate material law while the velocity node resolves the dynamic equilibrium of the flow system [31].…”

“…Initially the platform was called MUNROU (MUNjiza-ROUgier) and development efforts led to sophisticated material and fracture libraries as well as an efficient parallelization scheme. Over a decade later, a custom-developed 2D fluid solver was implemented for hydro-fracture analysis, where the fluid interacts within a contained solid domain and, instead of coupling, the solver was naturally integrated, i.e., the fluid and the solid domains were simulated using the same spatial discretization or mesh [31][32][33]. At this point the platform was renamed as the Hybrid Optimization Software Suite, a.k.a.…”

Study of the Rock Crack Propagation Induced by Blasting with a Decoupled Charge under High In Situ Stress

“…In their study, three different methods, i.e., the extended finite element method, the conventional finite element method, and the element deletion method, were compared in their paper to simulate rock fragmentation. Besides the finite element method, the discrete element method (DEM) and combined finite-discrete element method (FEM-DEM) are also popular for simulating rock fracturing under blasting [24][25][26][27][28][29][30][31][32]. Preece and Chung [33] developed an algorithm to analyze some unnatural behaviour of discrete elements during the formation of muck pile subsequent to explosive loading.…”