The relationships between tensile strength, mode I and mode II fracture toughness of rock: An empirical and microcracking perspective

The empirical relationships between tensile strength, mode I and mode II fracture toughness obtained by previous studies have the problem of a small amount of data for fitting, and more data are needed for further study. There is a discrepancy between the theoretical prediction and the experimental results of the relationship between mode II and mode I fracture toughness. Because of this, a review is conducted to determine the relationships among tensile strength, mode I fracture toughness, and mode II fracture toughness from the data gathered from the available literature. The results indicate that the mode I and mode II fracture toughness have linear relationships with tensile strength with the linear coefficient of 0.141 and 0.219, respectively. The linear coefficient between mode II and mode I fracture toughness is 2.389, indicating that the classical mixed mode criteria are mistaken the empirical relationship between mode II and mode I fracture toughness. The microcracking mechanism and failure model are quantified and compared in detail among tensile test, mode I and mode II fracture toughness tests based on moment tensor. It found that the nature of the source can be related to each other, which gives some light on the reason for the existence of certain relationships between these macroscopic parameters from a microcracking perspective.