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.

中文翻译：

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渐进破坏过程中脆性岩石局部微裂纹损伤引发的多应力降分析模型

高围压下完整脆性岩石应力-应变本构曲线的应力降对于评价地震机理和深部地下工程的安全性具有重要意义。完整岩石中微裂纹的生长强烈影响应力降。然而，在完整岩石的应力-应变曲线中，很少提出微裂纹生长依赖的多应力降的理论模型。在这项研究中，提出了一种依赖于与微裂纹扩展和应变增量相关的损伤变量的本构模型来解释应力-应变曲线中的多应力下降，包括完整岩石的应变硬化和软化阶段。该模型是通过结合机翼裂纹扩展模型、轴向应变与机翼裂纹扩展之间的建议关系制定的，以及与轴向应变有关的损伤的步进函数。这种与轴向应变相关的损伤阶梯函数近似用于模拟由局部微裂纹积累和聚结引起的单个小的剪切带的发展过程。讨论了建议的损伤步进函数中的参数对包含应力降的应力-应变曲线的影响。该理论模型定性地解释了应力-应变曲线中多应力下降的实验现象，为评价地震机理和深部地下工程的安全性提供了重要意义。这种与轴向应变相关的损伤阶梯函数近似用于模拟由局部微裂纹积累和聚结引起的单个小的剪切带的发展过程。讨论了建议的损伤步进函数中的参数对包含应力降的应力-应变曲线的影响。该理论模型定性地解释了应力-应变曲线中多应力下降的实验现象，为评价地震机理和深部地下工程的安全性提供了重要意义。这种与轴向应变相关的损伤阶梯函数近似用于模拟由局部微裂纹积累和聚结引起的单个小的剪切带的发展过程。讨论了建议的损伤步进函数中的参数对包含应力降的应力-应变曲线的影响。该理论模型定性地解释了应力-应变曲线中多应力下降的实验现象，为评价地震机理和深部地下工程的安全性提供了重要意义。