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单轴压缩条件下裂隙粗糙度对渗透系数的影响

王帅 于庆磊 王玲

王帅, 于庆磊, 王玲. 单轴压缩条件下裂隙粗糙度对渗透系数的影响[J]. 工程科学学报. doi: 10.13374/j.issn2095-9389.2020.05.26.001
引用本文: 王帅, 于庆磊, 王玲. 单轴压缩条件下裂隙粗糙度对渗透系数的影响[J]. 工程科学学报. doi: 10.13374/j.issn2095-9389.2020.05.26.001
WANG Shuai, YU Qing-lei, WANG Ling. Effect of fracture roughness on permeability coefficient under uniaxial compression[J]. Chinese Journal of Engineering. doi: 10.13374/j.issn2095-9389.2020.05.26.001
Citation: WANG Shuai, YU Qing-lei, WANG Ling. Effect of fracture roughness on permeability coefficient under uniaxial compression[J]. Chinese Journal of Engineering. doi: 10.13374/j.issn2095-9389.2020.05.26.001

单轴压缩条件下裂隙粗糙度对渗透系数的影响

doi: 10.13374/j.issn2095-9389.2020.05.26.001
基金项目: 国家自然科学基金资助项目(51574060);国家重点研发计划资助项目(2016YFC0801602);唐山市科技计划资助项目(19130216g)
详细信息
    通讯作者:

    E-mail:wangshuai@ncst.edu.cn

  • 中图分类号: TG142.71

Effect of fracture roughness on permeability coefficient under uniaxial compression

More Information
  • 摘要: 裂隙粗糙度是影响裂隙岩体渗流特性和流体流动复杂性的重要因素,为了深入研究单轴压缩条件下粗糙度对渗透系数的影响,采用3D打印技术和数字建模方法制备了粗糙度不同的裂隙试样,通过自制的试验装置对不同法向压力下的裂隙试样进行了试验。结果表明,在没有法向压力的条件下,随着粗糙度的增加,渗透系数以负指数函数形式减小,采用Forchheimer方程定量的分析了渗流流量与水力梯度之间的非线性关系,Forchheimer方程可以很好地描述粗糙裂隙表面的流动过程,线性项系数随着粗糙度的增大而减小,非线性项系数随着粗糙度的增大而增大;在恒定法向压力且大于水压的条件下,裂隙试样的渗透系数随着粗糙度的增大线性减小,随着水压的增大,粗糙度对渗透系数的影响作用增强;定义了系数$\delta $,分析了在有无法向压力条件下,粗糙度对渗透系数影响的差异性,$\delta $随着水力梯度的增加而增加,随着法向压力的增加而减小。研究结果可以加深对粗糙裂隙表面流体流动的认识,为进一步研究岩体流动特性奠定坚实的基础。
  • 图  1  扫描JRC的标准曲线图

    Figure  1.  Standard profile curve of JRC

    图  2  吻合的裂隙曲线图

    Figure  2.  Curve diagram of mating fracture

    图  3  粗糙裂隙三维模型示意图

    Figure  3.  Rough fracture 3D model diagram

    图  4  Makebot程序中建立的三维模型

    Figure  4.  3D model established in Makebot

    图  5  打印成型的三维实体模型

    Figure  5.  3D solid model of printing molding

    图  6  RayBot 3D打印机

    Figure  6.  RayBot 3D printer

    图  7  试验系统装置示意图

    Figure  7.  Schematic of the test system device

    图  8  法向加载系统

    Figure  8.  Normal loading system

    图  9  模拟裂隙系统

    Figure  9.  Simulated fracture system

    图  10  不同水压下JRC与K0的关系曲线

    Figure  10.  Relationship between JRC and K0 under different hydraulics pressures

    图  11  流体在粗糙裂隙中流动示意图

    Figure  11.  Schematic of fluid flow in rough fracture

    图  12  不同粗糙度裂隙$ - \nabla P$Q的关系曲线

    Figure  12.  Relationship between $ - \nabla P$ and Q with different roughness fractures

    图  13  法向压力恒定不同水压下JRC与K的关系曲线。(a)法向压力为0.25 MPa;(b)法向压力为0.50 MPa; (c)法向压力为0.75 MPa;(d)法向压力为1.00 MPa

    Figure  13.  Relationship between JRC and K under different water pressures when normal pressure is constant: (a) normal pressure of 0.25 MPa; (b) normal pressure of 0.50 MPa; (c) normal pressure of 0.75 MPa; (d) normal pressure of 1.00 MPa

    图  14  参数$\delta $与压力梯度$ - \nabla P$的关系曲线。(a)法向压力为0.25 MPa;(b)法向压力为1.00 MPa

    Figure  14.  Relationship between $\delta $ and $ - \nabla P$: (a) normal pressure of 0.25 MPa; (b) normal pressure of 1.00 MPa

    表  1  数字化后JRC的标准曲线图[15]

    Table  1.   Standard curve diagram of JRC after digitization

    NumberStandard joint profileJRC value (Specific value)
    10–2 (0.4)
    22–4 (2.8)
    34–6 (5.8)
    46–8 (6.7)
    58–10 (9.5)
    610–12 (10.8)
    712–14 (12.8)
    814–16 (14.5)
    916–18 (16.7)
    1018–20 (18.7)
    下载: 导出CSV

    表  2  无法向压力改变水压的试验方案

    Table  2.   Test scheme for changing hydraulic pressures without normal pressures

    NumberHydraulic pressure,
    P/MPa
    Change value in fracture
    aperture/mm
    10.040.16
    20.090.17
    30.140.19
    40.190.21
    50.240.23
    60.290.24
    下载: 导出CSV

    表  3  Forchheimer 方程拟合的数值

    Table  3.   Values of Forchheimer equation fitting

    JRC (Specific value)Coefficient, ACoefficient, BCorrelation coefficient, R2
    6 (10.8)3.19−0.990.99
    7 (12.8)1.84−0.490.99
    8 (14.5)1.39−0.310.99
    9 (16.7)1.08−0.150.99
    10 (18.7)0.86−0.090.99
    下载: 导出CSV

    表  4  线性函数拟合的数值

    Table  4.   Values of linear function fitting

    Normalpressure, F/MPaHydraulic pressure, P/MPaCoefficient,
    a
    Coefficient,
    b
    Correlation coefficient, R2Normalpressure, F/MPaHydraulic pressure, P/MPaCoefficient,
    a
    Coefficient,
    b
    Correlation coefficient, R2
    0.250.0426.54−1.040.981.000.0412.16−0.510.94
    0.0928.72−1.120.990.0913.23−0.510.94
    0.1431.51−1.230.980.1416.18−0.610.97
    0.1935.21−1.350.970.1917.63−0.670.99
    0.2445.29−1.890.980.2425.34−1.050.96
    0.2960.13−2.650.980.2936.60−1.640.98
    下载: 导出CSV

    表  5  法向压力恒定不同水力压力下渗透系数的变化量

    Table  5.   Permeability change under different hydraulic pressures and constant normal pressure

    Normal pressure, F/MPaHydraulic pressure, P/MPaPermeability change, K/(m·s−1)Normal pressure, F/MPaHydraulic pressure, P/MPaPermeability change, K/(m·s−1)
    0.250.048.410.750.043.61
    0.098.870.093.33
    0.149.670.144.53
    0.1910.370.196.56
    0.2415.290.249.37
    0.2920.590.2913.88
    0.500.046.371.000.043.75
    0.096.720.094.17
    0.147.180.144.53
    0.199.140.195.12
    0.2410.660.248.53
    0.2916.870.2912.12
    下载: 导出CSV

    表  6  不同粗糙度裂隙渗流宽度的变化情况

    Table  6.   Variation of apertures of fractures with different roughnesses

    Normal pressure,
    F/MPa
    Hydraulic pressure,
    P/MPa
    Change value in fracture aperture with different JCR, e/mmNormal pressure,
    F/MPa
    Hydraulic pressure,
    P/MPa
    Change value in fracture aperture with different JCR, e /mm
    10.812.814.516.718.710.812.814.516.718.7
    0.250.040.060.050.040.050.041.000.040.030.030.020.020.02
    0.090.060.050.050.050.040.090.030.030.020.020.02
    0.140.070.060.060.050.040.140.030.040.030.020.02
    0.190.070.060.060.050.040.190.040.040.030.030.02
    0.240.080.070.0.60.060.050.240.040.040.040.030.03
    0.290.080.080.070.060.060.290.040.040.040.030.03
    下载: 导出CSV

    表  7  负指数函数拟合的数值

    Table  7.   Values of negative exponential function fitting

    Hydraulic pressure, F/MPaCoefficient, aCoefficient, bCorrelation coefficient, R2
    0.0417.15−1.720.95
    0.0926.88−1.860.91
    0.1465.03−2.180.96
    0.1988.40−2.290.97
    0.2490.23−2.430.96
    0.29102.56−3.010.95
    下载: 导出CSV
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