Modeling nonplanar hydraulic fracture propagation using the XFEM: An implicit level-set algorithm and fracture tip asymptotics

We describe the development of a fluid-coupled 2D extended finite element method (XFEM) algorithm to model the propagation of nonplanar radially-symmetric hydraulic fractures. The model determines the fracture propagation trajectory according to the maximum tangential stress criterion of Erdogan and Sih (1963). An implicit level-set algorithm (ILSA) is employed for locating the moving fracture front. The aim of the paper is to validate the radially-symmetric XFEM-ILSA model for nonplanar fracture propagation for mixed modes I and II. First, the results of the model are compared to the analytical solution for viscosity-dominated propagation of a penny-shaped crack. Next, we compare the results of the XFEM-ILSA scheme to the results of laboratory experiments and the results of an axisymmetric displacement discontinuity model for the near-surface propagation of hydraulic fractures with fluid lag (Bunger et al., 2013). For this comparison, a mixed-mode toughness tip asymptote is employed within ILSA to locate the fracture front. An improved algorithm is used for locating the fluid front within the fracture.