ABSTRACT
A better understanding of the fracture process in rock is needed to explain certain observed behavior from fracture testing and to provide assistance in selecting appropriate methods for applying fracture mechanics to actual rock mechanics problems. First, the widely accepted formulation for the crack tip plastic zone in metals is reviewed. Observations on how rock fracture differs from metal fracture motivates a change from the Von Mises yield condition to a maximum normal stress criterion. This results in a crack tip microcrack zone description that is consistent with observed fracture toughness behavior for rock.
The model is extended to include the application of confining stresses. This includes anisotropic in situ stress states as well as hydrostatic compression. Verification of this model rests on its ability to explain observed fracture behavior; no direct verification is available as yet. Finally, a suggestion is made for improving hydraulic fracture containment models based on average crack-tip stresses rather than the stress intensity factor.
In the past five years or so there has been a growing interest in applications of linear elastic fracture mechanics to problems involving rock. Much of this interest in rock fracture stems from energy research. Engineers who are concerned with optimum resource recovery find they must deal with rock as a structural material. Resource recovery techniques such as stimulation of oil and gas wells by hydraulic fracturing, fragmentation of oil shale beds for in situ retorting, and thermal-stress induced fracturing of geothermal sources, for example, would benefit from a better understanding of the fracture process and requirements for crack propagation.
Most investigations to date that deal with fracture mechanics of rock have emphasized direct measurements of fracture parameters (e.g., Schmidt, 1976; Barker, 1977) and direct applications of fracture mechanics principles (e.g., Simonson et al., 1978; Hanson et al., 1978; Warpinski et al., 1979). Some emphasis has focused on descriptions of the fracture process (e.g., Kobayashi and Fourney, 1978), but much more work is needed if one is to fully understand the results of these fracture measurements and to have confidence in the appropriateness of these applications.
Fracture mechanics is based on the stess intensity factor, K, which essentially describes the entire stress field at a crack tip in a linear elastic material. When a sufficient level of stress intensity is applied to a material the crack will extend. This critical value of K is referred to as fracture toughness, Kic , when linear elastic conditions prevail. Since stresses are known to be very large at the crack tip, a process zone develops within which the stresses are inelastic (plastic in metals). Linear elastic conditions prevail, then, as long as this zone of inelastic behavior remains small relative to the other dimensions of the problem.
The apparent fracture toughness of rock has been shown to depend on crack length (Ingraffea and Schmidt, 1978; Schmidt and Lutz, 1979) which is similar to the behavior of many metallic materials (Nelson 1972; Jones from the plastic zone in metals. A description of this
