Advanced Search
  • 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
Volume 45 Issue 11
Turn off MathJax
Article Contents
Abstract
References
Related Articles
Supplements
HU Kai, GAO Xiaowei, XU Bingbing, ZHENG Yingren. Element differential method for poroelastic problems[J]. Chinese Journal of Geotechnical Engineering, 2023, 45(11): 2403-2410. DOI: 10.11779/CJGE20221022
Citation: HU Kai, GAO Xiaowei, XU Bingbing, ZHENG Yingren. Element differential method for poroelastic problems[J]. Chinese Journal of Geotechnical Engineering, 2023, 45(11): 2403-2410. DOI: 10.11779/CJGE20221022
shu

Element differential method for poroelastic problems

  • 1.

    State Key Laboratory of Structural Analysis for Industrial Equipment, School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China

  • 2.

    Army Service College, Chongqing 400041, China

More Information
  • Received Date: August 18, 2022
  • Available Online: March 09, 2023
    Graphical Abstract
    • Abstract
  • A numerical model for solving the coupling problem of fluid flow and solid mechanics in porous media is established based on the Biot's consolidation theory, and the numerical analysis and calculation are carried out by using a new strong-form finite element method (element differential method, EDM). By comparing with the weak-form methods, the control equation for poroelastic problems can be discretized directly by the element differential method without any numerical integration calculation. Therefore, the method has a relatively simple discrete format when solving the multi-field coupling problem, and it shows high efficiency when calculating the coefficient matrix. The numerical method uses the Lagrange element in the finite element method, which can obtain relatively accurate and stable results compared with the strong-form meshless method. By introducing the element differential method and the implicit time iteration scheme, the displacement and pore pressure of each time step in the porous media can be calculated directly. Two classical numerical models are selected, one is the one-dimensional Terzaghi column model, and the other is the two-dimensional saturated soil zone model. For these two problems, the accuracy and stability of the proposed are verified by comparing with the results of analytical solution and finite element method.
    • FullText(HTML)
    • References (27)
  • [1]
    TERZAGHI K. Theoretical Soil Mechanics[M]. New York: John Wiley and Sons. 1943.
    [2]
    BIOT M A. General theory of three-dimensional consolidation[J]. Journal of Applied Physics, 1941, 12(2): 155-164. doi: 10.1063/1.1712886
    [3]
    BIOT M A. Theory of propagation of elastic waves in a fluid — saturated porous solid[J]. Journal of the Acoustical Society of America, 1956, 28: 168-191. doi: 10.1121/1.1908239
    [4]
    BORJA R I. Finite element formulation for transient pore pressure dissipation: a variational approach[J]. International Journal of Solids and Structures, 1986, 22(11): 1201-1211. doi: 10.1016/0020-7683(86)90076-4
    [5]
    SANDHU R S, WILSON E L. Finite-element analysis of seepage in elastic media[J]. Journal of the Engineering Mechanics Division, 1969, 95(3): 641-652. doi: 10.1061/JMCEA3.0001124
    [6]
    KADEETHUM T, LEE S, NICK H M. Correction to: finite element solvers for biot's poroelasticity equations in porous media[J]. Mathematical Geosciences, 2021, 53(5): 1095. doi: 10.1007/s11004-021-09942-0
    [7]
    GHASSEMI A, CHENG A H D, DIEK A, et al. A complete plane strain fictitious stress boundary element method for poroelastic media[J]. Engineering Analysis With Boundary Elements, 2001, 25(1): 41-48. doi: 10.1016/S0955-7997(00)00046-1
    [8]
    SOARES D. Iterative dynamic analysis of linear and nonlinear fully saturated porous media considering edge-based smoothed meshfree techniques[J]. Computer Methods in Applied Mechanics and Engineering, 2013, 253: 73-88. doi: 10.1016/j.cma.2012.10.010
    [9]
    KHOSHGHALB A, KHALILI N. A stable meshfree method for fully coupled flow-deformation analysis of saturated porous media[J]. Computers and Geotechnics, 2010, 37(6): 789-795. doi: 10.1016/j.compgeo.2010.06.005
    [10]
    邸元, 唐小微. 饱和多孔介质大变形分析的一种有限元-有限体积混合方法[J]. 计算力学学报, 2008, 25(4): 483-487, 493. https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG200804016.htm

    DI Yuan, TANG Xiaowei. An finite element-finite volume hybrid method for large deformation analysis of porous media[J]. Chinese Journal of Computational Mechanics, 2008, 25(4): 483-487, 493. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJG200804016.htm
    [11]
    PERAZZO F, LÖHNER R, PEREZ-POZO L. Adaptive methodology for meshless finite point method[J]. Advances in Engineering Software, 2008, 39(3): 156-166. doi: 10.1016/j.advengsoft.2007.02.007
    [12]
    高效伟, 徐兵兵, 吕军, 等. 自由单元法及其在结构分析中的应用[J]. 力学学报, 2019, 51(3): 703-713. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201903005.htm

    GAO Xiaowei, XU Bingbing, LÜ Jun, et al. Free element method and its application in structural analysis[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 703-713. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201903005.htm
    [13]
    GAO X W, GAO L F, ZHANG Y, et al. Free element collocation method: a new method combining advantages of finite element and mesh free methods[J]. Computers & Structures, 2019, 215: 10-26.
    [14]
    FANTUZZI N. New insights into the strong formulation finiteelement method for solving elastostatic andelastodynamic problems[J]. Curved and Layered Structures, 2014, 1(1): 94-127.
    [15]
    TORNABENE F, FANTUZZI N, BACCIOCCHI M. The GDQ method for the free vibration analysis of arbitrarily shaped laminated composite shells using a NURBS-based isogeometric approach[J]. Composite Structures, 2016, 154: 190-218. doi: 10.1016/j.compstruct.2016.07.041
    [16]
    樊礼恒, 王东东, 刘宇翔, 等. 节点梯度光滑有限元配点法[J]. 力学学报, 2021, 53(2): 467-481. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB202102013.htm

    FAN Liheng, WANG Dongdong, LIU Yuxiang, et al. A finite element collocation method with smoothed nodal gradients[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(2): 467-481. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB202102013.htm
    [17]
    GAO X W, HUANG S Z, CUI M A, et al. Element differential method for solving general heat conduction problems[J]. International Journal of Heat and Mass Transfer, 2017, 115: 882-894. doi: 10.1016/j.ijheatmasstransfer.2017.08.039
    [18]
    GAO X W, LI Z Y, YANG K, et al. Element differential method and its application in thermal-mechanical problems[J]. International Journal for Numerical Methods in Engineering, 2018, 113(1): 82-108. doi: 10.1002/nme.5604
    [19]
    CUI M A, XU B B, LV J, et al. Numerical solution of multi-dimensional transient nonlinear heat conduction problems with heat sources by an extended element differential method[J]. International Journal of Heat and Mass Transfer, 2018, 126: 1111-1119. doi: 10.1016/j.ijheatmasstransfer.2018.05.100
    [20]
    GAO X W, LIU H Y, XU B B, et al. Element differential method with the simplest quadrilateral and hexahedron quadratic elements for solving heat conduction problems[J]. Numerical Heat Transfer, Part B: Fundamentals, 2018, 73(4): 206-224. doi: 10.1080/10407790.2018.1461491
    [21]
    LV J, SONG C, GAO X W. Element differential method for free and forced vibration analysis for solids[J]. International Journal of Mechanical Sciences, 2019, 151: 828-841. doi: 10.1016/j.ijmecsci.2018.12.032
    [22]
    LV J, SHAO M J, CUI M A, et al. An efficient collocation approach for piezoelectric problems based on the element differential method[J]. Composite Structures, 2019, 230: 111483. doi: 10.1016/j.compstruct.2019.111483
    [23]
    胡凯, 高效伟, 徐兵兵. 求解固体力学问题的强-弱耦合形式单元微分法[J]. 力学学报, 2022, 54(7): 2050-2058. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB202207026.htm

    HU Kai, GAO Xiaowei, XU Bingbing. Strong weak coupling form element differential method for solving solid mechanics problems[J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(7): 2050-2058. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB202207026.htm
    [24]
    ZHENG Y T, GAO X W, LV J, et al. Weak-form element differential method for solving mechanics and heat conduction problems with abruptly changed boundary conditions[J]. International Journal for Numerical Methods in Engineering, 2020, 121(16): 3722-3741.
    [25]
    TERZAGHI K. Die berechnung der durchlassigkeitsziffer des tones aus dem verlauf der hydrodynamischen spannungsercheinungen[J]. Sitzungsbere Akad Wissen Wien Math Naturwis, 1923(132): 105-124.
    [26]
    ALEXANDER H, CHENG D. Poroelasticity[M]. Switzerland: Springer Cham, 2016.
    [27]
    GAO X W, LIU H Y, LV J, et al. A novel element differential method for solid mechanical problems using isoparametric triangular and tetrahedral elements[J]. Computers & Mathematics With Applications, 2019, 78(11): 3563-3585.
    • Related Articles

  • Related Articles

    [1]CHEN Hang, CHENG Yonghui, HU Shenggang, LI Bo. Centrifugal model tests on deformation characteristics of a bank collapse section in middle reaches of Yangtze River[J]. Chinese Journal of Geotechnical Engineering, 2024, 46(S1): 127-131. DOI: 10.11779/CJGE2024S10007
    [2]HUANG Juehao, WANG Hongchao, CHEN Jian, FU Xiaodong, YAN Xiaoling, MA Chao. Effects of intermittent cyclic loading with cyclic confining pressure on deformation behaviors of saturated clay[J]. Chinese Journal of Geotechnical Engineering, 2023, 45(S1): 67-70. DOI: 10.11779/CJGE2023S10038
    [3]WANG Nan-su, HONG Cheng-yu, ZHU Min, ZHANG Yi-fan, WANG Jun. Internal deformation characteristics of soil samples in additive manufacturing based on FBG technology[J]. Chinese Journal of Geotechnical Engineering, 2021, 43(5): 940-947. DOI: 10.11779/CJGE202105019
    [4]WU Ting-yu, GUO Lin, CAI Yuan-qiang, WANG Jun. Deformation behavior of K0-consolidated soft clay under traffic load-induced stress paths[J]. Chinese Journal of Geotechnical Engineering, 2017, 39(5): 859-867. DOI: 10.11779/CJGE201705010
    [5]DENG Hua-feng, LI Jian-lin, LIU Jie, ZHU Min, LUO Qian, YUAN Xian-fan. Influence of immersion-air dry circulation function on deformation and fracture features of sandstone[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(9): 1620-1626.
    [6]TONG Zhaoxia, ZHANG Jianmin, YU Yilin, ZHANG Ga. Effects of intermediate principal stress parameter on deformation behavior of sands under cyclic rotation of principal stress axes[J]. Chinese Journal of Geotechnical Engineering, 2009, 31(6): 946-952.
    [7]TONG Zhaoxia, YU Yilin, ZHANG Jianmin, ZHANG Ga. Deformation behavior of sands subjected to cyclic rotation of principal stress axes[J]. Chinese Journal of Geotechnical Engineering, 2008, 30(8): 1196-1202.
    [8]WANG Jianhua, XU Zhonghua, WANG Weidong. Analysis of deformation behavior of deep excavations supported by permanent structure[J]. Chinese Journal of Geotechnical Engineering, 2007, 29(12): 1899-1903.
    [9]ZHANG Qihua, XU Songlin, LIU Zude. Study of deformation feature of slope and its modeling[J]. Chinese Journal of Geotechnical Engineering, 2001, 23(5): 631-633.
    [10]SU He-yuan. 抽、灌水作用下上海土层变形特征的探讨[J]. Chinese Journal of Geotechnical Engineering, 1979, 1(1): 24-35.
    • Supplements (1)

  • Other Related Supplements

  • Cited by

    Periodical cited type(5)

    1. 陈祎，刘明昊，赵智慧. 钻孔灌注桩废弃泥浆快速絮凝脱水技术与机理研究. 建筑施工. 2025(01): 6-11 .
    2. 原媛，刘丝丝，崔勇涛，赖智龙，廖德祥. 生物酶用于河湖底泥脱水减量调理的对比研究. 水资源与水工程学报. 2025(01): 154-162 .
    3. 孙万吉，陈建，梁志学，李朝阳，赵永享. 碱渣-矿渣-水玻璃对流态固化土的影响研究. 中国新技术新产品. 2024(19): 116-118+140 .
    4. 唐伟超，赵东平，王风，朱龙，汤青山，和琦. 砂卵土-泥岩复合地层土压平衡盾构渣土脱水试验. 现代隧道技术. 2024(S1): 684-693 .
    5. 张达志. 基桩施工产生的废弃泥浆絮凝脱水后的土体工程性质研究. 四川水力发电. 2024(S2): 29-34 .

    Other cited types(3)

Catalog

    Get Citation
    PDF
    XML
    Article views (258) PDF downloads (69) Cited by(8)
    Related
    Copyright © 2010 Editorial By Chinese Journal of Geotechnical Engineering 苏ICP备05007122号-11公安联网备案号：32010602011255
    Editorial Office address：34 Hujuguan,Nanjing 210024,ChinaPostal Code：210024Tel：025-85829534，85829556E-mail: ge@nhri.cn

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return