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岩体三维裂隙网络地质熵与渗透特性关系研究

樊鑫成 叶祖洋 黄诗冰 程爱平

樊鑫成, 叶祖洋, 黄诗冰, 程爱平. 岩体三维裂隙网络地质熵与渗透特性关系研究. 力学学报, 2023, 55(3): 1-13 doi: 10.6052/0459-1879-22-579
引用本文: 樊鑫成, 叶祖洋, 黄诗冰, 程爱平. 岩体三维裂隙网络地质熵与渗透特性关系研究. 力学学报, 2023, 55(3): 1-13 doi: 10.6052/0459-1879-22-579
Fan Xincheng, Ye Zuyang, Huang Shibing, Cheng Aiping. Study on connectivity and entropy scale of three-dimensional fracture network. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(3): 1-13 doi: 10.6052/0459-1879-22-579
Citation: Fan Xincheng, Ye Zuyang, Huang Shibing, Cheng Aiping. Study on connectivity and entropy scale of three-dimensional fracture network. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(3): 1-13 doi: 10.6052/0459-1879-22-579

岩体三维裂隙网络地质熵与渗透特性关系研究

doi: 10.6052/0459-1879-22-579
基金项目: 国家自然科学基金(42077243)资助项目
详细信息
    作者简介:

    樊鑫成, 硕士研究生, 主要研究方向为岩体裂隙渗流. E-mail: fanxc@wust.edu.cn

    通讯作者:

    叶祖洋, 教授, 主要研究方向为裂隙岩体渗流及多场耦合机理. E-mail: yezuyang@wust.edu.cn

  • 中图分类号: O357.3

STUDY ON CONNECTIVITY AND ENTROPY SCALE OF THREE-DIMENSIONAL FRACTURE NETWORK

Funds: Supported by the National Natural Science Foundation of China(Grant No. 42077243)
  • 摘要: 裂隙网络是岩体地下水的主要流动通道, 而工程岩体中裂隙网络错综复杂, 裂隙网络的几何特征和连通性对其渗透性有着重要影响. 为了综合量化裂隙迹长、间距、倾角、开度对裂隙网络连通性和渗透性的影响, 基于信息熵原理, 提出了三维裂隙网络地质熵理论和连通性指标−熵尺度, 对比熵尺度与其他传统三维裂隙网络连通性指标, 验证了熵尺度评价三维裂隙网络连通性和渗透性的合理性. 结合锦屏一级水电站左岸边坡裂隙统计分布, 建立三维裂隙网络渗流数值计算方法, 分析不同裂隙迹长、倾角、间距、开度条件下三维裂隙面密度、无量纲逾渗密度、熵尺度和渗透系数的变化关系. 结果表明: 当体积率一定, 考虑开度影响时, 三维裂隙面密度和无量纲逾渗密度无法定量表征迹长和间距对裂隙网络连通性的影响; 裂隙迹长与熵尺度和渗透系数呈负相关关系, 裂隙间距和开度与熵尺度和渗透系数呈正相关关系, 裂隙倾角变化对熵尺度和渗透系数影响较小; 熵尺度与渗透系数的非线性关系近似满足二次多项式.

     

  • 图  1  (a) 三维裂隙网络与子域划分和(b) 子域与裂隙相交关系

    Figure  1.  (a) The 3D fracture network and subdomain mesh and (b) the intersection between the subdomain and fractures

    图  2  相对熵变差图

    Figure  2.  Differential chart of HR

    图  3  裂隙三角形单元与六面体子域的切割关系

    Figure  3.  Relationship between triangular element of fracture and subdomain

    图  4  裂隙网络模型

    Figure  4.  Fracture network model

    图  5  三维裂隙网络渗流模型

    Figure  5.  Three-dimensional fracture network seepage model

    图  6  连通性指标与渗透系数的关系

    Figure  6.  Relationship between connectivity index and permeability coefficient

    图  7  不同几何特征裂隙网络模型

    Figure  7.  Fracture network model of different geometric characteristics

    图  8  不同迹长裂隙网络的熵尺度变化

    Figure  8.  Variation of fracture entropy scale with different lengths

    图  9  不同间距裂隙网络的熵尺度变化

    Figure  9.  Variation of fracture entropy scale with different spacings

    图  10  不同倾角裂隙网络的熵尺度变化

    Figure  10.  Variation of fracture entropy scale with different dips

    图  11  不同开度均值裂隙网络的熵尺度变化

    Figure  11.  Variation of fracture entropy scale with different apertures

    图  12  不同开度标准差裂隙网络的熵尺度变化

    Figure  12.  Variation of fracture entropy scale with different aperture standard deviations

    图  13  裂隙面局部坐标系

    Figure  13.  Local coordinate system of fracture surface

    图  14  相交裂隙渗流示意图

    Figure  14.  Illustration of seepage flow at fracture intersection

    图  15  不同迹长裂隙网络水头分布

    Figure  15.  The hydraulic head distributions with different lengths

    图  16  不同迹长裂隙网络流量分布

    Figure  16.  The flow rate distributions with different lengths

    图  17  不同迹长裂隙网络的熵尺度和渗透系数关系

    Figure  17.  Variation of fracture entropy scale and permeability coefficient with different lengths

    图  18  不同间距裂隙网络水头分布

    Figure  18.  The hydraulic head distributions with different spacings

    图  19  不同间距裂隙网络流量分布

    Figure  19.  The flow rate distributions with different spacings

    图  20  不同间距裂隙网络的熵尺度和渗透系数关系

    Figure  20.  Variation of fracture entropy scale and permeability coefficient with different spacings

    图  21  不同间距裂隙网络水头分布

    Figure  21.  The hydraulic head distributions with different dips

    图  22  不同间距裂隙网络流量分布

    Figure  22.  Variation of fracture entropy scale with different dips

    图  23  不同倾角裂隙网络的熵尺度和渗透系数关系

    Figure  23.  Variation of fracture entropy scale and permeability coefficient with different dip angles

    图  24  熵尺度与渗透系数变化规律

    Figure  24.  Variation of entropy scale and permeability coefficient

    表  1  不同网格尺度下的熵尺度

    Table  1.   Entropy scale with different grid scales

    Grid scaleHRHS
    1015
    50.9925272.537365
    3.3333330.9860261.726512
    2.50.9813871.323399
    20.9730931.08842
    1.6666670.9688020.930529
    1.4285710.9631760.819883
    1.250.9589640.736894
    1.1111110.953430.673758
    10.9491580.623163
    0.9090910.944880.582159
    0.8333330.9409870.548137
    0.7692310.9356390.520206
    0.7142860.9326790.49564
    0.6666670.929320.474633
    0.6250.9230880.457349
    0.5882350.9204730.441198
    0.5555560.917550.427018
    0.5263160.9141080.414559
    0.50.9106860.403432
    下载: 导出CSV

    表  2  传统三维连通性指标

    Table  2.   Traditional 3D connectivity index

    SymbolExpressionReferenceDescription
    $ {\rho _N} $${\rho _N} = \dfrac{ {\displaystyle\sum {\tau (i,j)} } }{V}$Ref. [22]V is the volume of rockmass
    $ \overline L $$\overline L = \dfrac{ {\displaystyle\sum\limits_{n = 1}^N { {l_i} } } }{V}$Ref. [23]N is the number of fracture
    intersecting lines,
    li is the length of fracture intersection line
    $ {P_{32}} $${P_{32} } = \dfrac{ {\displaystyle\sum\nolimits_i^N S } }{V}$Ref. [10]S is the area of the fracture surface,
    N is the number of fracture surface
    ${\rho '_{3 {\rm{D}}} }$${\rho '_{3 {\rm{D}}} } = {\rho _V}{V_{ex} }$Ref. [15]$ {\rho _V} $is the fracture density,
    $ {V_{ex}} $is the excluded volume
    下载: 导出CSV

    表  3  裂隙模型几何参数

    Table  3.   Geometric parameters of fracture model

    GroupFracture setMean length/mDip direction/(°)Dip angle/(°)Spacing/mAperture/μm
    Mean eStandard deviation
    A1[2,3]30960273.20
    215677
    B12.530960[1,3]72.60
    215677
    C12.530960278.10
    2156[60,80]
    D12.5309602[20,100][0,10]
    215677
    E1[2,3]30960[1,3][20,300]0
    2156[60,80]
    下载: 导出CSV
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  • 收稿日期:  2022-12-06
  • 录用日期:  2023-02-23
  • 网络出版日期:  2023-02-24

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