Advanced Search
  • Indexed in Scopus
  • Source Journal for Chinese Scientific and Technical Papers and Citations
  • Included in A Guide to the Core Journal of China
  • Indexed in Ei Compendex
Volume 42 Issue 9
Turn off MathJax
Article Contents
Abstract
References
Related Articles
WANG Rui, ZHOU Hong-wei, ZHUO Zhuang, XUE Dong-jie, YANG Shuai. Finite difference method for space-fractional seepage process in unsaturated soil[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(9): 1759-1764. DOI: 10.11779/CJGE202009021
Citation: WANG Rui, ZHOU Hong-wei, ZHUO Zhuang, XUE Dong-jie, YANG Shuai. Finite difference method for space-fractional seepage process in unsaturated soil[J]. Chinese Journal of Geotechnical Engineering, 2020, 42(9): 1759-1764. DOI: 10.11779/CJGE202009021
shu

Finite difference method for space-fractional seepage process in unsaturated soil

  • 1.

    College of Civil Engineering, Hebei University of Engineering, Handan 056038, China

  • 2.

    School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing 100083, China

  • 3.

    Rowan University,New Jersey, 08028, USA

More Information
  • Received Date: January 28, 2018
  • Available Online: December 07, 2022
    Abstract

  • The transport process and seepage properties of underground water in unsaturated soil are of great research significance. Firstly, the transport process of underground water in unsaturated soil in an anomalous diffusion perspective is analyzed, and by involving the Conformable derivative, the space-fractional anomalous diffusion equation in one-dimensional situation is derived. Secondly, the discretization schemes of this seepage equation are derived by using the full-implicit finite difference method. The iterative matrix of numerical modelling is derived as well. In the end, the effectiveness of the numerical solution in the space-fractional anomalous diffusion equation is verified by comparing the numerical solution with the experimental data in the existing paper. In addition, the sensitivity of the parameters in the seepage equation is analyzed. The results show that the new model can well characterize the transport process of underground water in unsaturated soil, and the Conformable derivative is suitable for this method.

    • FullText(HTML)
    • References (20)
  • [1]
    陈正汉. 非饱和土与特殊土力学的基本理论研究[J]. 岩土工程学报, 2014, 36(2): 201-272. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201402002.htm

    CHEN Zheng-han. On basic theories of unsaturated soils and special soils[J]. Chinese Journal of Geotechnical Engineering, 2014, 36(2): 201-272. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC201402002.htm
    [2]
    BUCKINGHAM E. Studies on the movement of soilmoisture[J]. US Department of Agriculture, Bureau of Soils B, 1907, 38: 1-61.
    [3]
    RICHARDS L A. Capillary conduction of liquids through porous medium[J]. Physics, 1931, 1: 318-333. doi: 10.1063/1.1745010
    [4]
    RICHARDS L A. The usefulness of capillary potential to soil-moisture and plant investigations[J]. J Agr Research, 1928, 37: 719-742.
    [5]
    NEUMAN S P. Universal scaling of hydraulic conductivities and dispersivities in geologic media[J]. Water Resources Research, 1990, 26(8): 1749-1758. doi: 10.1029/WR026i008p01749
    [6]
    HATANO Y, HATANO N. Dispersive transport of ions in column experiments: an explanation of long‐tailed profiles[J]. Water Resources Research, 1998, 34(5): 1027-1033. doi: 10.1029/98WR00214
    [7]
    HAGGERTY R, MCKENNA S A, MEIGS L C. On the late‐time behavior of tracer test breakthrough curves[J]. Water Resources Research, 2000, 36(12): 3467-3479.
    [8]
    孙洪广, 陈文, 蔡行. 空间分数阶导数“反常”扩散方程数值算法的比较[J]. 计算物理, 2009, 26(5): 719-724. doi: 10.3969/j.issn.1001-246X.2009.05.011

    SUN Hong-guang, CHEN Wen, CAI Xing. Comparative study of numerical algorithms for ‘anomalous’ diffusion equation with spatial fractional derivatives[J]. Chinese Journal of Computational Physics, 2009, 26(5): 719-724. (in Chinese) doi: 10.3969/j.issn.1001-246X.2009.05.011
    [9]
    常福宣, 陈进, 黄薇. 反常扩散与分数阶对流–扩散方程[J]. 物理学报, 2005, 54(3): 1113-1117. doi: 10.3321/j.issn:1000-3290.2005.03.020

    CHANG Fu-xuan, CHEN Jin, HUANG Wei, et al. Anomalous diffusion and fractional advection-diffusion equation[J]. Acta Physica Sinica, 2005, 54(3): 1113-1117. (in Chinese) doi: 10.3321/j.issn:1000-3290.2005.03.020
    [10]
    孙洪广, 常爱莲, 陈文, 等. 反常扩散：分数阶导数建模及其在环境流动中的应用[J]. 中国科学：物理学力学天文学, 2015, 45(10): 104702. https://www.cnki.com.cn/Article/CJFDTOTAL-JGXK201510002.htm

    SUN Hong-guang, CHANG Ai-lian, CHEN Wen, et al. Anomalous diffusion: fractional derivative equation models and applications in environmental flows[J]. Scientia Sinica, 2015, 45(10): 104702. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JGXK201510002.htm
    [11]
    ZHOU H W, YANG S, ZHANG S Q. Conformable derivative approach to anomalous diffusion[J]. Physica A: Statistical Mechanics and its Applications, 2018, 491: 1001-1013. doi: 10.1016/j.physa.2017.09.101
    [12]
    KHALIL R, AL HORANI M, YOUSEF A, et al. A new definition of fractional derivative[J]. Journal of Computational and Applied Mathematics, 2014, 264: 65-70. doi: 10.1016/j.cam.2014.01.002
    [13]
    PACHEPSKY Y, TIMLIN D, RAWLS W. Generalized Richards' equation to simulate water transport in unsaturated soils[J]. Journal of Hydrology, 2003, 272(1/2/3/4): 3-13.
    [14]
    PACHEPSKY Y A, TIMLIN D. Water transport in soils as in fractal media[J]. Journal of Hydrology, 1998, 204: 98-107.
    [15]
    MILLER E E, MILLER R D. Physical theory for capillary flow phenomena[J]. Journal of Applied Physics, 1956, 27(4): 324-332. doi: 10.1063/1.1722370
    [16]
    OZISIK N. Finite Difference Methods in Heat Transfer[M]. Boca Raton: CRC Press, 1994.
    [17]
    EL ABD A, CZACHOR A, MILCZAREK J. Neutron radiography determination of water diffusivity in fired clay brick[J]. Applied Radiation and Isotopes, 2009, 67(4): 556-559.
    [18]
    陈正汉, 谢定义, 王永胜. 非饱和土的水气运动规律及其工程性质研究[J]. 岩土工程学报, 1993, 15(3): 9-20. doi: 10.3321/j.issn:1000-4548.1993.03.002

    CHEN Zheng-han, XIE Ding-yi, WANG Yong-sheng, et al. Experimental study of laws of fulid motion, suction and pore pressures in unsaturated soil[J]. Chinese Journal of Geotechnical Engineering, 1993, 15(3): 9-20. (in Chinese) doi: 10.3321/j.issn:1000-4548.1993.03.002
    [19]
    PARLANCE M B, PRASAD S N, PARLANGE J Y, et al. Extension of the Heaslet‐Alksne technique to arbitrary soil water diffusivities[J]. Water Resources Research, 1992, 28(10): 2793-2797. doi: 10.1029/92WR01683
    [20]
    梅岭, 姜朋明, 李鹏, 等. 非饱和土的土水特征曲线试验研究[J]. 岩土工程学报, 2013, 35(增刊1): 124-128. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC2013S1019.htm

    MEI Ling, JIANG Peng-ming, LI Peng, et al. Soil-water characteristic curve tests on unsaturated soil[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(S1): 124-128. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC2013S1019.htm
    • Related Articles

  • Related Articles

    [1]LI Guang-xin. Load and resistance in stability analysis of geotechnical engineering with safety factor method[J]. Chinese Journal of Geotechnical Engineering, 2021, 43(5): 918-925. DOI: 10.11779/CJGE202105016
    [2]SUN Chao-wei, CHAI Jun-rui, XU Zeng-guang, QIN Yuan, LI Gang. Stability charts for determining safety factors of 3D homogeneous slopes[J]. Chinese Journal of Geotechnical Engineering, 2018, 40(11): 2068-2077. DOI: 10.11779/CJGE201811013
    [3]JIANG Shui-hua<sup>1, 2</sup>, LI Dian-qing<sup>1, 2</sup>, ZHOU Chuang-bing<sup>1, 2</sup>. Non-intrusive stochastic finite element method for slope reliability analysis based on Latin hypercube sampling[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(zk2): 70-76.
    [4]LI Da-yong, GUO Yan-xue, GAO Yu-feng. Principle and application of pole point method of Mohr's circle[J]. Chinese Journal of Geotechnical Engineering, 2013, 35(10): 1883-1888.
    [5]GUO Yang, KE Zhai-bang. Practical research on detecting cracks in pipe piles using stress wave method[J]. Chinese Journal of Geotechnical Engineering, 2011, 33(sup2): 159-162.
    [6]MA Yongzheng, ZHENG Hong, ZHU Hehua, CAI Yongchang. Effect of cohesion on evaluating slope stability factor of safety by DDA method[J]. Chinese Journal of Geotechnical Engineering, 2009, 31(7): 1088-1093.
    [7]CHEN Wei, WANG Junxing, XIN Liping, ZHANG Wei. Lower bound method of plastic limit analysis for wedge stability[J]. Chinese Journal of Geotechnical Engineering, 2009, 31(3): 431-436.
    [8]LI Liang, CHI Shichun, LIN Gao. A new kind of complex method and its application to the search for the critical failure surface[J]. Chinese Journal of Geotechnical Engineering, 2005, 27(4): 448-452.
    [9]ZHENG Hong, LI Chunguang, Lee C.F., GE Xiurun. Finite element method for solving the factor of safety[J]. Chinese Journal of Geotechnical Engineering, 2002, 24(5): 626-628.
    [10]YANG Mingcheng, ZHEN Yingren. Local minimum factor-of-safety method based on limit equilibrium theory[J]. Chinese Journal of Geotechnical Engineering, 2002, 24(5): 600-604.

Catalog

    YANG Shuai
    • 2.

      School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing 100083, China

    1. On this Site
    2. On Google Scholar
    3. On PubMed
    Get Citation
    PDF
    XML
    Article views (404) PDF downloads (189) Cited by()
    Related
    Website Copyright © 2010 Nanjing Hydraulic Research Institute 苏ICP备05007122号-11公安联网备案号：32010602011255
    Editorial Office address：No.34 Hujuguan, Nanjing 210024, ChinaPostal Code：210024Tel：+86-25-85829534, 85829556E-mail: ge@nhri.cn

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return