Analysis of Confining Pressure Dependency of Apparent Fracture Toughness of Rock Based on Cohesive Crack Model

摘要

Apparent fracture toughness of a rock under confining pressures is analyzed based on a cohesiverncrack model. In rocks, the stress intensity factor required for the crack propagation, which is calledrnthe apparent fracture toughness in this study, varies with the confining pressure. This study providesrnanalytical solutions of the apparent fracture toughness in mode I or II, using the cohesive crack model.rnThe cohesive crack model represents the formation of the fracture process zone in rocks. Thernproblem analyzed in this study is a mode I or II crack growth induced by hydraulic fracturing in arntwo-dimensional crack with a cohesive zone under confining pressures. The size of the cohesivernzone is assumed to be negligibly small in comparison to the crack length. The analyses arernperformed for two types of the cohesive stress distribution, namely the constant cohesive stressrn(Dugdale model) and the linearly decreasing cohesive stress. Furthermore, the problem for a morerngeneral cohesive stress distribution is analyzed based on the fracture energy concept. The analyticalrnsolution suggests a substantial increase in the apparent fracture toughness due to increased confiningrnpressure, when the size of the fracture process zone is negligibly small.