There is an long-standing debate in the rock mechanics community about the dependence of fracture toughness KIc on the confining stress. One of the tests used to assess this dependence relies on injecting fluid into a slotted borehole drilled along the axis of a cylindrical sample and interpreting the toughness from the breakdown pressure (Abou-Sayed et al. 1978). However, the interpretation of the observed breakdown pressure relies critically on assuming that (i) the fluid pressure in the slots and the cracks ahead is uniform and (ii) the peak (breakdown) pressure is the fracture initiation pressure. The model described in this paper challenges these assumptions by considering a fluid lag at the tip of the hydraulic fracture growing from the pre-existing notches and by incorporating the hydraulic compliance of the injection system. This model indicates that the peak pressure generally differs from the fracture initiation pressure due to an episode of stable hydraulic fracture propagation following initiation. The difference between the peak pressure and the fracture initiation pressure increases with the fluid viscosity and the confining pressure, which leads to an artificial dependence of the toughness on the confining pressure if the peak pressure is interpreted as the initiation pressure. Comparison between the predicted and experimental peak pressure for a series of tests on cement samples indicates similar trends between experiments and numerical simulations. However, the predicted peak pressure generally underestimates the experimental one.
There is a long-standing debate in the geomechanics community as to whether the fracture toughness depends on the confining stress in rocks (Schmidt and Huddle, 1977; Schmidt, 1980; Ko and Kemeny, 2007; Garagash, 2019; Yue et al., 2020; Gehne et al., 2020). Although fracture toughness is treated as a constant material parameter in the theory of linear elastic fracture mechanics (LEFM) (Rice, 1968), a dependence of the resistance to fracture propagation on the confining stress is expected in quasi-brittle materials. Indeed, these materials are characterized by the presence of a process zone ahead of the crack tip (Barenblatt, 1962; Ballarini et al., 1984; Garagash, 2019; Bazant and Le, 2017). The confining stress acting across this cohesive zone contributes to the energy dissipation associated with the creation of new surfaces. The combined energy dissipation can be captured via an apparent toughness KIc. Here the term "toughness" is used to encompass both the intrinsic material property KIc and the stress-related energy dissipation, in accordance with the terminology used in the literature.
