Comparison between laboratory experiments and coupled simulations of saucer-shaped hydraulic fractures in homogeneous brittle-elastic solids

Hydraulic fractures that grow at shallow depth or, more generally, near a free surface, curve towards the surface to become saucer-shaped. These saucer-shaped hydraulic fractures pose challenges for modeling that include the need to track the evolution of the crack path and to follow two distinct moving boundaries corresponding to the leading edge of the crack and the fluid front. Results from a coupled, implicit time stepping numerical model agree well with detailed laboratory experimental data for fluid-driven cracks in glass and PMMA. Specifically, the model and laboratory results show good agreement for the crack path, the evolution of the fluid and fracture fronts, the crack opening, and the injection fluid pressure. This strong comparison not only demonstrates the viability of the numerical model, but more generally the results demonstrate that considering coupling among fluid flow, elastic deformation, and radially symmetric crack growth captures enough of the relevant physical processes to accurately predict the leading order behavior of the physical system realized in the laboratory using homogeneous brittle-elastic solids.