留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

剪切粗糙裂隙渗流多尺度分形表征

薛东杰 侯孟冬 程建超 贾震 刘殷彤 辛翠 徐颜卓 王路军

薛东杰, 侯孟冬, 程建超, 贾震, 刘殷彤, 辛翠, 徐颜卓, 王路军. 剪切粗糙裂隙渗流多尺度分形表征[J]. 矿业科学学报, 2023, 8(5): 663-676. doi: 10.19606/j.cnki.jmst.2023.05.008
引用本文: 薛东杰, 侯孟冬, 程建超, 贾震, 刘殷彤, 辛翠, 徐颜卓, 王路军. 剪切粗糙裂隙渗流多尺度分形表征[J]. 矿业科学学报, 2023, 8(5): 663-676. doi: 10.19606/j.cnki.jmst.2023.05.008
Xue Dongjie, Hou Mengdong, Cheng Jianchao, Jia Zhen, Liu Yintong, Xin Cui, Xu Yanzhuo, Wang Lujun. Fractal model of shear-induced rough fracture flow by cross-scale description of its geometry[J]. Journal of Mining Science and Technology, 2023, 8(5): 663-676. doi: 10.19606/j.cnki.jmst.2023.05.008
Citation: Xue Dongjie, Hou Mengdong, Cheng Jianchao, Jia Zhen, Liu Yintong, Xin Cui, Xu Yanzhuo, Wang Lujun. Fractal model of shear-induced rough fracture flow by cross-scale description of its geometry[J]. Journal of Mining Science and Technology, 2023, 8(5): 663-676. doi: 10.19606/j.cnki.jmst.2023.05.008

剪切粗糙裂隙渗流多尺度分形表征

doi: 10.19606/j.cnki.jmst.2023.05.008
基金项目: 

中央高校基本科研业务经费重点领域交叉创新项目 JCCXLJ01

国家能源集团2030重大项目先导项目 GJNY2030XDXM-19-01.2

煤炭开采水资源保护与利用国家重点实验室开放基金 GJNY-20-113-04

详细信息
    作者简介:

    薛东杰(1986— ),男,山东济宁人,博士,副教授,博导,主要从事非线性渗流力学行为研究等方面的研究工作。Tel:15101127335,E-mail:xuedongjie@163.com

  • 中图分类号: TP028.8

Fractal model of shear-induced rough fracture flow by cross-scale description of its geometry

  • 摘要: 甘肃北山为高放废物深地质处置库场址的主预选区。针对场址区花岗岩受剪切破坏形成裂隙的渗流特性进行研究,具有重要的工程建设指导意义。为探究北山花岗岩多尺度粗糙裂隙几何特征对非线性渗流场演化的影响规律,对剪切条件下花岗岩裂隙断面的几何特征及渗流特性进行了分形建模研究。结果表明,粗糙裂隙的粗糙程度和开度在模型尺度变化过程中存在完全的自相似性,二者的分布特征在分布空间尺度变化过程中始终保持一致;渗流速度场、梯度场及散度场只存在局部特征的延续,尤其是不同尺度下对应的数量场均服从于正态分布;随着观察尺度的增大场内空间起伏逐渐减小,三场内的尖锐突变逐渐消失且向平滑过渡,这意味着观察尺度越大,粗糙裂隙渗流被误判为平行板渗流的概率越大,即粗糙断面渗流特性的精准描述依赖于几何尺度。
  • 图  1  压缩剪切试验示意

    Figure  1.  Schematic diagram of compression shear test

    图  2  样品剪切断面可视化重构

    Figure  2.  Visual reconstruction of two opposite fractured surfaces

    图  3  样品粗糙断面分形建模

    Figure  3.  Fractal modeling of rough section of sample

    图  4  样品粗糙断面分形维数

    Figure  4.  Fractal dimension of rough section of sample

    图  5  样品剪切表面相对粗糙高度的正态分布

    Figure  5.  Normal distribution of relative roughness height of sample shear surface

    图  6  样品剪切表面倾斜角度的正态分布

    Figure  6.  Normal distribution of tilt angle of sample shear surface

    图  7  样品剪切表面连接线长度的正态分布

    Figure  7.  Normal distribution of the length of the connecting line on the shear surface of the sample

    图  8  粗糙岩石裂隙整体形貌示意图

    Figure  8.  Schematic diagram of rough rock fracture

    图  9  开度分形模型数值建模

    Figure  9.  Numerical simulation of fractal model of fracture openness

    图  10  裂隙开度分布特征

    Figure  10.  Normal distribution of fracture openness

    图  11  粗糙裂隙渗流速度场

    Figure  11.  Velocity field of rough fracture seepage

    图  12  基于MATLAB的渗流速度场建模

    Figure  12.  MATLAB-based visualization of seepage velocity field

    图  13  渗流流速分布特征

    Figure  13.  Distribution characteristics of seepage velocity field

    图  14  渗流速度场的分形建模

    Figure  14.  Fractal modeling of seepage velocity field

    图  15  分形渗流速度场分布特征

    Figure  15.  Distribution of fractal seepage velocity field

    图  16  渗流速度梯度场的分形建模

    Figure  16.  Fractal modeling of gradient field describing the seepage velocity

    图  17  分形渗流梯度场分布特征

    Figure  17.  Distribution of fractal seepage gradient field

    图  18  渗流速度散度场的分形建模

    Figure  18.  Fractal modeling of dispersion field describing seepage velocity

    图  19  分形渗流散度场分布特征

    Figure  19.  Distribution of fractal seepage divergence field

    表  1  COMSOL软件模拟所需定量参数

    Table  1.   Quantitative parameters for COMSOL simulation

    名称 取值 描述
    rho 1 000 kg/m3 流体密度
    mu 0.001 Pa·s 流体动力黏度
    下载: 导出CSV

    表  2  COMSOL软件模拟所需变量参数

    Table  2.   Variable for COMSOL simulation

    名称 表达式 单位 描述
    a data(xy)/1 000 m 裂隙开度
    KS a2·rho·g_const/mu m/s 水利传导率
    TS KSa m2/s 导水系数
    u -KSΗx m/s x方向速度
    v -KSΗy m/s y方向速度
    U sqrt(u2+v2) m/s 速度
    注:Η—因变量。
    下载: 导出CSV
  • [1] 薛东杰, 周宏伟, 任伟光, 等. 北山花岗岩深部节理间距分布多重分形研究[J]. 岩土力学, 2016, 37(10): 2937-2944. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201610027.htm

    Xue Dongjie, Zhou Hongwei, Ren Weiguang, et al. Multi-fractal characteristics of joint geometric distribution of granite in Beishan[J]. Rock and Soil Mechanics, 2016, 37(10): 2937-2944. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201610027.htm
    [2] 王超圣, 周宏伟, 裴浩, 等. 甘肃北山地区花岗岩破坏过程能量聚集和耗散特征研究[J]. 矿业科学学报, 2018, 3(6): 536-542. http://kykxxb.cumtb.edu.cn/article/id/182

    Wang Chaosheng, Zhou Hongwei, Pei Hao, et al. Study on energy concentration and dissipation of Beishan granite in Gansu during failure process[J]. Journal of Mining Science and Technology, 2018, 3(6): 536-542. http://kykxxb.cumtb.edu.cn/article/id/182
    [3] Huang D, Li Y R. Conversion of strain energy in Triaxial Unloading Tests on Marble[J]. International Journal of Rock Mechanics and Mining Sciences, 2014, 66: 160-168. doi: 10.1016/j.ijrmms.2013.12.001
    [4] 李守巨, 刘迎曦, 冯文文, 等. 岩体裂隙中渗流场有限元随机模拟分析[J]. 岩土力学, 2009, 30(7): 2119-2125. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200907051.htm

    Li Shouju, Liu Yingxi, Feng Wenwen, et al. Randomly numerical simulation of water flow field in fractured rock mass with finite element method[J]. Rock and Soil Mechanics, 2009, 30(7): 2119-2125. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200907051.htm
    [5] Zimmerman R W, Bodvarsson G S. Hydraulic conductivity of rock fractures[J]. Transport in Porous Media, 1996, 23(1): 1-30.
    [6] Sisavath S, Al-Yaaruby A, Pain C C, et al. A simple model for deviations from the cubic law for a fracture undergoing dilation or closure[J]. Pure and Applied Geophysics, 2003, 160(5): 1009-1022.
    [7] Koyama T, Neretnieks I, Jing L. A numerical study on differences in using Navier-Stokes and Reynolds equations for modeling the fluid flow and particle transport in single rock fractures with shear[J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(7): 1082-1101. doi: 10.1016/j.ijrmms.2007.11.006
    [8] Yeo I W, Ge S M. Applicable range of the Reynolds equation for fluid flow in a rock fracture[J]. Geosciences Journal, 2005, 9(4): 347-352. doi: 10.1007/BF02910323
    [9] Zhang Q, Luo S H, Ma H C, et al. Simulation on the water flow affected by the shape and density of roughness elements in a single rough fracture[J]. Journal of Hydrology, 2019, 573: 456-468. doi: 10.1016/j.jhydrol.2019.03.069
    [10] 朱红光, 谢和平, 易成, 等. 破断岩体裂隙的流体流动特性分析[J]. 岩石力学与工程学报, 2013, 32(4): 657-663. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201304003.htm

    Zhu Hongguang, Xie Heping, Yi Cheng, et al. Analysis of properties of fluid flow in rock fractures[J]. Chinese Journal of Rock Mechanics and Engineering, 2013, 32(4): 657-663. https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201304003.htm
    [11] Xu R N, Jiang P X. Numerical simulation of fluid flow in microporous media[J]. International Journal of Heat and Fluid Flow, 2008, 29(5): 1447-1455. doi: 10.1016/j.ijheatfluidflow.2008.05.005
    [12] Wang L C, Cardenas M B, Slottke D T, et al. Modification of the Local Cubic Law of fracture flow for weak inertia, tortuosity, and roughness[J]. Water Resources Research, 2015, 51(4): 2064-2080. doi: 10.1002/2014WR015815
    [13] Xue D J, Zhang Z P, Chen C, et al. Spatial correlation-based characterization of acoustic emission signal-cloud in a granite sample by a cube clustering approach[J]. International Journal of Mining Science and Technology, 2021, 31(4): 535-551. doi: 10.1016/j.ijmst.2021.05.008
    [14] Xue D J, Lu L L, Zhou J, et al. Cluster modeling of the short-range correlation of acoustically emitted scattering signals[J]. International Journal of Coal Science & Technology, 2021, 8(4): 575-589.
    [15] Xiong F, Wei W, Xu C S, et al. Experimental and numerical investigation on nonlinear flow behaviour through three dimensional fracture intersections and fracture networks[J]. Computers and Geotechnics, 2020, 121: 103446.
    [16] Koyama T, Fardin N, Jing L, et al. Numerical simulation of shear-induced flow anisotropy and scale-dependent aperture and transmissivity evolution of rock fracture replicas[J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(1): 89-106.
    [17] 孙洪泉, 谢和平. 岩石断裂表面的分形模拟[J]. 岩土力学, 2008, 29(2): 347-352. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200802019.htm

    Sun Hongquan, Xie Heping. Fractal simulation of rock fracture surface[J]. Rock and Soil Mechanics, 2008, 29(2): 347-352. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX200802019.htm
    [18] 刘殷彤. 正交剪切条件下裂隙渗流分形建模研究[D]. 北京: 中国矿业大学(北京), 2020.
    [19] 周宏伟, 谢和平, Kwasniewski M A. 粗糙表面分维计算的立方体覆盖法[J]. 摩擦学学报, 2000, 20(6): 455-459. https://www.cnki.com.cn/Article/CJFDTOTAL-MCXX200006012.htm

    Zhou Hongwei, Xie Heping, Kwasniewski M A. Fractal dimension of rough surface estimated by the cubic covering method[J]. Tribology, 2000, 20(6): 455-459. https://www.cnki.com.cn/Article/CJFDTOTAL-MCXX200006012.htm
    [20] Chen Y D, Liang W G, Lian H J, et al. Experimental study on the effect of fracture geometric characteristics on the permeability in deformable rough-walled fractures[J]. International Journal of Rock Mechanics and Mining Sciences, 2017, 98: 121-140.
    [21] Zou L C, Jing L R, Cvetkovic V. Shear-enhanced nonlinear flow in rough-walled rock fractures[J]. International Journal of Rock Mechanics and Mining Sciences, 2017, 97: 33-45.
    [22] Xue D J, Liu Y T, Zhou H W, et al. Fractal characterization on anisotropy and fractal reconstruction of rough surface of granite under orthogonal shear[J]. Rock Mechanics and Rock Engineering, 2020, 53(3): 1225-1242.
    [23] Zhang Q G, Ju Y, Gong W B, et al. Numerical simulations of seepage flow in rough single rock fractures[J]. Petroleum, 2015, 1(3): 200-205.
    [24] Chen S J. Fracture and seepage characteristics in the floor strata when mining above a confined aquifer[J]. Journal of China University of Mining and Technology, 2012, 41(4): 536-542.
    [25] Ter Braak C J F, Prentice I C. A theory of gradient analysis[M]. Amsterdam: Elsevier, 1988: 271-317.
    [26] 刘荣道. 场论中的梯度、散度、旋度和两个重要的积分公式[J]. 湖北大学成人教育学院学报, 2002, 20(1): 58-61. https://www.cnki.com.cn/Article/CJFDTOTAL-HDAJ200201018.htm

    Liu Rongdao. Gradient, divergence, curl and two important integral formulas in field theory[J]. Journal of Adult Education College of Hubei University, 2002, 20(1): 58-61. https://www.cnki.com.cn/Article/CJFDTOTAL-HDAJ200201018.htm
  • 加载中
图(19) / 表(2)
计量
  • 文章访问数:  140
  • HTML全文浏览量:  69
  • PDF下载量:  43
  • 被引次数: 0
出版历程
  • 收稿日期:  2023-02-19
  • 修回日期:  2023-05-17
  • 刊出日期:  2023-10-31

目录

    /

    返回文章
    返回