Firstly, an X-ray diffraction test is carried out to investigate brittle rock specimens’ composition, and a triaxial compression test is conducted to study the deformation behaviors and mechanical properties. Then, assuming that the rock material is able to be divided into the elastic part satisfying the Hooke’s law and the damage part where rock strength follows lognormal distribution, this paper determines a damage variable and establishes a damage constitutive model which effectively reflects the residual strength in the process of rock failure. Meanwhile, testing data are used to validate the reliability of the proposed model in this paper and the dependence of statistic parameters on the confining pressure. Finally, impacts caused by statistic parameters variation on compression strength are analyzed comprehensively, and we also conduct a comparison between this proposed model and other models from other literatures, thereby showing the reliability and rationality of this proposed model. In addition, the research outcomes presented in this paper also can effectively offer significant reference for the development of rock mechanics and rock engineering.

中文翻译：

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基于岩石强度统计的岩石三轴损伤本构模型

首先进行X射线衍射试验研究​​脆性岩石试样的成分，并进行三轴压缩试验研究其变形行为和力学性能。然后，假设岩石材料能够分为满足胡克定律的弹性部分和岩石强度服从对数正态分布的损伤部分，确定损伤变量，建立损伤本构模型，有效反映剩余强度。岩石破坏的过程。同时，通过试验数据验证了本文提出的模型的可靠性和统计参数对围压的依赖性。最后综合分析统计参数变化对抗压强度的影响，我们还将该模型与其他文献中的其他模型进行了比较，从而展示了该模型的可靠性和合理性。此外，本文的研究成果也可以有效地为岩石力学和岩石工程的发展提供重要的参考。