考虑剪胀特性和峰后形态的岩石损伤本构模型

doi:10.13722/j.cnki.jrme.2021.0107

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摘要考虑受载岩石损伤破坏过程中的剪胀扩容特性，基于统计损伤理论建立一种新型三维损伤本构模型，并推导三轴与常规三轴压缩下模型的解析解。该模型认为岩石由未损伤部分和损伤部分组成，二者共同承担外部荷载；其中，未损伤部分只发生弹性变形；而损伤部分同时发生弹、塑性变形，变形规律受残余强度和剪胀角影响。针对加载过程中不同种类岩石表现出的不同应力–应变曲线峰后形态，将指数函数形式的修正系数R引入Weibull分布函数，并基于Mohr-Coulomb准则构建微元强度函数，建立考虑峰后形态的损伤演化方程。模型参数F0，m可由三轴压缩试验曲线的峰值特征获得，而参数k由曲线的峰后形态决定并能够衡量岩石脆性的强弱。适用性验证表明，新建统计损伤本构模型的理论计算结果与含砾粗砂岩、粉砂岩、Ohya stone的常规三轴压缩试验结果相吻合，能够准确地描述岩石破坏过程中的应变软化、剪胀特性、残余强度与弹塑性应变演化规律，并能准确反应真三轴条件下岩石各向异性变形特征；同时该模型揭示了加载过程中岩石黏结抗力弱化、摩擦抗力强化现象的损伤力学机制。

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	梁明纯1
	2
	苗胜军1
	2
	蔡美峰1
	2
	黄正均1
	2
	杨鹏锦1
	2

关键词 ：岩石力学, 残余强度, 剪胀特性, 峰后形态, 应变软化, 统计损伤模型

Abstract：Based on the statistical damage mechanics theory，a three-dimension damage model reflecting the characteristics of dilatancy was established. In the proposed model，load is borne by the undamaged part and the damaged part of rock. The deformation of the undamaged part of rock is elastic，while the deformation of the damaged part includes elastic and plastic deformations under the influence of the residual strength and the dilatancy angle. In order to adapt to the different post-peak shapes of the stress-strain curve，a new damage evolution equation is established by introducing the modified factor R in an exponential form into the Weibull distribution function，and a micro-element strength function is established based on the Mohr-Coulomb criterion. Parameters F0 and m of the model can be obtained from the peak point of triaxial compression test，and parameter k depends on the post-peak shape of the curve and can measure the brittleness of the rock. Applicability verification indicates that the theoretical calculation results of the statistical damage constitutive model are in good agreement with the conventional triaxial compression test results of pebbled coarse sandstone，siltstone and Ohya stone. Therefore，the model can accurately describe the strain softening，dilatancy characteristics，residual strength and elastoplastic strain evolution during the failure process of rock. Besides，the model can describe the anisotropic deformation characteristics of rock under true triaxial condition，and can reveal the damage mechanism of cohesive resistance weakening and frictional resistance strengthening.

Key words： rock mechanics residual strength dilatation post-peak shape strain softening statistical damage model

引用本文:

梁明纯1，2，苗胜军1，2，蔡美峰1，2，黄正均1，2，杨鹏锦1，2. 考虑剪胀特性和峰后形态的岩石损伤本构模型[J]. 岩石力学与工程学报, 2021, 40(12): 2392-2401.
LIANG Mingchun1，2，MIAO Shengjun1，2，CAI Meifeng1，2，HUANG Zhengjun1，2，YANG Pengjin1，2. A damage constitutive model of rock with consideration of dilatation and post-peak shape of the stress-strain curve. , 2021, 40(12): 2392-2401.

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http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2021.0107 或 http://rockmech.whrsm.ac.cn/CN/Y2021/V40/I12/2392

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