基于节理张量的岩体等效弹性力学参数计算方法研究

doi:10.3724/1000-6915.jrme.2024.0445

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摘要裂隙的粗糙度及空间分布不仅是岩体各向异性体现的重要因素，同时也是复杂裂隙岩体进行等效强度及变形特性研究的基础。鉴于传统节理张量模型常将裂隙简化为平面，而自然裂隙实则为粗糙起伏表面的研究现状，改进现有节理张量，并详实推导粗糙型离散裂隙网络(RDFN)的等效弹性力学参数计算方法。引入分形理论，构建算例模型，精确量化裂隙粗糙度，对比分析平面型离散裂隙网络(DFN)和粗糙型离散裂隙网络(RDFN)的计算效果。为进一步验证研究的可靠性，采用数值软件生成简单模型，并计算得到模型的解析解与数值解。结果表明：(1) 考虑结构粗糙度的等效弹性力学参数计算方法较好地消除了节理张量的局限性。(2) 基于W-M分形函数构建的RDFN算例模型具有显著的粗糙特性，且公式中的分形维数(D)以及分形粗糙度(G)对裂隙表面粗糙度有较大影响。(3) 相较于DFN模型，固有的结构粗糙度显著影响RDFN模型的等效弹性力学参数，影响程度为5%～15%。(4) 简单数值模型的数值解与解析解的结果接近，误差较小，充分验证了基于改进节理张量进行本构关系计算的准确性。相关研究结果对粗糙裂隙的岩体等效弹性行为的分析具有重要参考价值。

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	尹敬涵1
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	崔臻1
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	盛谦1
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	孙鑫1
	2
	张茂础3

关键词 ：岩石力学, 岩体, 离散裂隙网络, 节理张量, 分形, 等效弹性力学参数

Abstract：Fracture roughness and spatial distribution significantly influence the anisotropic behavior of rock masses. Traditional fabric tensor models often simplify fractures as planes，whereas natural fractures exhibit rough surfaces. This study aims to modified the existing fabric tensor and derive a detailed method for calculating the equivalent elastic mechanical parameters of rough discrete fracture networks(RDFN). By introducing fractal theory，a case model is constructed，and a comparative analysis between planar discrete fracture networks(DFN) and RDFN is conducted. To further enhance the reliability of the study，a simple model is generated using numerical software，and both analytical and numerical solutions of the model are computed. The results indicate that：(1) the modified method that considers roughness effectively mitigates the limitations of the fabric tensor. (2) The RDFN case model constructed based on the W-M fractal function exhibits significant rough characteristics，with the fractal dimension (D) and fractal roughness(G) greatly impacting the surface roughness of fractures. (3) Compared to the DFN model，the inherent roughness influences the equivalent elastic mechanical parameters of RDFN models by approximately 5% to 15%. (4) The numerical solutions of the simple numerical models closely match the analytical solutions，with minimal error，validating the accuracy of the constitutive relationship based on the modified fabric tensor. These findings provide valuable insights for analyzing the equivalent elastic behavior of rock masses with rough fractures.

Key words： rock mechanics rock mass discrete fracture network fabric tensor fractal theory equivalent elastic mechanical parameters

引用本文:

尹敬涵1，2，崔臻1，2，盛谦1，2，孙鑫1，2，张茂础3. 基于节理张量的岩体等效弹性力学参数计算方法研究[J]. 岩石力学与工程学报, 2025, 44(1): 152-163.
YIN Jinghan1，2，CUI Zhen1，2，SHENG Qian1，2，SUN Xin1，2，ZHANG Maochu3. Research on the calculation method for equivalent elastic mechanical parameters of rock masses based on the fabric tensor. , 2025, 44(1): 152-163.

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https://rockmech.whrsm.ac.cn/CN/10.3724/1000-6915.jrme.2024.0445 或 https://rockmech.whrsm.ac.cn/CN/Y2025/V44/I1/152

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