How does the heterogeneous interface influence hydraulic fracturing?

Under the influence of the nonlinear fluid-solid coupling, hydraulic fracture exhibits various propagation modes (such as toughness- or viscosity-dominated), which stem from the competition between the solid deformation and fluid flow. Based on the homogeneous assumption, the basic theoretical analysis has divided toughness and viscosity scales in the tip region. However, regarding more realistic and complex geological conditions, like layered heterogeneity, knowledge of fluid-driven fracture propagation is still unclear. This work establishes a theoretical model and solving approach to reveal the multiscale asymptotic behavior during hydraulic fracture passing through the heterogeneous interface (i.e., discontinuous elastic properties). The influence of material discontinuity, regarded as the remote force, in the near-tip, intermediate, and far-field scales is analyzed by the asymptotic analysis and validated by the numerical solutions. Notably, solutions at the intermediate scale manifest as individual feature owing to the heterogeneity: as the crack in front of the interface, just a specific transition solution governed by the property and position of the interface appears; once the crack tip passes the interface, the interface-governed transition solution and interface solution occur simultaneously and interact as the crack tip moves away from the interface. Such multiscale property results in the interface-governed fluid-solid interaction in the tip region, and finally leads to changes in interface failure and propagation mode. On the one hand, the criterion for interface failure should be modified by simultaneously incorporating the heterogeneity of solid domain and multiscale nature of tip solution, especially for viscosity- or interface-dominated propagation regimes. On the other hand, the propagation mode in a heterogeneous domain is controlled by two characteristics: traditional l/l_mk for toughness-viscosity competition associated with c/L_μ for material discontinuity effect proposed in the present work. These insights provide the theoretical foundation for modeling hydraulic fracture propagation in layered heterogeneous domains.