Confining pressure dependency of LEFM parameter in rock based on cohesive crack analysis

Linear elastic fracture mechanics (LEFM) parameter, such as mode I stress intensity factor required to crack propagation for rock under confining pressure is analyzed based on a cohesive crack model. In rocks, the LEFM parameter varies with the confining pressure. This study provides analytical solutions of relation between the LEFM parameter and the fracture toughness using a cohesive crack model, which is a model for the fracture process zone. The fracture toughness is defined by the cohesive crack model. 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 the cohesive stress distribution, namely the constant cohesive stress and the linearly decreasing cohesive stress. The analytical solutions are confirmed by comparing with the results of numerical computations performed using the body force method. The analytical solution suggests a substantial increase in the LEFM parameter due to increased confining pressures, even if the size of the fracture process zone is small.