基于Logistic分布的脆性岩石应变软化损伤本构模型及其验证

doi:10.3724/1000-6915.jrme.2024.0711

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摘要计损伤本构模型及其脆性评价方法，是岩石力学领域的热门研究课题。在分析岩石初始压密阶段非线性变形特征的基础上，以裂纹完全压密点作为临界点，首先基于切线模量变化特征及Logistic分布，建立压密阶段本构模型；随后基于连续损伤力学理论及统计损伤理论，假定岩石微元强度服从Logistic分布和Mohr-Coulomb准则，建立能够反映岩石压密阶段之后变形特征的损伤本构模型。进而基于岩石损伤演化全过程特性，提出一种新的脆性评价指标。最后，利用砂砾岩、闪长花岗岩、红砂岩、石英岩、大理岩及Maharashtra砂岩的单轴和常规三轴压缩试验数据对所建本构模型及脆性指标进行合理性验证。研究结果表明：（1）基于Logistic分布构建的分段本构模型，能够较准确地模拟不同岩性岩石在单轴和常规三轴压缩下的应力–应变全过程，试样的峰值强度和峰值应变均得到较准确描述。（2）损伤演化速度与围压成反比关系，即增大围压可以抑制损伤的发展速度，增强岩石延性变形能力，降低其脆性程度。（3）模型中的参数m和f0分别影响压密阶段曲线上凹程度和长度，参数M和F0分别影响脆性破坏程度和峰值强度。这4个模型参数控制岩石各阶段的变形特性、强度特性和脆性特征，共同决定理论本构关系曲线的形态。（4）综合考虑岩石峰前损伤程度、峰值应变及峰后损伤演化速度所建立的脆性评价指标，具有一定合理性。通过6种岩石不同围压下的试验结果，验证了新脆性指标的可行性，为从岩石损伤本构模型角度构建脆性指标提供了一定参考价值，对丰富岩石脆性分析与评价具有一定意义。

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	郭允朋1
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	刘冬桥1
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	杨圣开3
	王炀4
	李杰宇5
	凌凯1
	2

关键词 ：岩石力学, 初始压密, Logistic分布, 统计损伤本构模型, 脆性评价

Abstract：The statistical damage constitutive model of rocks and the evaluation methods for brittleness are prominent research topics in the field of rock mechanics. This paper analyzes the nonlinear deformation characteristics during the initial compaction stage of rocks, identifying the full crack compaction point as the critical juncture. First, a constitutive model for the compaction stage is developed based on the changes in tangent modulus and logistic distribution characteristics. Subsequently, drawing on the principles of continuous damage mechanics and statistical damage, we assume that the strength of microelements adheres to the logistic distribution and the Mohr-Coulomb criterion, thereby establishing a damage constitutive model that captures the deformation characteristics post-compaction. Furthermore, a novel brittleness evaluation index is proposed, reflecting the entire damage evolution characteristics. Finally, the proposed constitutive model and brittleness index are validated using uniaxial and conventional triaxial compression test data from glutenite, granodiorite, red sandstone, quartzite, marble, and Maharashtra sandstone. The findings indicate that: (1) The segmented constitutive model based on logistic distribution accurately simulates the complete stress-strain process of various rock types under uniaxial and conventional triaxial compression, effectively describing both peak strength and peak strain of the samples. (2) The speed of damage evolution is inversely proportional to confining pressures; thus, increasing confining pressure can suppress damage development, enhance ductility, and reduce brittleness. (3) The parameters m and f0 influence the degree and length of concavity on the compaction stage curve, while parameters M and F0 affect the degree of brittle failure and peak strength. Collectively, these four model parameters govern the deformation characteristics, strength properties, and brittleness of the rock, ultimately shaping the theoretical constitutive relation curve. (4) The brittleness evaluation index, which comprehensively considers the pre-peak damage degree, peak strain, and post-peak damage evolution speed of rocks, demonstrates rationality, and the feasibility of this new index is corroborated through experimental results across six rock types under varying confining pressures. This research offers valuable insights for constructing brittleness indexes grounded in the rock damage constitutive model, thereby enhancing the analysis and evaluation of rock brittleness.

Key words： rock mechanics initial compaction Logistic distribution statistical damage constitutive model brittleness evaluation

引用本文:

郭允朋1，2，刘冬桥1，2，杨圣开3，王炀4，李杰宇5，凌凯1，2. 基于Logistic分布的脆性岩石应变软化损伤本构模型及其验证[J]. 岩石力学与工程学报, 2025, 44(7): 1828-1845.
GUO Yunpeng1, 2, LIU Dongqiao1, 2, YANG Shengkai3, WANG Yang4, LI Jieyu5, LING Kai1, 2. Strain softening damage constitutive model and its verification for brittle rocks based on Logistic distribution. , 2025, 44(7): 1828-1845.

链接本文:

https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2024.0711 或 https://rockmech.whrsm.ac.cn/CN/Y2025/V44/I7/1828

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