EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

椭球颗粒体系剪切过程中自由体积的分布与演化

邹宇雄 马刚 李易奥 王頔 邱焕峰 周伟

邹宇雄, 马刚, 李易奥, 王頔, 邱焕峰, 周伟. 椭球颗粒体系剪切过程中自由体积的分布与演化. 力学学报, 2021, 53(9): 2374-2383 doi: 10.6052/0459-1879-21-255
引用本文: 邹宇雄, 马刚, 李易奥, 王頔, 邱焕峰, 周伟. 椭球颗粒体系剪切过程中自由体积的分布与演化. 力学学报, 2021, 53(9): 2374-2383 doi: 10.6052/0459-1879-21-255
Zou Yuxiong, Ma Gang, Li Yiao, Wang Di, Qiu Huanfeng, Zhou Wei. Distribution and evolution of free volume of ellipsoidal particle systems during shearing. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2374-2383 doi: 10.6052/0459-1879-21-255
Citation: Zou Yuxiong, Ma Gang, Li Yiao, Wang Di, Qiu Huanfeng, Zhou Wei. Distribution and evolution of free volume of ellipsoidal particle systems during shearing. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2374-2383 doi: 10.6052/0459-1879-21-255

椭球颗粒体系剪切过程中自由体积的分布与演化

doi: 10.6052/0459-1879-21-255
基金项目: 国家重点研发计划(2018YFC1508503), 国家杰出青年科学基金(51825905)和国家自然科学雅砻江联合基金(U1865204)资助项目
详细信息
    作者简介:

    马刚, 副教授, 主要研究方向: 高坝结构设计理论与筑坝颗粒材料力学性质. E-mail: magang630@whu.edu.cn

  • 中图分类号: TU43,TV641

DISTRIBUTION AND EVOLUTION OF FREE VOLUME OF ELLIPSOIDAL PARTICLE SYSTEMS DURING SHEARING

  • 摘要: 颗粒材料是一种复杂的多体相互作用体系, 由大量离散的颗粒和其周围的自由体积组成. 虽然颗粒的自由体积与颗粒材料的力学性能和变形特征的相关性已得到证实, 但是由于表征上的困难, 目前对非球形颗粒体系的局部自由体积的认识还不够充分. 本文采用连续离散耦合分析方法进行了不同主轴长度的椭球颗粒试样的三轴剪切数值模拟, 基于Set Voronoi算法对剪切过程中的颗粒试样进行了Voronoi元胞分割, 分析了颗粒试验在剪切过程中自由体积的统计分布特性和演化规律, 研究了颗粒形态对自由体积的影响. 剪切过程中Voronoi元胞的各向异性逐渐增强, 且各项异性增强程度随颗粒非球度的增加而增大, 表明非球颗粒在剪切过程中经历更加强烈的重排列. 具有不同非球度的椭球颗粒体系的局部孔隙比均服从k−T分布, 且这个分布仅与颗粒体系的全局孔隙比相关, 不受颗粒形态和剪切状态的影响. 局部孔隙比的波动呈现非对称拉普拉斯分布, 非对称参数刻画了局部自由体积收缩和膨胀的博弈, 其与全局孔隙比呈线性关系.

     

  • 图  1  颗粒形状描述

    Figure  1.  Particle shape descriptors

    图  2  数值试样

    Figure  2.  Numerical sample

    图  3  颗粒柱坍塌试验

    Figure  3.  Granular column collapse tests

    图  4  不同非球度的椭球颗粒偏应力−轴向应变

    Figure  4.  Curves of deviatoric stress versus axial strain for ellipsoidal particles with different asphericity

    图  5  不同非球度的椭球颗粒体积应变−轴向应变

    Figure  5.  Curves of volumetric strain versus axial strain for ellipsoidal particles with different asphericity

    图  6  Set Voronoi 剖分二维示意图

    Figure  6.  Two-dimensional illustration of Set Voronoi tessellation

    图  7  圆球和椭球颗粒的Voronoi元胞

    Figure  7.  Voronoi cells of spherical and ellipsoidal particles

    图  8  不同非球度的椭球颗粒在不同加载阶段的Voronoi元胞球度概率密度分布

    Figure  8.  Probability density distributions of sphericity of Voronoi cells at the different loading states for ellipsoidal particles with different asphericity

    图  9  不同非球度的椭球颗粒在临界状态的Voronoi元胞球度概率密度分布

    Figure  9.  Probability density distributions of sphericity of Voronoi cells at critical state for ellipsoidal particles with different asphericity

    图  10  临界状态下Voronoi元胞球度与颗粒形状参数$\alpha $的关系

    Figure  10.  Relationship between Voronoi cell sphericity and shape parameter $\alpha $ of particle at critical state

    图  11  不同非球度的椭球颗粒在不同加载阶段的局部孔隙比概率密度分布

    Figure  11.  Probability density distributions of local void ratio at the different loading states for ellipsoidal particles with different asphericity

    图  12  不同非球度的椭球颗粒在全局孔隙比相同时局部孔隙比概率密度分布

    Figure  12.  Probability density distributions of local void ratio at the states as same global void ratio for ellipsoidal particles with different asphericity

    图  13  局部孔隙比的标准差与全局孔隙比的关系

    Figure  13.  Relationship between standard deviation of local void ratio and global void ratio

    图  14  不同非球度的椭球颗粒试样在不同加载阶段的局部孔隙比波动概率密度分布

    Figure  14.  Probability density distributions of local void ratio fluctuations at the different loading states for particles with different shapes

    图  15  非对称参数$\kappa $与全局孔隙比的关系

    Figure  15.  Relationship between asymmetric parameter $\kappa $ and global void ratio

    表  1  FDEM数值模拟细观参数

    Table  1.   Parameters used in the FDEM simulation

    ParameterUnitValue
    densitykg/m32600
    friction coefficient0.5
    normal penaltyN/m34 × 1011
    tangential penaltyN/m34 × 1011
    Young’s modulusGPa40
    Poisson’s ratio0.2
    normal critical damping fraction0.03
    tangential critical damping fraction0.03
    下载: 导出CSV
  • [1] Rowe PW. The stress-dilatancy relation for static equilibrium of an assembly of particles in contact. Proceedings of the Royal Society of London, 1962, 269(1339): 500-527
    [2] Vardoulakis I, Goldscheider M, Gudehus G. Formation of shear bands in sand bodies as a bifurcation problem. International Journal for Numerical and Analytical Methods in Geomechanics, 1978, 2(2): 99-128 doi: 10.1002/nag.1610020203
    [3] Jaeger HM, Nagel SR, Behringer RP. Granular solids, liquids, and gases. Reviews of Modern Physics, 1996, 68(4): 1259-1273 doi: 10.1103/RevModPhys.68.1259
    [4] 季顺迎. 非均匀颗粒材料的类固-液相变行为及本构方程. 力学学报, 2007, 39(2): 223-237 (Ji Shunying. The quasi-solid-liquid phase transition of non-uniform granular materials and their constitutive equation. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(2): 223-237 (in Chinese) doi: 10.3321/j.issn:0459-1879.2007.02.012
    [5] Roscoe KH, Schofield AN, Thurairajah A. Yielding of clays in states wetter than critical. Géotechnique, 1963, 13(3): 211-240
    [6] 李广信. 高等土力学. 北京: 清华大学出版社, 2004

    (Li Guangxin. Advanced Soil Mechanics. Beijing: Tsinghua University Press, 2004 (in Chinese))
    [7] 姚仰平, 张民生, 万征等. 基于临界状态的砂土本构模型研究. 力学学报, 2018, 50(3): 589-598 (Yao Yangping, Zhang Minsheng, Wan Zheng, et al. Constitutive model for sand based on the critical state. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 589-598 (in Chinese) doi: 10.6052/0459-1879-17-334
    [8] 陈云敏, 马鹏程, 唐耀. 土体的本构模型和超重力物理模拟. 力学学报, 2020, 52(04): 901-915 (Chen Yunmin, Ma Pengcheng, Tang Yao. Constitutive models and hypergravity physical simulation of soils. Chinese Journal of Geotechnical Engineering, 2020, 52(04): 901-915 (in Chinese)
    [9] 蒋明镜. 现代土力学研究的新视野——宏微观土力学. 岩土工程学报, 2019, 41(2): 195-254 (Jiang Mingjing. New paradigm for modern soil mechanics: Geomechanics from micro to macro. Chinese Journal of Geotechnical Engineering, 2019, 41(2): 195-254 (in Chinese)
    [10] 刘清秉, 项伟, Budhu M等. 砂土颗粒形状量化及其对力学指标的影响分析. 岩土力学, 2011, 32(S1): 190-197 (Liu Qingbing, Xiang Wei, Budhu M, et al. Study of particle shape quantification and effect on mechanical property of sand. Rock and Soil Mechanics, 2011, 32(S1): 190-197 (in Chinese)
    [11] Yang J, Luo XD. Exploring the relationship between critical state and particle shape for granular materials. Journal of the Mechanics and Physics of Solids, 2015, 84: 196-213 doi: 10.1016/j.jmps.2015.08.001
    [12] Suh HS, Kim KY, Lee J, et al. Quantification of bulk form and angularity of particle with correlation of shear strength and packing density in sands. Engineering Geology, 2017, 20: 256-265
    [13] 邹宇雄, 周伟, 陈远等. 颗粒形状对岩土颗粒材料传力特性的影响机制. 水力发电学报, 2020, 39(5): 17-26 (Zou Yuxiong, Zhou Wei, Chen Yuan, et al. Mechanism of particle shape on force transfer properties of granular geo-materials. Journal of Hydroelectric Engineering, 2020, 39(5): 17-26 (in Chinese)
    [14] Murphy KA, Dahmen KA, Jaeger HM. Transforming mesoscale granular plasticity through particle shape. Physical Review X, 2019, 9(1): 011014 doi: 10.1103/PhysRevX.9.011014
    [15] Cho GC, Dodds J, Santamarina JC. Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. Journal of Geotechnical and Geoenvironmental Engineering, 2006, 132(5): 591-602 doi: 10.1061/(ASCE)1090-0241(2006)132:5(591)
    [16] Zhao S, Zhang N, Zhou X, et al. Particle shape effects on fabric of granular random packing. Powder Technology, 2017, 310: 175-186 doi: 10.1016/j.powtec.2016.12.094
    [17] Majmudar TS, Behringer RP. Contact force measurements and stress-induced anisotropy in granular materials. Nature, 2005, 435: 1079-1082 doi: 10.1038/nature03805
    [18] Chen Y, Ma G, Zhou W, et al. An enhanced tool for probing the microscopic behavior of granular materials based on X-ray micro-CT and FDEM. Computers and Geotechnics, 2021, 132: 103974 doi: 10.1016/j.compgeo.2020.103974
    [19] Cundall PA, Strack ODL. A discrete numerical model for granular assemblies. Geotechnique, 1979, 29(30): 331-336
    [20] Munjiza A, Owen DRJ, Bicanic N. A combined finite-discrete element method in transient dynamics of fracturing solids. Engineering Computations, 1995, 12(2): 145-174 doi: 10.1108/02644409510799532
    [21] Munjiza A. The Combined Finite–Discrete Element Method. Cichester: John Wiley and Son, 2004
    [22] Oda M. Initial fabrics and their relations to mechanical properties of granular material. Soilsand Foundation, 1972, 12(1): 17-36 doi: 10.3208/sandf1960.12.17
    [23] Radjai F, Wolf DE, Jean M, et al. Bimodal character of stress transmission in granular packings. Physical Review Letters, 1998, 80(1): 61-64 doi: 10.1103/PhysRevLett.80.61
    [24] Ouadfel H, Rothenburg L. “Stress–force–fabric” relationship for assemblies of ellipsoids. Mechanics of Materials, 2001, 33(4): 201-221 doi: 10.1016/S0167-6636(00)00057-0
    [25] 刘嘉英, 周伟, 马刚等. 颗粒材料三维应力路径下的接触组构特性. 力学学报, 2019, 51(1): 26-35 (Liu Jiaying, Zhou Wei, Ma Gang, et al. Contact fabric characteristics of granular materials under three dimensional stress paths. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 26-35 (in Chinese) doi: 10.6052/0459-1879-18-338
    [26] 钱劲松, 陈康为, 张磊. 粒料固有各向异性的离散元模拟与细观分析. 力学学报, 2018, 50(5): 1041-1050 (Qian Jinsong, Chen Kangwei, Zhang Lei. Simulation and micro-mechanics analysis of inherent anisotropy of granular by distinct element method. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1041-1050 (in Chinese)
    [27] Edwards SF, Oakeshott RBS. Theory of powders. Physica A: Statistical Mechanics and its Applications, 1989, 157(3): 1080-1090 doi: 10.1016/0378-4371(89)90034-4
    [28] Mehta A, Edwards S. Statistical mechanics of powder mixtures. Physica A: Statistical Mechanics and its Applications, 1989, 157(3): 1091-1100 doi: 10.1016/0378-4371(89)90035-6
    [29] Kang DH, Choo J, Yun TS. Evolution of pore characteristics in the 3D numerical direct shear test. Computers and Geotechnics, 2013, 49: 53-61 doi: 10.1016/j.compgeo.2012.10.009
    [30] Zhao S, Evans TM, Zhou X. Three-dimensional voronoi analysis of monodisperse ellipsoids during triaxial shear. Powder Technology, 2018, 323: 323-336 doi: 10.1016/j.powtec.2017.10.023
    [31] Luchnikov VA, Medvedev NN, Oger L, et al. Voronoi-Delaunay analysis of voids in systems of nonspherical particles. Physical Review E, 1999, 59(6): 7205-7212 doi: 10.1103/PhysRevE.59.7205
    [32] Dong K, Wang C, Yu A. Voronoi analysis of the packings of non-spherical particles. Chemical Engineering Science, 2016, 153: 330-343 doi: 10.1016/j.ces.2016.07.013
    [33] Ma G, Zhou W, Regueiro RA, et al. Modeling the fragmentation of rock grains using computed tomography and combined FDEM. Powder Technology, 2017, 308: 388-397 doi: 10.1016/j.powtec.2016.11.046
    [34] Ma G, Zhou W, Chang XL, et al. Combined FEM/DEM modeling of triaxial compression tests for rockfills with polyhedral particles. International Journal of Geomechanics, 2014, 14(4): 04014014 doi: 10.1061/(ASCE)GM.1943-5622.0000372
    [35] 马刚, 周伟, 常晓林等. 堆石体三轴剪切试验的三维细观数值模拟. 岩土工程学报, 2011, 33(5): 746-753 (Ma Gang, Zhou Wei, Chang Xiaolin, et al. 3D mesoscopic numerical simulation of triaxial shear tests for rockfill. Chinese Journal of Geotechnical Engineering, 2011, 33(5): 746-753 (in Chinese)
    [36] 常晓林, 马刚, 周伟等. 颗粒形状及粒间摩擦角对堆石体宏观力学行为的影响. 岩土工程学报, 2012, 34(4): 646-653 (Chang Xiaolin, Ma Gang, Zhou Wei, et al. Influences of particle shape and inter-particle friction angle on macroscopic response of rockfill. Chinese Journal of Geotechnical Engineering, 2012, 34(4): 646-653 (in Chinese)
    [37] Barrett PJ. The shape of rock particles, a critical review. Sedimentology, 1980, 27(3): 291-303 doi: 10.1111/j.1365-3091.1980.tb01179.x
    [38] Domokos G, Kun F, Sipos AÁ, et al. Universality of fragment shapes. Scientific Reports, 2015, 5: 9147 doi: 10.1038/srep09147
    [39] Imre B, Rabsamen S, Springman SM. A coefficient of restitution of rock materials. Computers & Geosciences, 2008, 34(4): 339-350
    [40] Tatone BSA, Grasselli G. A calibration procedure for two-dimensional laboratory-scale hybrid finite-discrete element simulations. International Journal of Rock Mechanics & Mining Sciences, 2015, 75: 56-72
    [41] 邹宇雄, 马刚, 李易奥等. 抗转动对颗粒材料组构特性的影响研究. 岩土力学, 2020, 41(8): 2829-2838 (Zou Yuxiong, Ma Gang, Li Yiao, et al. Impact of rotation resistance on fabric of granular materials. Rock and Soil Mechanics, 2020, 41(8): 2829-2838 (in Chinese)
    [42] Rycroft CH. Voro++: A three-dimensional Voronoi cell library in C++. Chaos, 2009, 19(4): 041111 doi: 10.1063/1.3215722
    [43] Schaller FM, Kapfer SC, Evans ME, et al. Set Voronoi diagrams of 3D assemblies of aspherical particles. Philosophical Magazine, 2013, 93(31-33): 3993-4017 doi: 10.1080/14786435.2013.834389
    [44] Kou B, Cao Y, Li J, et al. Translational and rotational dynamical heterogeneities in granular systems. Physical Review Letters, 2018, 121(1): 018002 doi: 10.1103/PhysRevLett.121.018002
    [45] Schaller FM, Neudecker M, Saadatfar M, et al. Local origin of global contact numbers in frictional ellipsoid packings. Physical Review Letters, 2015, 114(15): 158001 doi: 10.1103/PhysRevLett.114.158001
    [46] Guo N, Zhao J. The signature of shear-induced anisotropy in granular media. Computers and Geotechnics, 2013, 47: 1-15 doi: 10.1016/j.compgeo.2012.07.002
    [47] Zhao S, Zhao J, Guo N. Universality of internal structure characteristics in granular media under shear. Physical Review E, 2020, 101(1): 012906 doi: 10.1103/PhysRevE.101.012906
    [48] Guo N, Zhao J. Local fluctuations and spatial correlations in granular flows under constant-volume quasistatic shear. Physical Review E, 2014, 89(4): 042208 doi: 10.1103/PhysRevE.89.042208
    [49] Aste T, Di Matteo T. Emergence of gamma distributions in granular materials and packing models. Physical Review E, 2008, 77(2): 021309 doi: 10.1103/PhysRevE.77.021309
  • 加载中
图(15) / 表(1)
计量
  • 文章访问数:  96
  • HTML全文浏览量:  46
  • PDF下载量:  26
  • 被引次数: 0
出版历程
  • 收稿日期:  2021-06-08
  • 录用日期:  2021-07-20
  • 网络出版日期:  2021-07-21
  • 刊出日期:  2021-09-18

目录

    /

    返回文章
    返回