Method study of calculating the permeability coefficient of fractured rock mass with dense sections
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摘要:
裂隙岩体渗流具有非均匀性和各向异性，其复杂性体现在单裂隙的密度、产状和迹长等参数上以及裂隙网络的连通性上，而裂隙网络的连通性是三维裂隙岩体渗流参数计算的一个难题。目前三维裂隙岩体渗流参数的计算方法因其模型的不同而各有优缺点。为分析裂隙岩体水力各向异性及其渗透系数，基于降维思路，提出了三维裂隙岩体密集切面求解渗透系数的新方法。该方法在三维裂隙网络模拟的基础上，通过不同方向密集切面逼近裂隙岩体，将三维裂隙网络分解成多个连续的二维切面裂隙网络，对切面裂隙网络使用图论法分析裂隙水力的连通性和渗透路径，设置水头边界条件计算渗透系数，通过空间上线、面、体的关系，将二维空间上的渗透系数计算结果表达三维空间上的方向性，构建三维裂隙岩体网络的渗透张量。将切面渗透系数视为渗透椭圆计算切面等效渗透系数，给出了一种新的岩体等效渗透张量的求解公式。同时讨论了尺度效应和裂隙岩体渗透各向异性的表征方式，通过构建三维和二维裂隙网络，截取不同大小的单元体计算渗透系数，得出典型单元体的边长为20 m，并通过野外现场钻孔压水实验验证了方法的可行性。研究成果可以为求解不同尺度、非均质裂隙岩体各方向渗透系数提供参考。
Abstract:Objective The seepage of fractured rock masses has non-uniformity and anisotropy, and its complexity is reflected in parameters such as density, orientation, and trace length of individual fractures, as well as the connectivity of fracture networks. The connectivity of fracture networks is a difficult problem in calculating the seepage parameters of three-dimensional fractured rock masses. At present, the calculation methods for seepage parameters of three-dimensional fractured rock masses have their own advantages and disadvantages due to different models. To analyze the hydraulic anisotropy and permeability coefficient of fractured rock masses, a new method for solving the permeability coefficient of three-dimensional fractured rock mass dense sections based on dimensionality reduction is proposed.
Methods This method, founded on the simulation of three-dimensional fracture networks, approximates the fractured rock masses through dense sections in different directions, decomposing the three-dimensional fracture network into multiple continuous two-dimensional sectional fracture networks, using graph theory to analyze the hydraulic connectivity and permeability paths, and water head boundary conditions are set to calculate the permeability coefficient. Through the relationship between lines, surfaces, and volumes in space, the calculated permeability coefficient in two-dimensional space is expressed as the directionality in three-dimensional space, and the permeability tensor of the three-dimensional fractured rock mass network is constructed.
Results By treating the section permeability coefficient as a permeability ellipse, the new method calculates the equivalent permeability coefficient of the section and provides a solution formula for the equivalent permeability tensor of the rock mass. It also discusses the scale effect and the representation of anisotropy in the rock mass. By constructing three-dimensional and two-dimensional fracture networks, different sizes of unit cells were intercepted to calculate the permeability coefficient, and the side length of a typical unit cell was determined to be 20m. The feasibility of the method was verified through field drilling water pressure experiments.
Conclusion This method offers a reference for solving the permeability coefficients in different directions of heterogeneous fractured rock masses of various scales.
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图 1 切面法求解裂隙岩体渗透系数流程图
$K^y_{yz}. $yz平面的切面上沿y轴方向的渗透系数；$K^z_{yz}. $yz平面的切面上沿z轴方向的渗透系数；$K^x_{xz}. $xz平面的切面上沿x轴方向的渗透系数；$K^z_{xz}. $xz平面的切面上沿z轴方向的渗透系数；$K^x_{xy}. $xy平面的切面上沿x轴方向的渗透系数；$K^y_{xy}. $xy平面的切面上沿y轴方向的渗透系数；Kx. 三维坐标轴上沿x轴的渗透张量；Ky. 三维坐标轴上沿y轴的渗透张量；Kz. 三维坐标轴上沿z轴的渗透张量；下同
Figure 1. Flowchart for the determination of permeability coefficient of fractured rock mass by section method
图 2 三维离散裂隙网络（a）切分成二维离散裂隙（b）过程图
Figure 2. Process diagram for segmenting a three-dimensional discrete fracture network into two-dimensional fractures.
图 3 裂隙网络与渗流网络示意图
Figure 3. Schematic diagram of fracture network and percolation network.
图 8 模拟试验与压水试验渗透系数对比
Figure 8. Comparison of permeability coefficients between simulation experiment and water pressure test
图 9 单元体尺寸与渗透系数关系图
Figure 9. Relationship between unit size and permeability coefficient. (a) Before smoothing treatment, (b) After smoothing treatment
图 10 不同尺度模型的二维裂隙网络
Figure 10. Two-dimensional fracture networks of models at different scales
图 12 模型渗流场水头等值线分布切面图
Figure 12. Section of equipotential line distribution in hydraulic head in seepage field. (a)The direction of water flow is along the X-axis, (b) The direction of water flow is along the Y-axis, (c) The direction of water flow is along the Z-axis.
表 1 裂隙统计及数值模拟基本参数
Table 1. Basic parameters for fracture statistics and numerical simulation
钻孔 裂隙组 倾向/
(°)标准差/
(°)倾角/
(°)标准差/
(°)密度/
(条·m−3)迹长/
mZK01 1 91 10.83 44 16.14 0.17 4.6 2 257 9.10 43 16.46 0.12 5.8 3 290 6.28 41 17.09 0.09 6.7 ZK02 1 231 12.19 63 15.98 0.17 4.7 2 75 15.83 78 17.64 0.15 4.1 3 312 12.52 62 13.18 0.12 6.4 4 2 1.2 64 12.79 0.06 4.6 5 170 6.12 87 13.12 0.06 5.9 
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表 2 数据结果分析
Table 2. Analysis of Data Results
绝对误差 相对误差/% ZK01 ZK02 ZK01 ZK02 0.00099 0.000693 27.58 70.21 0.00305 0.003058 49.43 844.75 0.01372 0.00005 80.71 1.22 0.01337 0.001783 90.34 1007.34 0.00191 0.001587 8.84 745.07 0.00043 0.002838 13.44 5415.27 0.004538 0.00084 4905.41 30.43 0.00301 0.00037 3781.91 4.48 0.002201 0.002139 1583.45 6991.50 0.00072 0.001519 36.18 3714.18 0.00207 0.003366 65.09 7597.52 0.001738 0.00009 186.48 3.81 0.00015 0.00244 14.02 59.08 0.004887 1212.66 0.001545 753.66 0.003349 2080.12 0.000879 336.78 0.00018 79.34 0.002415 1123.26
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