A generalized nonlinear three-dimensional failure criterion based on fracture mechanics

Based on fracture mechanics theory and wing crack model, a three-dimensional strength criterion for hard rock was developed in detail in this paper. Although the basic expression is derived from initiation and propagation of a single crack, it can be extended to microcrack cluster so as to reflect the macroscopic failure characteristic. Besides, it can be derived as Hoek–Brown criterion when the intermediate principal stress σ2 is equal to the minimum principal stress σ3 (Zuo et al., 2015). In addition, the opening direction of the microcrack cluster decreases with the increase of the intermediate principal stress coefficient, which could be described by an empirical function and verified by 10 kinds of hard rocks. Rock strength is influenced by the coupled effect of stress level and the opening direction of the microcrack clusters related to the stress level. As the effects of these two factors on the strength are opposite, the intermediate principal stress effect is induced.