The constitutive models of rock are essentially the general depictions of the mechanical responses of rock mass under complex geological environments. Statistical distribution-based constitutive models are of great efficacy in reflecting the rock failure process and the stress–strain relation from the perspective of damage, while most of which were achieved by adopting Drucker–Prager criterion or Mohr–Coulomb criterion to characterize microelement failure. In this study, underpinned by Hoek–Brown strength criterion and damage theory, a new statistical damage constitutive model, which is simple in terms of model expression and capable of reflecting the strain softening characteristics of rock in post-peak stage, was established. First, the rock in the failure process was divided into infinite microelements including elastic part satisfying Hooke’s law and damaged part retaining residual strength. Based on strain equivalence hypothesis, the relation between rock microelement strength and damage variable was derived. By assuming the statistical law of microelement strength obeying Weibull distribution and the microelement failure conforming to Hoek–Brown criterion, the new statistical damage constitutive model based on Hoek–Brown criterion was, therefore, gained. The mathematical expressions of the corresponding model parameters were subsequently deduced in accordance with the geometric characteristics of the deviatoric stress–strain curve. Last, the existing conventional triaxial compression test data of representative rock samples under different confining stresses were employed to compare with the theoretical curves by proposed model, the consistency between which was quantified by utilizing the correlation factor evaluation method. The result indicated that the proposed model could well describe the entire stress–strain relationship of rock failure process and manifest the characteristics of rock residual strength. It is of great significance to the researches on rock damage and softening issues and rock reinforcement treatments.

岩石的本构模型本质上是复杂地质环境下岩体力学响应的一般描述。基于统计分布的本构模型在从损伤的角度反映岩石破坏过程和应力应变关系方面非常有效，而其中大部分是通过采用 Drucker-Prager 准则或 Mohr-Coulomb 准则来表征微量元素破坏来实现的。本研究以Hoek-Brown强度准则和损伤理论为基础，建立了一种新的统计损伤本构模型，该模型表达简单，能够反映峰后阶段岩石的应变软化特征。第一的，破坏过程中的岩石被划分为无限微单元，包括满足胡克定律的弹性部分和保留剩余强度的损坏部分。基于应变等价假设，推导出岩石微单元强度与损伤变量之间的关系。假设微量元素强度服从威布尔分布的统计规律，微量元素失效符合Hoek-Brown准则，得到了基于Hoek-Brown准则的新的统计损伤本构模型。随后根据偏应力-应变曲线的几何特征推导出相应模型参数的数学表达式。最后的，利用现有不同围压条件下代表性岩样的常规三轴压缩试验数据与提出的模型理论曲线进行比较，并利用相关因子评价方法量化理论曲线之间的一致性。结果表明，该模型能够较好地描述岩石破坏过程的整个应力应变关系，体现岩石残余强度的特征。对岩石损伤软化问题及岩石加固处理的研究具有重要意义。结果表明，该模型能够较好地描述岩石破坏过程的整个应力应变关系，体现岩石残余强度的特征。对岩石损伤软化问题及岩石加固处理的研究具有重要意义。结果表明，该模型能够较好地描述岩石破坏过程的整个应力应变关系，体现岩石残余强度的特征。对岩石损伤软化问题及岩石加固处理的研究具有重要意义。