• 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 Weiyu, LEI Guohui, ZHAO Xin, DAI Chuanjie, GU Yuxi. Understanding governing equations for one-dimensional finite strain consolidation of saturated soils[J]. Chinese Journal of Geotechnical Engineering, 2025, 47(4): 829-839. DOI: 10.11779/CJGE20240077
Citation: WANG Weiyu, LEI Guohui, ZHAO Xin, DAI Chuanjie, GU Yuxi. Understanding governing equations for one-dimensional finite strain consolidation of saturated soils[J]. Chinese Journal of Geotechnical Engineering, 2025, 47(4): 829-839. DOI: 10.11779/CJGE20240077

Understanding governing equations for one-dimensional finite strain consolidation of saturated soils

More Information
  • Received Date: January 23, 2024
  • Available Online: June 05, 2024
  • Various forms of governing equations are available for one-dimensional finite strain consolidation of saturated soils. They are expressed using either Eulerian or Lagrangian description, each with different dependent variables, including porosity, void ratio, strain, consolidation ratio and excess pore pressure. To better understand the applicability of these equations, the coordinate transformation relationship between the two descriptions is established in terms of porosity, void ratio and displacement considering the compressibility of solid. The transformation relationship between the time derivatives of dependent variable in the two descriptions is also established. The applicability of the two descriptions to solving consolidation problems is analyzed. Considering the compressibility and inertia of solid and liquid, a governing equation system for one-dimensional finite strain consolidation in Eulerian description is derived, including continuity equation, momentum balance equation and Darcy's law. After neglecting the compressibility and inertia of solid and liquid, the system of equations is simplified into a differential equation with a single dependent variable. Through the coordinate transformation and time derivative transformation, the consolidation differential equation with Lagrangian description is also obtained. The differential equations are degenerated into various existing forms of the finite strain consolidation governing equations, and the applicability of these governing equations is clarified through the basic assumptions involved in the degenerating process.
  • [1]
    三笠正人. 軟弱黏土の压密–新压密理論とその応用[M]. 東京: 鹿島出版会, 1963.

    MIKASA M. The Consolidation of soft Clay–a New Consolidation Theory and its Application[M]. Tokyo: Kajima Institute Publishing Co., Ltd., 1963. (in Japanese)
    [2]
    MIKASA M, TAKADA N, OSHIMA A, et al. Nonlinear consolidation theory for nonhomogeneous clay layers and its application[J]. Soils and Foundations, 1998, 38(4): 205-212. doi: 10.3208/sandf.38.4_205
    [3]
    LEE K. An analytical and experimental Study of Large Strain Soil Consolidation[D]. Oxford: University of Oxford, 1979.
    [4]
    LEE K, SILLS G C. A moving boundary approach to large strain consolidation of a thin soil layer[C]// Proceedings of the Third International Conference on Numerical Methods in Geomechanics, Rotterdam, 1979.
    [5]
    MCVAY M, TOWNSEND F, BLOOMQUIST D. Quiescent consolidation of phosphatic waste clays[J]. Journal of Geotechnical Engineering, 1986, 112(11): 1033-1049. doi: 10.1061/(ASCE)0733-9410(1986)112:11(1033)
    [6]
    MCVAY M C, TOWNSEND F C, BLOOMQUIST D G. One-dimensional Lagrangian consolidation[J]. Journal of Geotechnical Engineering, 1989, 115(6): 893–898. doi: 10.1061/(ASCE)0733-9410(1989)115:6(893)
    [7]
    TAN T S, SCOTT R F. Finite strain consolidation—a study of convection[J]. Soils and Foundations, 1988, 28(3): 64-74. doi: 10.3208/sandf1972.28.3_64
    [8]
    SCHIFFMAN R L, VICK S G, GIBSON R E. Behavior and properties of hydraulic fills [J]. Journal of Geotechnical Engineering, 1989, 115(2): 280.
    [9]
    LANCELLOTTA R, PREZIOSI L. A general nonlinear mathematical model for soil consolidation problems[J]. International Journal of Engineering Science, 1997, 35(10/11): 1045-1063.
    [10]
    GIBSON R E, ENGLAND G L, HUSSEY M J L. The theory of one-dimensional consolidation of saturated clays[J]. Géotechnique, 1967, 17(3): 261-273. doi: 10.1680/geot.1967.17.3.261
    [11]
    GIBSON R E, SCHIFFMAN R L, CARGILL K W. The theory of one-dimensional consolidation of saturated clays. Ⅱ. Finite nonlinear consolidation of thick homogeneous layers[J]. Canadian Geotechnical Journal, 1981, 18(2): 280-293. doi: 10.1139/t81-030
    [12]
    KOPPULA S D. The Consolidation of Soil in Two Dimensions and with Moving Boundaries[D]. Edmonton: University of Alberta, 1970.
    [13]
    KOPPULA S D, MORGENSTERN N R. On the consolidation of sedimenting clays[J]. Canadian Geotechnical Journal, 1982, 19(3): 260-268. doi: 10.1139/t82-033
    [14]
    WALLIS G B. One-dimensional Two-Phase Flow[M]. New York: McGraw-Hill, 1969.
    [15]
    BEAR J. Dynamics of Fluids in Porous Media[M]. New York: American Elsevier Pub Co, 1988.
    [16]
    COUSSY O. Poromechanics[M]. Chichester: John Wiley & Sons, 2004.
    [17]
    AMBROSI D. Infiltration through deformable porous media[J]. ZAMM, 2002, 82(2): 115-124. doi: 10.1002/1521-4001(200202)82:2<115::AID-ZAMM115>3.0.CO;2-4
    [18]
    EL TANI M. Hydrostatic paradox of saturated media[J]. Géotechnique, 2007, 57(9): 773-777. doi: 10.1680/geot.2007.57.9.773
    [19]
    DE BOER R, EHLERS W. The development of the concept of effective stresses[J]. Acta Mechanica, 1990, 83(1): 77-92.
    [20]
    LADE P V, DE BOER R. The concept of effective stress for soil, concrete and rock[J]. Géotechnique, 1997, 47(1): 61-78. doi: 10.1680/geot.1997.47.1.61
    [21]
    陈晶晶, 雷国辉. 决定饱和岩土材料变形的有效应力及孔压系数[J]. 岩土力学, 2012, 33(12): 3696-3703.

    CHEN Jingjing, LEI Guohui. Effective stress and pore pressure coefficient controlling the deformation of saturated geomaterials[J]. Rock and Soil Mechanics, 2012, 33(12): 3696-3703. (in Chinese)
    [22]
    PANE V, SCHIFFMAN R L. A note on sedimentation and consolidation[J]. Géotechnique, 1985, 35(1): 69-72. doi: 10.1680/geot.1985.35.1.69
    [23]
    WYCKOFF R D, BOTSET H G, MUSKAT M, et al. The measurement of the permeability of porous media for homogeneous fluids[J]. Review of Scientific Instruments, 1933, 4(7): 394-405. doi: 10.1063/1.1749155
    [24]
    MUSKAT M, WYCKOFF R D. The Flow of Homogeneous Fluids Through Porous Media[M]. New York: McGraw-Hill Book Company, Inc., 1937.
    [25]
    HARR M E. Groundwater and Seepage[M]. New York: McGraw-Hill Book Company, 1962: 10-15.
    [26]
    YIH C S. Stratified flows[M]. 2d ed. New York: Academic Press, 1980.
    [27]
    Kovács G. Seepage Hydraulics[M]. Amsterdam: Elsevier Scientific Publishing Company, 1981: 476-482.
    [28]
    NADER J J. Darcy's law and the differential equation of motion[J]. Géotechnique, 2009, 59(6): 551-552. doi: 10.1680/geot.2008.T.014
    [29]
    孔祥言. 高等渗流力学[M]. 3版. 合肥: 中国科学技术大学出版社, 2020.

    KONG Xiangyan. Advanced Seepage Mechanics[M]. 3rd ed. Hefei: University of Science and Technology of China Press, 2020. (in Chinese)
    [30]
    ZIENKIEWICZ O C, CHANG C T, BETTESS P. Drained, undrained, consolidating and dynamic behaviour assumptions in soils[J]. Géotechnique, 1980, 30(4): 385-395. doi: 10.1680/geot.1980.30.4.385
    [31]
    韩昌瑞. 有限变形理论及其在岩土工程中的应用[D]. 武汉: 中国科学院研究生院(武汉岩土力学研究所), 2009.

    HAN Changrui. Finite Deformation Theory and its Application in geotechnical Engineering[D]. Wuhan: Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, 2009. (in Chinese)
    [32]
    陈明祥. 大变形弹塑性理论-上册, Ⅰ[M]. 北京: 科学出版社, 2022.

    CHEN Mingxiang. Elasticity and Plasticity of Large Deformation[M]. Beijing: Science Press, 2022. (in Chinese)
    [33]
    吴健. 饱和软土复杂非线性大变形固结特性及应用研究[D]. 杭州: 浙江大学, 2008.

    WU Jian. Study on Complex Nonlinear Large Deformation Consolidation Characteristics and Application of Saturated Soft Soil[D]. Hangzhou: Zhejiang University, 2008. (in Chinese)
    [34]
    丁洲祥, 朱合华, 丁文其. 大变形固结理论连续性条件的严格表述[J]. 同济大学学报(自然科学版), 2009, 37(4): 471-474.

    DING Zhouxiang, ZHU Hehua, DING Wenqi. A strict form of continuity condition in large-strain consolidation theory[J]. Journal of Tongji University (Natural Science), 2009, 37(4): 471-474. (in Chinese)
    [35]
    ORTENBLAD A. Mathematical theory of the process of consolidation of mud deposits[J]. Journal of Mathematics and Physics, 1930, 9(1/2/3/4): 73-149.
    [36]
    MCNABB A. A mathematical treatment of one-dimensional soil consolidation[J]. Quarterly of Applied Mathematics, 1960, 17(4): 337-347. doi: 10.1090/qam/113405
    [37]
    LEHNER F K. On the consolidation of thick layers[J]. Géotechnique, 1984, 34(2): 259-262. doi: 10.1680/geot.1984.34.2.259

Catalog

    Article views (273) PDF downloads (63) Cited by()
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return