Volume 45 Issue 7
Jul.  2024
Turn off MathJax
Article Contents
LIU Panyong, GU Xin, ZHANG Qing. Peridynamics for Moisture Diffusion and Crack Propagation in Unsaturated Soil Desiccation[J]. Applied Mathematics and Mechanics, 2024, 45(7): 823-834. doi: 10.21656/1000-0887.450002
Citation: LIU Panyong, GU Xin, ZHANG Qing. Peridynamics for Moisture Diffusion and Crack Propagation in Unsaturated Soil Desiccation[J]. Applied Mathematics and Mechanics, 2024, 45(7): 823-834. doi: 10.21656/1000-0887.450002

Peridynamics for Moisture Diffusion and Crack Propagation in Unsaturated Soil Desiccation

doi: 10.21656/1000-0887.450002
  • Received Date: 2024-01-02
  • Rev Recd Date: 2024-03-11
  • Publish Date: 2024-07-01
  • Unsaturated soil desiccation cracking is a coupled hydro-mechanical problem. It seriously weakens the hydraulic and mechanical characteristics of soil, causing various natural disasters potentially. For the unsaturated soil, the mechanism of moisture diffusion and deformation is more complicated compared with saturated soil, attracting wide attention. Thus, a coupled hydro-mechanical bond-based peridynamic (BB PD) model was proposed to explore the moisture diffusion and crack propagation in unsaturated soil. Specifically, the moisture diffusion equation for unsaturated soil was recast with the peridynamic differential operator, and an improved micro-modulus was adopted to revise the bond force density in the BB PD. In addition, a hybrid algorithm combining the explicit difference scheme for solving the diffusion equation and the implicit scheme for solving the motion equation was adopted, to avoid the incongruity of time steps for two types equations under the same explicit scheme. The validity of the proposed model and algorithm was verified by the examples on the desiccation of an unsaturated soil block and the desiccation cracking of a 3D unsaturated soil plate. The results show the potential of peridynamics in capturing desiccation cracks of unsaturated soil.
  • (Contributed by ZHANG Qing, M.AMM Editorial Board)
  • loading
  • [1]
    BRONSWIJK J, HAMMINGA W, OOSTINDIE K. Field-scale solute transport in a heavy clay soil[J]. Water Resources Research, 1995, 31 (3): 517-526. doi: 10.1029/94WR02534
    [2]
    唐朝生, 施斌, 刘春. 膨胀土收缩开裂特性研究[J]. 工程地质学报, 2012, 20 (5) : 663-673. https://www.cnki.com.cn/Article/CJFDTOTAL-GCDZ201205004.htm

    TANG Chaosheng, SHI Bin, LIU Chun. Study on desiccation cracking behaviour of expansive soil[J]. Journal of Engineering Geology, 2012, 20 (5): 663-673. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GCDZ201205004.htm
    [3]
    YESILLER N, MILLER C, INCI G, et al. Desiccation and cracking behavior of three compacted landfill liner soils[J]. Engineering Geology, 2000, 57 (1/2): 105-121.
    [4]
    BOIVIN P, GARNIER P, VAUCLIN M. Modeling the soil shrinkage and water retention curves with the same equations[J]. Soil Science Society of America Journal, 2006, 70 (4): 1082-1093. doi: 10.2136/sssaj2005.0218
    [5]
    张晓宇, 许强, 刘春, 等. 黏性土失水开裂多场耦合离散元数值模拟[J]. 工程地质学报, 2017, 25 (6): 1430-1437. https://www.cnki.com.cn/Article/CJFDTOTAL-GCDZ201706005.htm

    ZHANG Xiaoyu, XU Qiang, LIU Chun, et al. Numerical simulation of drying cracking using multi-field coupling discrete element method[J]. Journal of Engineering Geology, 2017, 25 (6): 1430-1437. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GCDZ201706005.htm
    [6]
    CHAKRABARTI S, KODIKARA J, PARDO L. An overview of stabilisation methods and performance of local government roads in Australia[C]//International Symposium on Subgrade Stabilisation and In Situ Pavement Recycling Using Cement. Salamanca, Spain, 2001.
    [7]
    INTHARASOMBAT N, PUPPALA A J, WILLIAMMEE R. Compost amended soil treatment for mitigating highway shoulder desiccation cracks[J]. Journal of Infrastructure Systems, 2007, 13 (4): 287-298. doi: 10.1061/(ASCE)1076-0342(2007)13:4(287)
    [8]
    TANG C S, ZHU C, CHENG Q, et al. Desiccation cracking of soils: a review of investigation approaches, underlying mechanisms, and influencing factors[J]. Earth-Science Reviews, 2021, 216 : 103586. doi: 10.1016/j.earscirev.2021.103586
    [9]
    GLENNIE K W. Desert Sedimentary Environments[M]. Elsevier Amsterdam, 2010.
    [10]
    EL-MAARRY M R, WATTERS W, YOLDI Z, et al. Field investigation of dried lakes in western United States as an analogue to desiccation fractures on Mars[J]. Journal of Geophysical Research: Planets, 2015, 120 (12): 2241-2257. doi: 10.1002/2015JE004895
    [11]
    LEE F H, LO K W, LEE S L. Tension crack development in soils[J]. Journal of Geotechnical Engineering, 1988, 114 (8): 915-929. doi: 10.1061/(ASCE)0733-9410(1988)114:8(915)
    [12]
    MORRIS P H, GRAHAM J, WILLIAMS D J. Cracking in drying soils[J]. Canadian Geotechnical Journal, 1992, 29 (2): 263-277. doi: 10.1139/t92-030
    [13]
    KONRAD J M, AYAD R. A idealized framework for the analysis of cohesive soils undergoing desiccation[J]. Canadian Geotechnical Journal, 1997, 34 (4): 477-488. doi: 10.1139/t97-015
    [14]
    CHENG W, BIAN H, HATTAB M, et al. Numerical modelling of desiccation shrinkage and cracking of soils[J]. European Journal of Environmental and Civil Engineering, 2023, 27 (12): 3525-3545. doi: 10.1080/19648189.2022.2140208
    [15]
    YU P, WANG X, YU J, et al. XFEM simulation of soil crack evolution process considering the stress concentration and redistribution at the crack tip[J]. International Journal of Geomechanics, 2022, 22 (9): 04022137. doi: 10.1061/(ASCE)GM.1943-5622.0002505
    [16]
    VO T D, POUYA A, HEMMATI S, et al. Numerical modelling of desiccation cracking of clayey soil using a cohesive fracture method[J]. Computers and Geotechnics, 2017, 85 : 15-27. doi: 10.1016/j.compgeo.2016.12.010
    [17]
    POUYA A, VO T D, HEMMATI S, et al. Modeling soil desiccation cracking by analytical and numerical approaches[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2019, 43 (3): 738-763. doi: 10.1002/nag.2887
    [18]
    SÁNCHEZ M, MANZOLI O L, GUIMARÃES L J. Modeling 3-D desiccation soil crack networks using a mesh fragmentation technique[J]. Computers and Geotechnics, 2014, 62 : 27-39. doi: 10.1016/j.compgeo.2014.06.009
    [19]
    吴艳青, 张克实. 利用内聚力模型(CZM)模拟弹粘塑性多晶体的裂纹扩展[J]. 应用数学和力学, 2006, 27 (4): 454-462. http://www.applmathmech.cn/article/id/707

    WU Yanqing, ZHANG Keshi. Crack propagation in polycrystalline elastic-viscoplastic materials using cohesive zone models[J]. Applied Mathematics and Mechanics, 2006, 27 (4): 454-462. (in Chinese) http://www.applmathmech.cn/article/id/707
    [20]
    MIEHE C, MAUTHE S. Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 304 : 619-655. doi: 10.1016/j.cma.2015.09.021
    [21]
    HU T, GUILLEMINOT J, DOLBOW J E. A phase-field model of fracture with frictionless contact and random fracture properties: application to thin-film fracture and soil desiccation[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 368 : 113106. doi: 10.1016/j.cma.2020.113106
    [22]
    BUI H H, NGUYEN G D, KODIKARA J, et al. Soil cracking modelling using the mesh-free SPH method[C]// 12 th Australia New Zealand Conference on Geomechanics. New Zealand, Australia, 2015: 122-129.
    [23]
    TRAN H T, WANG Y, NGUYEN G D, et al. Modelling 3D desiccation cracking in clayey soils using a size-dependent SPH computational approach[J]. Computers and Geotechnics, 2019, 116 : 103209. doi: 10.1016/j.compgeo.2019.103209
    [24]
    TRAN T H. A coupled hydro-mechanical SPH framework to model desiccation cracking in clay soils[D]. Melbourne: Monash University, 2019.
    [25]
    TU Z, PENG C, LI C, et al. MPM-driven dynamic desiccation cracking and curling in unsaturated soils[J]. Computer Animation and Virtual Worlds, 2023, 34 (3/4): e2172.
    [26]
    VOGEL H J, HOFFMANN H, LEOPOLD A, et al. Studies of crack dynamics in clay soil, Ⅱ: a physically based model for crack formation[J]. Geoderma, 2005, 125 (3/4): 213-223.
    [27]
    ZHU L, SHEN T, MA R, et al. Development of cracks in soil: an improved physical model[J]. Geoderma, 2020, 366 : 114258. doi: 10.1016/j.geoderma.2020.114258
    [28]
    JIA X, HAO Y, LI P, et al. Nanoscale deformation and crack processes of kaolinite under water impact using molecular dynamics simulations[J]. Applied Clay Science, 2021, 206 : 106071. doi: 10.1016/j.clay.2021.106071
    [29]
    ZHANG Z, SONG X. Molecular dynamics modeling of cracks in dry clay sheets at the nanoscale[J]. Computers and Geotechnics, 2022, 152 : 105037. doi: 10.1016/j.compgeo.2022.105037
    [30]
    司马军, 蒋明镜, 周创兵. 黏性土干缩开裂过程离散元数值模拟[J]. 岩土工程学报, 2013, 35 (S2): 286-291. https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC2013S2049.htm

    SIMA Jun, JIANG Mingjing, ZHOU Chuangbing. Numerical simulation of desiccation cracking of clay soils by DEM[J]. Chinese Journal of Geotechnical Engineering, 2013, 35 (S2): 286-291. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-YTGC2013S2049.htm
    [31]
    LIN Z Y, WANG Y S, TANG C S, et al. Discrete element modelling of desiccation cracking in thin clay layer under different basal boundary conditions[J]. Computers and Geotechnics, 2021, 130 : 103931. doi: 10.1016/j.compgeo.2020.103931
    [32]
    刘小飞, 游世辉, 谢纯凯. 基于复杂网络的黏性土颗粒边坡堆积体失稳研究[J]. 应用数学和力学, 2020, 41 (9): 931-942. doi: 10.21656/1000-0887.400225

    LIU Xiaofei, YOU Shihui, XIE Chunkai. Study on instability of clay granular slope piles based on complex network[J]. Applied Mathematics and Mechanics, 2020, 41 (9): 931-942. (in Chinese) doi: 10.21656/1000-0887.400225
    [33]
    JABAKHANJI R. Peridynamic modeling of coupled mechanical deformations and transient flow in unsaturated soils[D]. West Lafayette: Purdue University, 2013.
    [34]
    TEE T Y. Methodology for integrated vapor pressure, hygroswelling, and thermo-mechanical stress modeling of IC packages[M]//Moisture Sensitivity of Plastic Packages of IC Devices. 2010: 221-243.
    [35]
    李天一, 章青, 夏晓舟, 等. 考虑混凝土材料非均质特性的近场动力学模型[J]. 应用数学和力学, 2018, 39 (8): 913-924. doi: 10.21656/1000-0887.380274

    LI Tianyi, ZHANG Qing, XIA Xiaozhou, et al. A peridynamic model for heterogeneous concrete materials[J]. Applied Mathematics and Mechanics, 2018, 39 (8): 913-924. (in Chinese) doi: 10.21656/1000-0887.380274
    [36]
    MENON S, SONG X. Coupled analysis of desiccation cracking in unsaturated soils through a non-local mathematical formulation[J]. Geosciences, 2019, 9 (10): 428. doi: 10.3390/geosciences9100428
    [37]
    YAN H, JIVKOV A P, SEDIGHI M. Modelling soil desiccation cracking by peridynamics[J]. Géotechnique, 2023, 73 (5): 388-400. doi: 10.1680/jgeot.21.00032
    [38]
    LIU P, GU X, LU Y, et al. Peridynamics for mechanism analysis of soil desiccation cracking: coupled hygro-mechanical model, staggered and monolithic solution[J]. Computer Methods in Applied Mechanics and Engineering, 2023, 406 : 115896. doi: 10.1016/j.cma.2023.115896
    [39]
    王琳琳. 多孔介质力学[M]. 北京: 石油工业出版社, 2022.

    WANG Linlin. Mechanics of Porous Media[M]. Beijing: Petron Industry Press, 2022. (in Chinese)
    [40]
    POUYA A. A finite element method for modeling coupled flow and deformation in porous fractured media[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2015, 39 (16): 1836-1852. doi: 10.1002/nag.2384
    [41]
    VAN GENUCHTEN M T. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils[J]. Soil Science Society of America Journal, 1980, 44 (5): 892-898. doi: 10.2136/sssaj1980.03615995004400050002x
    [42]
    MADENCI E, BARUT A, FUTCH M. Peridynamic differential operator and its applications[J]. Computer Methods in Applied Mechanics and Engineering, 2016, 304 : 408-451. doi: 10.1016/j.cma.2016.02.028
    [43]
    MADENCI E, BARUT A, PHAN N. Bond-based peridynamics with stretch and rotation kinematics for opening and shearing modes of fracture[J]. Journal of Peridynamics and Nonlocal Modeling, 2021, 3 : 211-254. doi: 10.1007/s42102-020-00049-4
    [44]
    GU X, LI X, XIA X, et al. A robust peridynamic computational framework for predicting mechanical properties of porous quasi-brittle materials[J]. Composite Structures, 2023, 303 : 116245. doi: 10.1016/j.compstruct.2022.116245
    [45]
    郁杨天, 章青, 顾鑫. 近场动力学与有限单元法的混合模型与隐式求解格式[J]. 浙江大学学报(工学版), 2017, 51 (7): 1324-1330. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDZC201707008.htm

    YU Yangtian, ZHANG Qing, GU Xin. Hybrid model of peridynamics and finite element method under implicit schemes[J]. Journal of Zhejiang University (Engineering Science), 2017, 51 (7): 1324-1330. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDZC201707008.htm
    [46]
    QUEVEDO R, ROMANEL C, ROEHL D. Numerical modeling of unsaturated soil behavior considering different constitutive models[C]//MATEC Web of Conferences. 2021: 02007.
    [47]
    TANG C S, SHI B, LIU C, et al. Experimental characterization of shrinkage and desiccation cracking in thin clay layer[J]. Applied Clay Science, 2011, 52 (1/2): 69-77.
    [48]
    张映梅. 非饱和重塑黄土水分蒸发试验研究[D]. 兰州: 兰州交通大学, 2020.

    ZHANG Yingmei. Experimental study on water evaporation of unsaturated remolded loess[D]. Lanzhou: Lanzhou Jiaotong University, 2020. (in Chinese)
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(9)

    Article Metrics

    Article views (310) PDF downloads(110) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return