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Volume 38 Issue 3
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DU Xiu-li, SONG Jia, LI Liang. Explicit-implicit staggered algorithm of u-p formulation for dynamic problems of fluid-saturated porous media[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(3): 395-403. DOI: 10.11779/CJGE201603002
Citation: DU Xiu-li, SONG Jia, LI Liang. Explicit-implicit staggered algorithm of u-p formulation for dynamic problems of fluid-saturated porous media[J]. Chinese Journal of Geotechnical Engineering, 2016, 38(3): 395-403. DOI: 10.11779/CJGE201603002
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Explicit-implicit staggered algorithm of u-p formulation for dynamic problems of fluid-saturated porous media

  • Key Lab of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing 100124, China

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  • Received Date: December 02, 2014
  • Published Date: March 24, 2016
    Graphical Abstract
    • Abstract
  • In order to describe the dynamic response of fluid-saturated porous media with the formulation of soil displacement u and pore pressure p, an explicit-implicit staggered algorithm is proposed based on the central difference method and precise time-integration method. The Gauss integration, trapezoid integration and the second-order Lagrange interpolation polynomial are utilized to simulate the soil displacement in the inhomogeneous term of the pore pressure formulation, respectively. Furthermore, an acubic spline interpolation method is developed based on the precise time-integration method, and it can avoid the computation of the inverse matrixes involved coupling velocity term. Finally, some cases are adopted to verify the proposed method. The computational results obtained by the proposed method have a good agreement with those by the Zienkiewicz's explicit-implicit method, indicating the effectiveness of the proposed approach.
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    • References (23)
  • [1]
    ZIENKIEWICZ O C, CHANG C T, BETTESS P. Drained, undrained, consolidating, and dynamic behavior assumptions in soils: Limits of validity[J]. Géotechnique, 1980, 30(4): 385-395.
    [2]
    李小军, 廖振鹏, 杜修力. 有阻尼体系动力问题的一种显式差分解法[J]. 地震工程与工程振动, 1992, 12(4): 74-79. (LI Xiao-jun, LIAO Zhen-peng, DU Xiu-li. An explicit finite difference method for viscoelastic dynamic problem[J]. Earthquake Engineering and Engineering Vibration, 1992, 12(4): 74-79. (in Chinese))
    [3]
    杜修力, 王进廷. 阻尼弹性结构动力计算的显式差分法[J]. 工程力学, 2000, 17(5): 37-43. (DU Xiu-li, WANG Jin-ting. An explicit difference formulation of dynamic response calculation of elastic structure with damping[J]. Engineering Mechanics, 2000, 17(5): 37-43. (in Chinese))
    [4]
    王进廷, 杜修力. 有阻尼体系动力分析的一种显式差分法[J]. 工程力学, 2002, 19(3): 109-112. (WANG Jin-ting, DU Xiu-li. An explicit difference method for dynamic analysis of a structure system with damping[J]. Engineering Mechanics, 2002, 19(3): 109-112. (in Chinese))
    [5]
    ZIENKIEWICZ O C, SHIOMI T. Dynamic behavior of saturated porous media: the generated Biot formulation and its numerical solution[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1984, 8(1): 71-96.
    [6]
    PARK K C. Stabilization of partitioned solution procedure for pore fluid-soil interaction analysis[J]. International Journal for Numerical Methods in Engineering, 1983, 19(11): 1669-1673.
    [7]
    SIMON B R, WU J S S, ZIENKIEWICZ O C, et al. Evaluation of u - w and u -π finite element methods for the dynamic response of saturated porous media using one-dimensional models[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1986, 10(5): 461-482.
    [8]
    ZIENKIEWICZ O C, PAUL D K, CHAN A H C. Unconditionally stable staggered solution procedure for soil-pore fluid interaction problems[J]. International Journal for Numerical Methods in Engineering, 1988, 26(5): 1039-1055.
    [9]
    HUANG M S, ZIENKIEWICZ O C. New unconditionally stable staggered solution procedures for coupled soil-pore fluid dynamic problems[J]. International Journal for Numerical Methods in Engineering, 1998, 43(6): 1029-1052.
    [10]
    HUANG M S, WU S M, ZIENKIEWICZ O C. Incompressible or nearly incompressible soil dynamic behavior-a new staggered algorithm to circumvent restrictions of mixed formulation[J]. Soil Dynamic and Earthquake Engineering, 2001, 21(2): 169-179.
    [11]
    HUANG M S, YUE Q Z, THAM L G, et al. On the stable finite element procedures for dynamic problems of saturated porous media[J]. International Journal for Numerical Methods in Engineering, 2004, 61(9): 1421-1450.
    [12]
    PREVOST J H. Wave propagation in fluid-saturated porous media: an efficient finite element procedure[J]. Soil Dynamics and Earthquake Engineering, 1985, 4(4): 183-201.
    [13]
    ZIENKIEWICZ O C, HUANG M S, WU J, et al. A new algorithm for the coupled soil-pore fluid problem[J]. Shock and Vibration, 1993, 1(1): 3-14.
    [14]
    赵成刚, 王进廷, 史培新, 等. 流体饱和两相多孔介质动力反应分析的显式有限元法[J]. 岩土工程学报, 2001, 23(2): 178-182. (ZHAO Cheng-gang, WANG Jin-ting, SHI Pei-xin, et al. Dynamic analysis of fluid-saturated porous media by using explicit finite element method [J]. Chinese Journal of Geotechnical Engineering, 2001, 23(2): 178-182. (in Chinese))
    [15]
    王进廷, 杜修力, 赵成刚. 液固两相饱和介质动力分析的一种显式有限元法[J]. 岩石力学与工程学报, 2002, 21(8): 1199-1204. (WANG Jin-ting, DU Xiu-li, ZHAO Cheng-gang. Explicit finite element method for dynamic analysis of fluid-saturated porous solid[J]. Chinese Journal of Rock Mechanics and Engineering, 2002, 21(8): 1199-1204. (in Chinese))
    [16]
    BIOT M A. Theory of propagation of elastic waves in a fluid-saturated porous solid, Ⅱ: Higher-frequency range[J]. The Acoustical Society of America, 1956, 28(2): 179-191.
    [17]
    钟万勰. 结构动力方程的精细时程积分法[J]. 大连理工大学学报, 1994, 34(2): 131-136. (ZHONG Wan-xie. On precise time-integration method for structural dynamics[J]. Journal of Dalian University of Technology, 1994, 34(2): 131-136. (in Chinese))
    [18]
    刘晶波, 杜修力. 结构动力学[M]. 北京: 机械工业出版社, 2005. (LIU Jing-bo, DU Xiu-li. Dynamics of structures[M]. Beijing: China Machine Press, 2005. (in Chinese))
    [19]
    汪梦甫, 周锡元. 结构动力方程的高斯精细时程积分法[J]. 工程力学, 2004, 21(4): 13-16. (WANG Meng-fu, ZHOU Xi-yuan. Gauss precise time-integration of structural dynamic analysis [J]. Engineering Mechanics, 2004, 21(4): 13-16. (in Chinese))
    [20]
    徐萃薇. 计算方法引论[M]. 北京: 高等教育出版社, 1985. (XU Cui-wei. Introductory lectures of computational methods[M]. Beijing: Higher Education Press, 1985. (in Chinese))
    [21]
    高小科, 邓子辰, 黄永安. 基于三次样条插值的精细积分法[J]. 振动与冲击, 2007, 26(9): 75-82. (GAO Xiao-ke, DENG Zi-chen, HUANG Yong-an. A high precise direct integration based on cubic spline interpolation[J]. Journal of vibration and shock, 2007, 26(9): 75-82. (in Chinese))
    [22]
    关 冶, 陆金甫. 数值分析基础[M]. 北京: 高等教育出版社, 2010. (GUAN Ye, LU Jin-fu. Fundamentals of numerical analysis[M]. Beijing: Higher Education Press, 2010. (in Chinese))
    [23]
    ZIENKIEWICZ O C, LEUNG K H, HINTON K. Liquefaction and permanent deformation under dynamic conditions-numerical solution and constitutive relations[M]// Soil Mechanics-Transient and Cyclic Loads, Constitutive Relations and Numerical Treatment, PANDE G N, ZIENKIEWICZ O C, ed. New York: John Wiley & Sons Ltd, 1982: 71-103.
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