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基于多孔介质土体分形特征的渗透系数研究

王宇 谷艳昌 王士军 段祥宝

王宇,谷艳昌,王士军,等. 基于多孔介质土体分形特征的渗透系数研究[J]. 水利水运工程学报,2022(3):50-58. doi:  10.12170/20210629001
引用本文: 王宇,谷艳昌,王士军,等. 基于多孔介质土体分形特征的渗透系数研究[J]. 水利水运工程学报,2022(3):50-58. doi:  10.12170/20210629001
(WANG Yu, GU Yanchang, WANG Shijun, et al. Permeability coefficient investigation based on fractal characteristics of porous media soil[J]. Hydro-Science and Engineering, 2022(3): 50-58. (in Chinese)) doi:  10.12170/20210629001
Citation: (WANG Yu, GU Yanchang, WANG Shijun, et al. Permeability coefficient investigation based on fractal characteristics of porous media soil[J]. Hydro-Science and Engineering, 2022(3): 50-58. (in Chinese)) doi:  10.12170/20210629001

基于多孔介质土体分形特征的渗透系数研究

doi: 10.12170/20210629001
基金项目: 国家重点研发计划课题资助项目(2018YFC0407106);国家自然科学基金资助项目(51979175);江苏省高等学校基础科学(自然科学)研究项目(21KJB560015)
详细信息
    作者简介:

    王 宇(1987—),男,江苏泗阳人,讲师,博士,主要从事岩土工程渗流分析与控制研究。E-mail:wangyu1987710@aliyun.com

  • 中图分类号: TU42

Permeability coefficient investigation based on fractal characteristics of porous media soil

  • 摘要: 堤坝工程渗流计算中确定土体渗透系数尤为重要。利用分形维数不同尺度域,分析渗透破坏试验土样无标度区,指出土体细颗粒含量是决定土体分形维数的主要因素。基于多孔介质毛管束模型,推导了渗透系数和孔隙率与分形维数之间分形关系解析式,阐释了多孔介质土体渗透系数影响因子包括分形系数、孔径大小、分形维数及流体黏滞系数。利用土体渗透破坏试验结果,进一步论证了渗透系数和孔隙率与分形维数之间的非线性关系。结果表明:当分形维数大于2.83时,孔隙率随着分形维数的增大而减小,但在颗粒吸着水和薄膜水形成的黏聚力影响下,渗透系数随着分形维数增大而减小的规律不明显。研究结果可为渗透破坏形成机制及发展过程分析提供理论依据,减少堤坝渗透破坏致灾隐患。
  • 图  1  某砂砾石粒度分布曲线

    Figure  1.  Sandy gravel size distribution curve

    图  2  不同试验土样无标度区范围

    Figure  2.  Scale-invariant space of different experimental soils

    图  3  某圆砾的粒度分布曲线

    Figure  3.  Round gravel size distribution curve

    图  4  多孔介质毛管束模型

    Figure  4.  Pipe bundle model of porous medium

    图  5  土体分形维数和孔隙率理论值与试验值对比

    Figure  5.  Comparison between theoretical values and experimental results of soil fractal dimension and porosity

    图  6  土体分形维数和渗透系数理论值与试验值对比

    Figure  6.  Comparison between theoretical values and experimental results of soil fractal dimension and permeability coefficient

    表  1  不同试验土样颗粒级配

    Table  1.   Particle size distribution of different experimental soils

    土样不同粒径区间质量百分比/%
    >20 mm20~10 mm10~5 mm5~2 mm2~1 mm1~0.5 mm0.5~0.25 mm0.25~0.10 mm0.10~0.075 mm0.075~0.025 mm<0.025 mm
    1 5.37 19.98 26.38 16.68 8.96 8.61 8.22 4.80 0.70 0.21 0.09
    2 8.32 17.92 29.97 15.85 9.12 8.55 8.34 1.80 0.08 0.04 0.01
    3 7.32 20.32 30.73 14.97 11.45 10.23 3.23 1.47 0.20 0.06 0.02
    4 6.85 19.42 26.56 18.54 13.22 9.43 4.18 1.70 0.07 0.02 0.01
    5 2.58 10.80 15.42 15.94 17.32 20.30 12.64 4.70 0.20 0.08 0.02
    6 1.16 5.30 9.70 9.93 11.22 19.37 18.32 14.55 8.45 1.98 0.02
    7 / / / 0.30 1.80 6.80 22.12 35.30 20.38 8.21 5.09
    8 / / / / 0.10 2.34 11.23 32.21 33.28 15.20 5.64
    9 / / / / / / / / 0.87 2.11 97.02
    10 / / / / / / / / 4.91 10.67 84.42
      注:编号1~4为圆砾,5~8为砂,9~10为黏土。
    下载: 导出CSV

    表  2  不同试验土样质量分形维数与无标度区统计结果

    Table  2.   Statistical results of mass fractal dimension and scale-invariant space of different experimental soils

    土样编号土样类别无标度区/mm无标度区土体
    颗粒含量/%
    分形维数相关系数
    下限上限
    1 圆砾 0.250 20.000 88.83 2.652 6 0.954 3
    2 圆砾 0.250 20.000 89.75 2.734 6 0.881 2
    3 圆砾 0.500 20.000 87.70 2.613 0 0.993 7
    4 圆砾 0.500 20.000 87.17 2.567 8 0.984 1
    5 粗砂 0.500 10.000 68.98 2.870 9 0.996 1
    6 中砂 0.250 10.000 68.54 2.839 5 0.936 9
    7 细砂 0.100 0.500 57.42 2.898 2 0.789 6
    8 粉砂 0.075 0.250 65.49 2.999 0 0.906 6
    9 黏土 0.002 0.005 97.02 2.995 1 0.903 9
    10 黏土 0.002 0.005 84.42 2.966 0 0.882 1
    下载: 导出CSV
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