• 全国中文核心期刊
  • 中国科技核心期刊
  • 美国工程索引(EI)收录期刊
  • Scopus数据库收录期刊
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

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

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

Catalog

    Article views (330) PDF downloads (186) Cited by()
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return