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    求解岩体裂隙产状三维概率分布的数值方法

    赵萌 唐辉明 詹红兵 张俊荣

    赵萌, 唐辉明, 詹红兵, 张俊荣, 2022. 求解岩体裂隙产状三维概率分布的数值方法. 地球科学, 47(4): 1470-1482. doi: 10.3799/dqkx.2021.056
    引用本文: 赵萌, 唐辉明, 詹红兵, 张俊荣, 2022. 求解岩体裂隙产状三维概率分布的数值方法. 地球科学, 47(4): 1470-1482. doi: 10.3799/dqkx.2021.056
    Zhao Meng, Tang Huiming, Zhan Hongbing, Zhang Junrong, 2022. A Numerical Method for Solving Three-Dimensional Probability Distribution of Rockmass Fracture Orientations. Earth Science, 47(4): 1470-1482. doi: 10.3799/dqkx.2021.056
    Citation: Zhao Meng, Tang Huiming, Zhan Hongbing, Zhang Junrong, 2022. A Numerical Method for Solving Three-Dimensional Probability Distribution of Rockmass Fracture Orientations. Earth Science, 47(4): 1470-1482. doi: 10.3799/dqkx.2021.056

    求解岩体裂隙产状三维概率分布的数值方法

    doi: 10.3799/dqkx.2021.056
    基金项目: 

    国家重点研发计划项目 2017YFC1501305

    国家重大科研仪器研制项目 41827808

    中国地质大学(武汉)中央高校基本科研业务费专项资金资助项目 1810491T13

    详细信息
      作者简介:

      赵萌(1991-),男,博士生,主要从事工程地质和岩土工程方面的学习和研究工作.ORCID:0000-0002-0922-0996. E-mail:zhaomeng@cug.edu.cn

      通讯作者:

      唐辉明,ORCID:0000-0002-0385-8155. E-mail: tanghm@cug.edu.cn

    • 中图分类号: P64

    A Numerical Method for Solving Three-Dimensional Probability Distribution of Rockmass Fracture Orientations

    • 摘要: 测线法是一种广泛使用的裂隙几何特征野外观测技术,但它获得的一维产状观测数据不能代表三维空间内的概率分布.在实测裂隙倾向和倾角之间相互独立的假设基础上,借用概率论和微积分建立了一维数据和三维分布的数值解关系式,进而提出一种由一维观测数据求解三维概率分布的方法.该方法的实现步骤是:(1)通过关系式数值求解产状的三维累积概率;(2)使用如Kolmogorov-Smirnov逼近法对累积概率进行分布形式和分布参数的估计.结合两类裂隙(层理面和节理面)的观测数据,比较了本文方法与Fouché方法的求解误差,并调查了样本容量对本文方法求解误差的影响.结果表明,本文方法求解误差更低.样本容量接近150时,可实现最低求解误差;当超过150时,求解误差不会随样本容量的增加而显著降低.同时,应用于互不平行的裂隙个体如节理面时,本文方法效果明显.而应用于近似平行的裂隙个体如层理面时,效果不明显.

       

    • 图  1  测线与裂隙交切关系模型(二维概化)

      假设包含于同一裂隙组的两个子集,子集1和子集2.图a为测线与子集1的夹角小于测线与子集2的夹角,即θ1 < θ2;图b为极端情况θ1=0° < θ2

      Fig.  1.  Illustration of intersection of scanline to fractures

      图  2  本文方法的实现流程

      Fig.  2.  Workflow of the presented method

      图  3  3D-DFN模型和其上的产状一维观测样本

      a. 3D-DFN模型,红线表示测线技术观测的裂隙;b.产状一维观测样本,采用上半球等角度赤平投影成图,N代表样本容量

      Fig.  3.  3D-DFN model and 1D orientation sample

      图  4  根方误差-样本容量

      a.三维产状服从正态分布,左图为倾向,右图为倾角;b. 对数正态分布;c.均匀分布;d.指数分布

      Fig.  4.  Root square error versus sample size

      图  5  案例Ⅰ

      a.采用测线观测层理面产状;b.实测产状一维观测样本;c.产状三维分布,左图是Fouché方法求解的,右图是本文方法求解的;d. 3D-DFN模型,红线表示被测线技术观测的裂隙,左图建模参数是Fouché方法求解的产状三维分布,右图建模参数是本文方法求解的产状三维分布;e.模拟产状一维观测样本,左图取样于Fouché方法求解的产状三维分布构建的模型,右图取样于本文方法求解的产状三维分布构建的模型

      Fig.  5.  Case Ⅰ

      图  6  案例Ⅱ

      a.实测产状一维观测样本;b.产状三维分布,左图是Fouché方法求解的,右图是本文方法求解的;c. 模拟产状一维观测样本,左图取样于Fouché方法求解的产状三维分布构建的模型,右图取样于本文方法求解的产状三维分布构建的模型

      Fig.  6.  Case Ⅱ

      图  7  双尾显著性概率-样本容量

      双尾显著性概率定量表达了模拟样本与实测样本在分布上的差异大小.a.倾向;b.倾角

      Fig.  7.  Two-tailed significance versus sample size

      图  8  一维产状观测分布和本文方法求解的三维分布的参数对比

      a.均值,左图是倾向,右图是倾角;b.标准差

      Fig.  8.  Comparison of 1D observation distribution parameters and 3D distribution parameters solved using the proposed method

      表  1  3D-DFN建模参数

      Table  1.   3D-DFN modeling parameters

      体密度(m-3 模拟区 应用区 测线
      长(m) 宽(m) 高(m) 长(m) 宽(m) 高(m) 倾伏向(°) 倾伏角(°)
      7 30 30 30 20 20 20 0 45
      模型 产状 半径(m) 样本容量
      倾向(°) 倾角(°)
      N(180, 102 N(45, 102 Exp(1.5) 50/100/150/200/300/500/1 000
      N(180, 152 N(45, 152 Exp(1.5) 50/100/150/200/300/500/1 000
      N(180, 202 N(45, 202 Exp(1.5) 50/100/150/200/300/500/1 000
      lnN(5.19, 0.062 lnN(3.78, 0.222 Exp(1.5) 50/100/150/200/300/500/1 000
      lnN(5.19, 0.082 lnN(3.75, 0.322 Exp(1.5) 50/100/150/200/300/500/1 000
      lnN(5.19, 0.112 lnN(3.72, 0.422 Exp(1.5) 50/100/150/200/300/500/1 000
      U(160, 200) U(25, 65) Exp(1.5) 50/100/150/200/300/500/1 000
      U(150, 210) U(15, 75) Exp(1.5) 50/100/150/200/300/500/1 000
      U(140, 220) U(5, 85) Exp(1.5) 50/100/150/200/300/500/1 000
      Exp(180) Exp(45) Exp(2.5) 50/100/150/200/300/500/1 000
      Exp(185) Exp(50) Exp(2.5) 50/100/150/200/300/500/1 000
      Exp(190) Exp(55) Exp(2.5) 50/100/150/200/300/500/1 000
      注:表中Nij2)为正态分布,其中i表示均值,j表示标准差;Exp(k)为指数分布,其中k表示均值;lnNlm2)为对数正态分布,其中l表示位置参数,m表示比例参数;Unp)为均匀分布,其中n表示上限,p表示下限.
      下载: 导出CSV

      表  2  采用Pearson卡方检验获得的产状独立性测试结果

      Table  2.   Orientation independence output using the Pearson chi-square test

      样本M-s 显著性概率 样本M-s 显著性概率 样本M-s 显著性概率 样本M-s 显著性概率 样本M-s 显著性概率 样本M-s 显著性概率
      Ⅰ-50 0.528 Ⅲ-50 0.819 Ⅴ-50 0.492 Ⅶ-50 0.512 Ⅸ-50 0.452 Ⅺ-50 0.429
      Ⅰ-100 0.526 Ⅲ-100 0.330 Ⅴ-100 0.827 Ⅶ-100 0.987 Ⅸ-100 0.475 Ⅺ-100 0.863
      Ⅰ-150 0.497 Ⅲ-150 0.592 Ⅴ-150 0.874 Ⅶ-150 0.835 Ⅸ-150 0.778 Ⅺ-150 0.537
      Ⅰ-200 0.259 Ⅲ-200 0.460 Ⅴ-200 0.629 Ⅶ-200 0.926 Ⅸ-200 0.565 Ⅺ-200 0.292
      Ⅰ-300 0.636 Ⅲ-300 0.673 Ⅴ-300 0.810 Ⅶ-300 0.562 Ⅸ-300 0.472 Ⅺ-300 0.415
      Ⅰ-500 0.773 Ⅲ-500 0.550 Ⅴ-500 0.754 Ⅶ-500 0.789 Ⅸ-500 0.969 Ⅺ-500 0.217
      Ⅰ-1000 0.830 Ⅲ-1000 0.543 Ⅴ-1000 0.424 Ⅶ-1000 0.733 Ⅸ-1000 0.987 Ⅺ-1000 0.246
      Ⅱ-50 0.297 Ⅳ-50 0.756 Ⅵ-50 0.396 Ⅷ-50 0.954 X-50 0.992 Ⅻ-50 0.942
      Ⅱ-100 0.327 Ⅳ-100 0.344 Ⅵ-100 0.607 Ⅷ-100 0.486 X-100 0.907 Ⅻ-100 0.859
      Ⅱ-150 0.316 Ⅳ-150 0.483 Ⅵ-150 0.256 Ⅷ-150 0.518 X-150 0.704 Ⅻ-150 0.803
      Ⅱ-200 0.252 Ⅳ-200 0.301 Ⅵ-200 0.316 Ⅷ-200 0.487 X-200 0.874 Ⅻ-200 0.925
      Ⅱ-300 0.593 Ⅳ-300 0.912 Ⅵ-300 0.313 Ⅷ-300 0.981 X-300 0.838 Ⅻ-300 0.478
      Ⅱ-500 0.505 Ⅳ-500 0.568 Ⅵ-500 0.372 Ⅷ-500 0.702 X-500 0.483 Ⅻ-500 0.938
      Ⅱ-1000 0.524 Ⅳ-1000 0.089 Ⅵ-1000 0.552 Ⅷ-1000 0.433 X-1000 0.209 Ⅻ-1000 0.260
      注:样本M-s中M是模型编号、s是样本容量.显著性概率指的是双尾值.
      下载: 导出CSV

      表  3  本文方法求解的产状三维概率分布

      Table  3.   3D probability distribution of orientations solved using the presented method

      样本 产状 样本 产状
      倾向(°) 倾角(°) 倾向(°) 倾角(°)
      Ⅰ-50 N(178.3, 8.02 N(46.1, 8.12 Ⅶ-50 U(160.3, 200.2) U(25.0, 64.9)
      Ⅰ-100 N(178.8, 8.52 N(46.5, 8.92 Ⅶ-100 U(160.4, 199.9) U(25.0, 64.9)
      Ⅰ-150 N(179.3, 8.52 N(45.6, 9.42 Ⅶ-150 U(160.3, 199.9) U(25.0, 64.9)
      Ⅰ-200 N(179.0, 9.22 N(45.3, 9.02 Ⅶ-200 U(160.3, 199.9) U(25.0, 64.9)
      Ⅰ-300 N(178.9, 9.42 N(45.5, 9.42 Ⅶ-300 U(160.1, 199.9) U(25.0, 65.0)
      Ⅰ-500 N(179.5, 10.12 N(45.0, 10.12 Ⅶ-500 U(160.1, 200.1) U(25.0, 65.0)
      Ⅰ-1000 N(179.7, 10.22 N(45.0, 10.12 Ⅶ-1000 U(160.0, 200.1) U(25.0, 65.0)
      Ⅱ-50 N(176.9, 13.72 N(46.2, 11.62 Ⅷ-50 U(154.5, 217.6) U(13.0, 72.1)
      Ⅱ-100 N(177.6, 14.92 N(45.9, 11.52 Ⅷ-100 U(153.5, 212.9) U(11.4, 71.7)
      Ⅱ-150 N(178.2, 15.12 N(45.8, 12.72 Ⅷ-150 U(151.7, 211.8) U(12.9, 72.0)
      Ⅱ-200 N(178.6, 15.32 N(45.2, 13.92 Ⅷ-200 U(152.2, 211.4) U(12.5, 71.2)
      Ⅱ-300 N(178.9, 15.32 N(44.8, 14.12 Ⅷ-300 U(150.7, 209.9) U(13.6, 73.2)
      Ⅱ-500 N(178.8, 14.72 N(45.2, 14.32 Ⅷ-500 U(150.8, 209.5) U(14.2, 74.1)
      Ⅱ-1000 N(179.4, 15.32 N(45.4, 14.72 Ⅷ-1000 U(150.3, 210.2) U(15.2, 73.7)
      Ⅲ-50 N(185.2, 16.62 N(43.5, 15.72 Ⅸ-50 U(145.9, 215.2) U(2.0, 82.0)
      Ⅲ-100 N(184.4, 18.92 N(40.2, 18.22 Ⅸ-100 U(141.3, 218.9) U(1.4, 78.5)
      Ⅲ-150 N(184.0, 19.92 N(43.2, 19.82 Ⅸ-150 U(142.4, 219.5) U(2.7, 80.4)
      Ⅲ-200 N(182.5, 19.22 N(43.2, 18.92 Ⅸ-200 U(142.4, 213.6) U(3.0, 80.6)
      Ⅲ-300 N(181.9, 18.62 N(44.5, 18.02 Ⅸ-300 U(141.3, 219.0) U(3.8, 81.6)
      Ⅲ-500 N(180.9, 18.92 N(43.1, 18.42 Ⅸ-500 U(142.8, 214.0) U(5.7, 82.7)
      Ⅲ-1000 N(180.2, 19.82 N(44.5, 18.92 Ⅸ-1000 U(140.1, 218.8) U(6.2, 84.1)
      Ⅳ-50 lnN(5.203, 0.0382 lnN(3.819, 0.1662 X-50 Exp(355.5) Exp(87.4)
      Ⅳ-100 lnN(5.198, 0.0502 lnN(3.803, 0.1972 X-100 Exp(311.6) Exp(83.1)
      Ⅳ-150 lnN(5.200, 0.0552 lnN(3.795, 0.2222 X-150 Exp(107.3) Exp(79.1)
      Ⅳ-200 lnN(5.199, 0.0562 lnN(3.797, 0.2082 X-200 Exp(133.1) Exp(72.6)
      Ⅳ-300 lnN(5.198, 0.0552 lnN(3.796, 0.2112 X-300 Exp(102.6) Exp(82.5)
      Ⅳ-500 lnN(5.196, 0.0572 lnN(3.796, 0.2202 X-500 Exp(104.5) Exp(81.7)
      Ⅳ-1000 lnN(5.194, 0.0562 lnN(3.796, 0.2162 X-1000 Exp(109.0) Exp(82.2)
      Ⅴ-50 lnN(5.210, 0.0552 lnN(3.869, 0.2422 Ⅺ-50 Exp(81.7) Exp(71.7)
      Ⅴ-100 lnN(5.199, 0.0702 lnN(3.831, 0.2562 Ⅺ-100 Exp(104.6) Exp(85.8)
      Ⅴ-150 lnN(5.194, 0.0772 lnN(3.752, 0.3102 Ⅺ-150 Exp(118.4) Exp(62.9)
      Ⅴ-200 lnN(5.199, 0.0752 lnN(3.764, 0.2952 Ⅺ-200 Exp(110.9) Exp(61.9)
      Ⅴ-300 lnN(5.197, 0.0772 lnN(3.752, 0.3062 Ⅺ-300 Exp(102.5) Exp(70.6)
      Ⅴ-500 lnN(5.194, 0.0772 lnN(3.757, 0.2962 Ⅺ-500 Exp(99.9) Exp(73.2)
      Ⅴ-1000 lnN(5.194, 0.0782 lnN(3.755, 0.3022 Ⅺ-1000 Exp(99.1) Exp(76.5)
      Ⅵ-50 lnN(5.210, 0.0762 lnN(3.845, 0.3492 Ⅻ-50 Exp(116.3) Exp(69.5)
      Ⅵ-100 lnN(5.197, 0.0882 lnN(3.801, 0.3762 Ⅻ-100 Exp(141.4) Exp(68.1)
      Ⅵ-150 lnN(5.196, 0.1032 lnN(3.757, 0.3942 Ⅻ-150 Exp(114.6) Exp(66.7)
      Ⅵ-200 lnN(5.192, 0.1012 lnN(3.768, 0.3882 Ⅻ-200 Exp(107.0) Exp(72.9)
      Ⅵ-300 lnN(5.192, 0.0992 lnN(3.755, 0.3982 Ⅻ-300 Exp(117.6) Exp(71.7)
      Ⅵ-500 lnN(5.193, 0.0982 lnN(3.759, 0.3932 Ⅻ-500 Exp(117.9) Exp(76.9)
      Ⅵ-1000 lnN(5.191, 0.1022 lnN(3.763, 0.3912 Ⅻ-1000 Exp(118.7) Exp(77.4)
      下载: 导出CSV

      表  4  3D-DFN建模部分参数

      Table  4.   3D-DFN modeling partial parameters

      体密度(m-3 直径(m) 隙宽(mm) 模拟区
      长(m) 宽(m) 高(m)
      4 Exp(0.5) Exp(1.2) 10 10 10
      下载: 导出CSV
    • [1] Alghalandis, Y.F., 2017. ADFNE: Open Source Software for Discrete Fracture Network Engineering, Two and Three Dimensional Applications. Computers & Geosciences, 102: 1-11. https://doi.org/10.1016/j.cageo.2017.02.002
      [2] Berrone, S., Canuto, C., Pieraccini, S., et al., 2015. Uncertainty Quantification in Discrete Fracture Network Models: Stochastic Fracture Transmissivity. Computers & Mathematics with Applications, 70(4): 603-623. https://doi.org/10.1016/j.camwa.2015.05.013
      [3] Bisdom, K., Bertotti, G., Bezerra, F.H., 2017. Inter-Well Scale Natural Fracture Geometry and Permeability Variations in Low-Deformation Carbonate Rocks. Journal of Structural Geology, 97: 23-36. https://doi.org/10.1016/j.jsg.2017.02.011
      [4] Brereton, R.G., 2015. The Chi Squared and Multinormal Distributions. Journal of Chemometrics, 29(1): 9-12. https://doi.org/10.1002/cem.2680
      [5] Carvalho, L., 2015. An Improved Evaluation of Kolmogorov's Distribution. Journal of Statistical Software, 65(3): 1-7. https://doi.org/10.18637/jss.v065.c03
      [6] Follin, S., Hartley, L., Rhén, I., et al., 2014. A Methodology to Constrain the Parameters of a Hydrogeological Discrete Fracture Network Model for Sparsely Fractured Crystalline Rock, Exemplified by Data from the Proposed High-Level Nuclear Waste Repository Site at Forsmark, Sweden. Hydrogeology Journal, 22(2): 313-331. https://doi.org/10.1007/s10040-013-1080-2
      [7] Fouché, O., Diebolt, J., 2004. Describing the Geometry of 3D Fracture Systems by Correcting for Linear Sampling Bias. Mathematical Geology, 36(1): 33-63. https://doi.org/10.1023/B:MATG.0000016229.37309.fd
      [8] Kang, J.T., Wu, Q., Tang, H.M., et al., 2019. Strength Degradation Mechanism of Soft and Hard Interbedded Rock Masses of Badong Formation Caused by Rock/Discontinuity Degradation. Earth Science, 44(11): 3950-3960(in Chinese with English abstract).
      [9] Kolmogorov, A.N., 1933. Foundations of Probability. American Mathematical Society Chelsea Publishing Company, Houston, Texas.
      [10] Manda, A.K., Mabee, S.B., 2010. Comparison of Three Fracture Sampling Methods for Layered Rocks. International Journal of Rock Mechanics and Mining Sciences, 47(2): 218-226. https://doi.org/10.1016/j.ijrmms.2009.12.004
      [11] Mauldon, M., Mauldon, J.G., 1997. Fracture Sampling on a Cylinder: From Scanlines to Boreholes and Tunnels. Rock Mechanics and Rock Engineering, 30(3): 129-144. https://doi.org/10.1007/BF01047389
      [12] Peacock, D.C.P., Harris, S.D., Mauldon, M., 2003. Use of Curved Scanlines and Boreholes to Predict Fracture Frequencies. Journal of Structural Geology, 25(1): 109-119. https://doi.org/10.1016/S0191-8141(02)00016-0
      [13] Pearson, K.X., 1900. On the Criterion That a Given System of Deviations from the Probable in the Case of a Correlated System of Variables is Such That It can be Reasonably Supposed to have Arisen from Random Sampling. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 50 (302): 157-175. doi: 10.1080/14786440009463897
      [14] Roy, P., du Frane, W.L., Kanarska, Y., et al., 2016. Numerical and Experimental Studies of Particle Settling in Real Fracture Geometries. Rock Mechanics and Rock Engineering, 49(11): 4557-4569. https://doi.org/10.1007/s00603-016-1100-3
      [15] Ruan, Y.K., Chen, J.P., Li, Y.Y., et al., 2016. Identification of Homogeneous Structural Domains of Jointed Rock Masses Based on Joint Occurrence and Trace Length. Rock and Soil Mechanics, 37(7): 2028-2032(in Chinese with English abstract).
      [16] Smirnov, N., 1948. Table for Estimating the Goodness of Fit of Empirical Distributions. The Annals of Mathematical Statistics, 19(2): 279-281. doi: 10.1214/aoms/1177730256
      [17] Tang, H.M., Huang, L., Bobet, A., et al., 2016. Identification and Mitigation of Error in the Terzaghi Bias Correction for Inhomogeneous Material Discontinuities. Strength of Materials, 48(6): 825-833. https://doi.org/10.1007/s11223-017-9829-9
      [18] Tang, H.M., Huang, L., Juang, C.H., et al., 2017. Optimizing the Terzaghi Estimator of the 3D Distribution of Rock Fracture Orientations. Rock Mechanics and Rock Engineering, 50(8): 2085-2099. https://doi.org/10.1007/s00603-017-1254-7
      [19] Tang, H.M., Zhang, J.R., Huang, L., et al., 2018. Correction of Line-Sampling Bias of Rock Discontinuity Orientations Using a Modified Terzaghi Method. Advances in Civil Engineering, 2018: 1-9. https://doi.org/10.1155/2018/1629039
      [20] Terzaghi, R.D., 1965. Sources of Error in Joint Surveys. Géotechnique, 15(3): 287-304. https://doi.org/10.1680/geot.1965.15.3.287
      [21] Williams-Stroud, S., Ozgen, C., Billingsley, R.L., 2013. Microseismicity-Constrained Discrete Fracture Network Models for Stimulated Reservoir Simulation. Geophysics, 78(1): B37-B47. https://doi.org/10.1190/geo2011-0061.1
      [22] Xia, D., Ge, Y.F., Tang, H.M., et al., 2020. Segmentation of Region of Interest and Identification of Rock Discontinuities in Digital Borehole Images. Earth Science, 45(11): 4207-4217(in Chinese with English abstract).
      [23] Zaree, V., Riahi, M.A., Khoshbakht, F., et al., 2016. Estimating Fracture Intensity in Hydrocarbon Reservoir: An Approach Using DSI Data Analysis. Carbonates and Evaporites, 31(1): 101-107. https://doi.org/10.1007/s13146-015-0246-5
      [24] 亢金涛, 吴琼, 唐辉明, 等, 2019. 岩石/结构面劣化导致巴东组软硬互层岩体强度劣化的作用机制. 地球科学, 44(11): 3950-3960. doi: 10.3799/dqkx.2019.110
      [25] 阮云凯, 陈剑平, 李严严, 等, 2016. 基于裂隙产状和迹长划分岩体统计均质区研究. 岩土力学, 37(7): 2028-2032. https://www.cnki.com.cn/Article/CJFDTOTAL-YTLX201607025.htm
      [26] 夏丁, 葛云峰, 唐辉明, 等, 2020. 数字钻孔图像兴趣区域分割与岩体结构面特征识别. 地球科学, 45(11): 4207-4217. doi: 10.3799/dqkx.2020.003
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    出版历程
    • 收稿日期:  2020-11-04
    • 网络出版日期:  2022-04-29
    • 刊出日期:  2022-04-25

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