Cohesive crack analysis of toughness increase due to confining pressure

Apparent fracture toughness in Mode I of microcracking materials such as rocks under confining pressure is analyzed based on a cohesive crack model. In rocks, the apparent fracture toughness for crack propagation varies with the confining pressure. This study provides analytical solutions for the apparent fracture toughness using a cohesive crack model, which is a model for the fracture process zone. The problem analyzed in this study is a fluid-driven fracture of a two-dimensional crack with a cohesive zone under confining pressure. The size of the cohesive zone is assumed to be negligibly small in comparison to the crack length. The analyses are performed for two types of cohesive stress distribution, namely the constant cohesive stress (Dugdale model) and the linearly decreasing cohesive stress. Furthermore, the problem for a more general cohesive stress distribution is analyzed based on the fracture energy concept. The analytical solutions are confirmed by comparing them with the results of numerical computations performed using the body force method. The analytical solution suggests a substantial increase in the apparent fracture toughness due to increased confining pressures, even if the size of the fracture process zone is small.