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

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
  • [1] MANDELBROT B B. Fractal: Form, chance and dimension[M]. San Francisco: Freeman, 1977.
    [2] OUYANG M, TAKAHASHI A. Influence of initial fines content on fabric of soils subjected to internal erosion[J]. Canadian Geotechnical Journal, 2016, 53(2): 299-313. doi:  10.1139/cgj-2014-0344
    [3] ISRAR J, INDRARATNA B. Study of critical hydraulic gradients for seepage-induced failures in granular soils[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2019, 145(7): 04019025. doi:  10.1061/(ASCE)GT.1943-5606.0002062
    [4] WANG Y, WANG S J, DUAN X B, et al. Physical modelling of initial seepage failure process[J]. International Journal of Physical Modelling in Geotechnics, 2015, 15(4): 1-9.
    [5] 陈建生, 何文政, 王霜, 等. 双层堤基管涌破坏过程中上覆层渗透破坏发生发展的试验与分析[J]. 岩土工程学报,2013,35(10):1777-1783. (CHEN Jiansheng, HE Wenzheng, WANG Shuang, et al. Laboratory tests on development of seepage failure of overlying layer during piping of two-stratum dike foundation[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(10): 1777-1783. (in Chinese)

    CHEN Jiansheng, HE Wenzheng, WANG Shuang, et al. Laboratory tests on development of seepage failure of overlying layer during piping of two-stratum dike foundation[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(10): 1777-1783. (in Chinese)
    [6] 朱晟, 邓石德, 宁志远, 等. 基于分形理论的堆石料级配设计方法[J]. 岩土工程学报,2017,39(6):1151-1155. (ZHU Sheng, DENG Shide, NING Zhiyuan, et al. Gradation design method for rockfill materials based on fractal theory[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(6): 1151-1155. (in Chinese) doi:  10.11779/CJGE201706023

    ZHU Sheng, DENG Shide, NING Zhiyuan, et al. Gradation design method for rockfill materials based on fractal theory[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(6): 1151-1155. (in Chinese) doi:  10.11779/CJGE201706023
    [7] 王宇, 王士军, 谷艳昌. 基于分形理论的多孔介质渗透破坏研究[J]. 中国农村水利水电,2016(3):80-83, 87. (WANG Yu, WANG Shijun, GU Yanchang. Research on seepage failure in porous media based on fractal theory[J]. China Rural Water and Hydropower, 2016(3): 80-83, 87. (in Chinese) doi:  10.3969/j.issn.1007-2284.2016.03.019

    WANG Yu, WANG Shijun, GU Yanchang. Research on seepage failure in porous media based on fractal theory[J]. China Rural Water and Hydropower, 2016(3): 80-83, 87. (in Chinese) doi:  10.3969/j.issn.1007-2284.2016.03.019
    [8] KONG X X, LIU Q S, LU H F. Effects of rock specimen size on mechanical properties in laboratory testing[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2021, 147(5): 04021013. doi:  10.1061/(ASCE)GT.1943-5606.0002478
    [9] YOUSEFI M, SEDGHI-ASL M, PARVIZI M. Seepage and boiling around a sheet pile under different experimental configuration[J]. Journal of Hydrologic Engineering, 2016, 21(12): 06016015. doi:  10.1061/(ASCE)HE.1943-5584.0001449
    [10] 卞士海, 李国英, 米占宽. 分形理论在堆石料流变中的应用[J]. 水利水运工程学报,2017(6):60-68. (BIAN Shihai, LI Guoying, MI Zhankuan. Application of fractal theory in rockfill rheology[J]. Hydro-Science and Engineering, 2017(6): 60-68. (in Chinese)

    BIAN Shihai, LI Guoying, MI Zhankuan. Application of fractal theory in rockfill rheology[J]. Hydro-Science and Engineering, 2017(6): 60-68. (in Chinese)
    [11] 王宇, 陈超, 陈祥勇. 土石坝渗流安全预测预警研究[J]. 水利水电技术,2018,49(11):68-74. (WANG Yu, CHEN Chao, CHEN Xiangyong. Study on prediction and early-warning of seepage safety for earth-rockfill dam[J]. Water Resources and Hydropower Engineering, 2018, 49(11): 68-74. (in Chinese)

    WANG Yu, CHEN Chao, CHEN Xiangyong. Study on prediction and early-warning of seepage safety for earth-rockfill dam[J]. Water Resources and Hydropower Engineering, 2018, 49(11): 68-74. (in Chinese)
    [12] 谢和平. 分形几何及其在岩土力学中的应用[J]. 岩土工程学报,1992,14(1):14-24. (XIE Heping. Fractal geometry and its application to rock and soil materials[J]. Chinese Journal of Geotechnical Engineering, 1992, 14(1): 14-24. (in Chinese) doi:  10.3321/j.issn:1000-4548.1992.01.002

    XIE Heping. Fractal geometry and its application to rock and soil materials[J]. Chinese Journal of Geotechnical Engineering, 1992, 14(1): 14-24. (in Chinese) doi:  10.3321/j.issn:1000-4548.1992.01.002
    [13] RAMADAN S H, EL NAGGAR M H. Field monitoring and numerical analysis of large-span three-sided reinforced concrete culvert[J]. Journal of Geotechnical and Geoenvironmental Engineering, 2021, 147(4): 04021008. doi:  10.1061/(ASCE)GT.1943-5606.0002489
    [14] 徐永福, 黄寅春. 分形理论在研究非饱和土力学性质中的应用[J]. 岩土工程学报,2006,28(5):635-638. (XU Yongfu, HUANG Yinchun. Fractal-textured soils and their unsaturated mechanical properties[J]. Chinese Journal of Geotechnical Engineering, 2006, 28(5): 635-638. (in Chinese) doi:  10.3321/j.issn:1000-4548.2006.05.017

    XU Yongfu, HUANG Yinchun. Fractal-textured soils and their unsaturated mechanical properties[J]. Chinese Journal of Geotechnical Engineering, 2006, 28(5): 635-638. (in Chinese) doi:  10.3321/j.issn:1000-4548.2006.05.017
    [15] TAO G L, WU X K, XIAO H L, et al. A unified fractal model for permeability coefficient of unsaturated soil[J]. Fractals, 2019, 27(1): 1940012. doi:  10.1142/S0218348X19400127
    [16] 段祥宝, 刘运化, 杨超, 等. 土体渗透变形及渗透破坏过程中分形特征初探[J]. 水电能源科学,2013,31(7):100-103, 214. (DUAN Xiangbao, LIU Yunhua, YANG Chao, et al. Preliminary study on fractal law of levees soil seepage deformation and failure[J]. Water Resources and Power, 2013, 31(7): 100-103, 214. (in Chinese)

    DUAN Xiangbao, LIU Yunhua, YANG Chao, et al. Preliminary study on fractal law of levees soil seepage deformation and failure[J]. Water Resources and Power, 2013, 31(7): 100-103, 214. (in Chinese)
    [17] 陶高梁, 李进, 崔惜琳. 不同颗粒级配的砂土渗流破坏特性[J]. 土木工程与管理学报,2019,36(2):90-97. (TAO Gaoliang, LI Jin, CUI Xilin. Seepage failure characteristics of sand with different grain composition[J]. Journal of Civil Engineering and Management, 2019, 36(2): 90-97. (in Chinese) doi:  10.3969/j.issn.2095-0985.2019.02.014

    TAO Gaoliang, LI Jin, CUI Xilin. Seepage failure characteristics of sand with different grain composition[J]. Journal of Civil Engineering and Management, 2019, 36(2): 90-97. (in Chinese) doi:  10.3969/j.issn.2095-0985.2019.02.014
    [18] RICHARDS K S, REDDY K R. Experimental investigation of initiation of backward erosion piping in soils[J]. Geotechnique, 2012, 62(10): 933-942. doi:  10.1680/geot.11.P.058
    [19] KIM H J, PARK J M, SHIN J H. Flow behaviour and piping potential at the soil-structure interface[J]. Geotechnique, 2019, 69(1): 79-84. doi:  10.1680/jgeot.17.T.020
    [20] 王小杰, 姜仁贵, 解建仓, 等. 基于分形和R/S分析的渭河干流径流变化特征研究[J]. 水利水运工程学报,2019(1):102-108. (WANG Xiaojie, JIANG Rengui, XIE Jiancang, et al. Analysis of runoff variation characteristics in the mainstream of Weihe River based on fractal theory and R/S analysis method[J]. Hydro-Science and Engineering, 2019(1): 102-108. (in Chinese)

    WANG Xiaojie, JIANG Rengui, XIE Jiancang, et al. Analysis of runoff variation characteristics in the mainstream of Weihe River based on fractal theory and R/S analysis method[J]. Hydro-Science and Engineering, 2019(1): 102-108. (in Chinese)
    [21] 刘星志, 吴悦, 潘诗婷, 等. 颗粒级配对非饱和红土土-水特征曲线的影响[J]. 水利水运工程学报,2018(5):103-110. (LIU Xingzhi, WU Yue, PAN Shiting, et al. Influences of different grain size contents on soil-water characteristic curve of unsaturated laterite based on fractal theory[J]. Hydro-Science and Engineering, 2018(5): 103-110. (in Chinese)

    LIU Xingzhi, WU Yue, PAN Shiting, et al. Influences of different grain size contents on soil-water characteristic curve of unsaturated laterite based on fractal theory[J]. Hydro-Science and Engineering, 2018(5): 103-110. (in Chinese)
    [22] TURCOTTE D L. Fractals and fragmentation[J]. Journal of Geophysical Research, 1986, 91(B2): 1921-1926. doi:  10.1029/JB091iB02p01921
    [23] TYLER S W, WHEATCRAFT S W. Fractal scaling of soil particle-size distributions: analysis and limitations[J]. Soil Science Society of America, 1992, 56(2): 362-369. doi:  10.2136/sssaj1992.03615995005600020005x
    [24] 王宇. 土石坝渗流分形特性与预警模型研究[D]. 南京: 南京水利科学研究院, 2017.

    WANG Yu. Study on seepage fractal characteristics and early-warning model of earth-rockfill dam[D]. Nanjing: Nanjing Hydraulic Research Institute, 2017. (in Chinese)
    [25] 刘炳瑞, 林建忠. 多颗粒在Giesekus流体Poiseuille流场中的异常迁移[J]. 水动力学研究与进展,2021,36(1):1-4. (LIU Bingrui, LIN Jianzhong. Abnormal migration of multi-particles in Poiseuille flow of Giesekus fluid[J]. Chinese Journal of Hydrodynamics, 2021, 36(1): 1-4. (in Chinese)

    LIU Bingrui, LIN Jianzhong. Abnormal migration of multi-particles in Poiseuille flow of Giesekus fluid[J]. Chinese Journal of Hydrodynamics, 2021, 36(1): 1-4. (in Chinese)
  • [1] 胡锦方, 潘亮, 张爱军, 任文渊, 梁志超.  棉秆纤维EPS颗粒轻量土配合比设计 . 水利水运工程学报, 2023, (1): 112-119. doi: 10.12170/20210801001
    [2] 申时钊, 涂小兵, 雷进生, 周珂, 刘金鑫, 唐亚周.  不同渗透系数的非均质黏土劈裂注浆数值模拟 . 水利水运工程学报, 2022, (5): 102-112. doi: 10.12170/20210826002
    [3] 范丹丹, 陈群, 亓立成, 王琛.  由抽水试验计算砂卵石含水层渗透系数的方法对比 . 水利水运工程学报, 2021, (4): 54-60. doi: 10.12170/20200829001
    [4] 王小杰, 姜仁贵, 解建仓, 汪妮, 李晓春.  基于分形和R/S分析的渭河干流径流变化特征研究 . 水利水运工程学报, 2019, (1): 102-108. doi: 10.16198/j.cnki.1009-640X.2019.01.013
    [5] 饶云康, 丁瑜, 倪强, 许文年, 刘大翔, 张恒.  基于GA-BP神经网络的粗粒土渗透系数预测 . 水利水运工程学报, 2018, (6): 92-97. doi: 10.16198/j.cnki.1009-640X.2018.06.012
    [6] 卞士海, 李国英, 米占宽.  分形理论在堆石料流变中的应用 . 水利水运工程学报, 2017, (6): 60-68. doi: 10.16198/j.cnki.1009-640X.2017.06.009
    [7] 张国栋, 廖爱明, 李泯蒂, 邱重阳, 徐志华.  碎石土渗透特性试验研究 . 水利水运工程学报, 2016, (5): 91-95.
    [8] 陆一忠, 陈生水, 米占宽.  防汛抢险训练场渗透破坏段设计方案试验分析 . 水利水运工程学报, 2015, (2): 67-72.
    [9] 王俊杰, 卢孝志, 邱珍锋, 梁越.  粗粒土渗透系数影响因素试验研究 . 水利水运工程学报, 2013, (6): 16-20.
    [10] 袁荣宏,白杰,吴桂芬.  水泥土渗透系数随围压变化的试验研究 . 水利水运工程学报, 2012, (5): 13-17.
    [11] 刘红岩,戎涛.  采用止水挡墙的基坑渗流场模拟 . 水利水运工程学报, 2008, (2): -.
    [12] 唐晓松,郑颖人.  水位下降过程中超孔隙水压力对边坡稳定性的影响 . 水利水运工程学报, 2007, (1): 1-6.
    [13] 傅志敏,向衍,周志芳.  基于Marc的混凝土坝与坝基渗透系数反演 . 水利水运工程学报, 2005, (1): 23-27.
    [14] 沈珠江,陈铁林.  岩样变形和破坏过程的二元介质模拟 . 水利水运工程学报, 2004, (1): 1-5.
    [15] 刘玉峰,黄勇,李忠辉,王消川.  吉利河水库大坝渗流观测资料分析 . 水利水运工程学报, 2004, (3): 75-78.
    [16] 张士辰,李雷.  粗砂渗透系数与抗渗强度概型分布 . 水利水运工程学报, 2004, (3): 58-61.
    [17] 朱伟,山村和也.  堤防地基渗透破坏机制及其治理 . 水利水运工程学报, 1999, (4): 338-347.
    [18] 徐尚壁.  压水试验求测渗透系数的射渗理论与方法 . 水利水运工程学报, 1996, (1): -.
    [19] 李大梁.  低透水性土的渗透系数测定 . 水利水运工程学报, 1984, (3): -.
    [20] 沙金煊.  多孔介质中的管涌研究 . 水利水运工程学报, 1981, (3): -.
  • 加载中
图(6) / 表 (2)
计量
  • 文章访问数:  335
  • HTML全文浏览量:  134
  • PDF下载量:  41
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-06-29
  • 网络出版日期:  2022-04-16
  • 刊出日期:  2022-07-03

/

返回文章
返回