Coupled multiphysics 3-D generalized finite element method simulations of hydraulic fracture propagation experiments

Intentional creation and propagation of fractures driven by fluid under high pressure have several applications in oil and gas exploration, geological mining, disposal of toxic waste, flow of molten magma within crevices/fissures, etc. Due to the need to design hydraulic fractures, especially in the oil and gas industry, and the limitation of their full scale/field testing, the use of laboratory experiments and/or numerical simulations remain viable alternatives. While several computational methods for this class of problems exist in the literature, their reliability and robustness hinge on their ability to replicate experimental results with acceptable confidence. This paper presents the application of a coupled multiphysics 3-D generalized finite element method (GFEM) for the simulation of hydraulic fracture experiments based on a regularized Irwin criterion and adaptive mesh refinement. Built with an automatic time step search, the algorithm computes the time step size that ensures the satisfaction of the propagation criterion. Modes I, II, and III stress intensity factors are computed using the displacement correlation method, while the fracture propagation direction is determined using the Schöllmann's criterion, which is a generalization of the maximum tangential stress criterion for 3-D stress state. The GFEM is validated against a hydraulic fracture experiment on PMMA specimen, on one hand, and against four different cases of experimental fractures within concrete (a granite-like) material which serves as the pioneer application of the algorithm to verify hydraulic fracture simulation in non-PMMA materials. The influence of the initial shear stresses along the fracture plane (assuming unnotched condition) on the resulting propagation paths in the latter benchmarked problem is also assessed and found to have good agreement with experimental observations.