An analytical model of multi-stress drops triggered by localized microcrack damage in brittle rocks during progressive failure

Stress drops in stress–strain constitutive curves of intact brittle rocks under high confining pressure have great significance for evaluating the earthquake mechanism and the safety of deep underground engineering. Microcrack growth in intact rock strongly influences the stress drops. However, the theoretical model of microcrack growth-dependent multi-stress drops rarely is proposed in stress–strain curves of intact rocks. In this study, a constitutive model depending on the damage variable relating to microcrack growth and strain increment is proposed to explain the multi-stress drops in stress–strain curves including strain hardening and softening phases of intact rocks. This model is formulated by combining the wing crack growth model, the suggested relationship between axial strain and wing crack growth, and the stepping function of damage relating to axial strain. This stepping function of damage relating to axial strain approximately is used to simulate the developing process of the small individual shear bands caused by the local microcrack accumulation and coalescence. The effects of parameters in the suggested stepping function of damage on the stress–strain curves containing stress drops are discussed. The theoretical model qualitatively explains the experimental phenomena of multi-stress drops in the stress–strain curves, which provides an important implication for evaluating the earthquake mechanism and the safety of deep underground engineering.