颗粒材料三维应力路径下的接触组构特性
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摘要
颗粒材料的宏观应力变形特征与其微观接触力、组构等紧密相关.一般而言,强接触系统属于颗粒内部体系的传力结构,其对应的组构张量是影响宏观应力性质的重要因素.细观数值方法 (如离散单元法)能够反映物理试验的基本规律,并且可以方便地提取宏微观数据来研究颗粒体系的应力变形机制.采用离散单元法(discrete element method, DEM)进行一系列等p等b应力路径下颗粒材料的真三轴试验,在此基础上研究了三维应力路径下颗粒材料的宏微观力学参数的演化过程、三维组构张量与应力张量多重联系以及强接触体系反映的宏观应力特征.研究表明:颗粒体系偏应力峰值状态和临界状态均存在与加载路径无关的宏微观特征;三维应力路径下组构张量与应力张量存在非共轴性,但其联合不变量演化过程表现出加载路径无关的特征;与弱接触系统的组构张量相比,强接触系统的组构张量更能反映宏观应力张量的特征;强弱接触体系的组构张量对颗粒体系宏观响应的贡献不同,其分界点存在一定取值范围,但采用平均接触力较为简单合理.
Macroscopic mechanical characteristics of granular materials are closely related to the microscopic contact force and fabric. Generally speaking, the strong contact system contributes to the force transmission of internal granular system, and then its corresponding fabric tensor has important influence on the macroscopic stress. Microscopic numerical methods, such as discrete element method, can reproduce the laboratory tests with reasonable macroscopic responses and extract macro-and micro-data conveniently for investigating the underlying mechanism of the granular system. Based on discrete element method(DEM), a series of true triaxial tests for granular materials under constant p and constant b stress paths are carried out, and the evolutions of macro-and micro-mechanical parameters of granular materials, the multiple relationship between three-dimensional fabric tensor and stress tensor and the macro-stress characteristics reflected by strong contact system are studied. The results demonstrate that some macro-and microscopic parameters at the stresspeak and critical state in the granular system are independent on the loading path. Non-coaxiality between fabric tensor and stress tensor is observed under three-dimensional stress path, but the evolution of the joint invariant of the two tensors is independent on the 3 D loading path. Compared to fabric tensor of weak contact system, the fabric tensor of strong contact system reflects better the characteristics of macroscopic stress tensor. Fabric tensors of strong and weak contact systems contribute differently to the granular macroscopic response. To divide the strong and weak contact system, there is a range for the threshold, however adopting the average contact force is relatively simple and reasonable.
Macroscopic mechanical characteristics of granular materials are closely related to the microscopic contact force and fabric. Generally speaking, the strong contact system contributes to the force transmission of internal granular system, and then its corresponding fabric tensor has important influence on the macroscopic stress. Microscopic numerical methods, such as discrete element method, can reproduce the laboratory tests with reasonable macroscopic responses and extract macro-and micro-data conveniently for investigating the underlying mechanism of the granular system. Based on discrete element method(DEM), a series of true triaxial tests for granular materials under constant p and constant b stress paths are carried out, and the evolutions of macro-and micro-mechanical parameters of granular materials, the multiple relationship between three-dimensional fabric tensor and stress tensor and the macro-stress characteristics reflected by strong contact system are studied. The results demonstrate that some macro-and microscopic parameters at the stresspeak and critical state in the granular system are independent on the loading path. Non-coaxiality between fabric tensor and stress tensor is observed under three-dimensional stress path, but the evolution of the joint invariant of the two tensors is independent on the 3 D loading path. Compared to fabric tensor of weak contact system, the fabric tensor of strong contact system reflects better the characteristics of macroscopic stress tensor. Fabric tensors of strong and weak contact systems contribute differently to the granular macroscopic response. To divide the strong and weak contact system, there is a range for the threshold, however adopting the average contact force is relatively simple and reasonable.
引文
1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 Presss,2004(in Chinese))
2程展林,丁红顺,吴良平.粗粒土试验研究.岩土工程学报,2007,29(8):1151-1158(Cheng Zhanlin,Ding Hongshun,Wu Liangping.Experimental study on mechanical behaviour of granular material.Chinese Journal of Geotechnical Engineering,2007,29(8):1151-1158(in Chinese))
3黄茂松,姚仰平,尹振宇等.土的基本特性及本构关系与强度理论研究进展//中国土木工程学会全国土力学及岩土工程学术大会,2015(Huang Maosong,Yao Yangping,Yin Zhenyu,et al.Progress in the study of elementary mechanical behaviors,constitutive modeling and failure criterion of soils//The 12th National Conference on Soil Mechanics and Geotechnical Engineering of China Civil Engineering Society,2015(in Chinese))
4 Darve F,Laouafa F.Instabilities in granular materials and application to landslides.Mechanics of Cohesive-frictional Materials,2000,5(8):627-652
5 Nicot F,Darve F.A micro-mechanical investigation of bifurcation in granular materials.International Journal of Solids&Structures,2007,44(20):6630-6652
6 Nicot F,Darve F.The H-microdirectional model:Accounting for a mesoscopic scale.Mechanics of Materials,2011,43(12):918-929
7 Small M,Walker D M,Tordesillas A,et al.Characterizing chaotic dynamics from simulations of large strain behavior of a granular material under biaxial compression.Chaos:An Interdisciplinary Journal of Nonlinear Science,2013,23(1):013113
8 Zhou W,Liu J,Ma G,et al.Macroscopic and microscopic behaviors of granular materials under proportional strain path:A DEMstudy.International Journal for Numerical and Analytical Methods in Geomechanics,2016,40(18):2450-2467
9钱建固,黄茂松.轴对称状态下土体剪切带触发形成的分叉理论.岩土工程学报,2003,25(4):400-404(Qian Jiangu,Huang Maosong.Bifurcation of soils at inception of shear band under axisymmetric conditions.Chinese Jounal of Geotechnical Engineering,2003,25(4):400-404(in Chinese))
10 Drescher A,Jong GDJD.Photoelastic verification of a mechanical model for the flow of a granular material.Journal of the Mechanics&Physics of Solids,1972,20(5):337-340
11王雨婷.摩擦特性对颗粒材料宏细观力学特征的影响.[硕士论文].武汉:武汉大学,2017(Wang Yuting.The influence of friction properties on macro-mechanical characteristics of granular materials.[Master Thesis].Wuhan:Wuhan University,2017(in Chinese))
12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))
13熊迅,李天密,马棋棋等.石英玻璃圆环高速膨胀碎裂过程的离散元模拟.力学学报,2018,50(3):622-632(Xiong Xun,Li Tianmi,Ma Qiqi,et al.Discrete element simulations of the high velocity expension and fragmentation of qartz glass rings.Chinese Journal of Theoretical and Applied Mechanics,2018,50(3):622-632(in Chinese))
14周博,黄润秋,汪华斌等.基于离散元法的砂土破碎演化规律研究.岩土力学,2014,35(9):2709-2716(Zhou Bo,Huang Ruiqiu,Wang Huabin,et al.Study of evolution of sand crushability based on discrete elements method.Rock&Soil Mechanics,2014,35(9):2709-2716(in Chinese))
15刘嘉英,马刚,周伟等.抗转动特性对颗粒材料分散性失稳的影响研究.岩土力学,2017,38(5):1472-1480(Liu Jiaying,Ma Gang,Zhou Wei,et al.Impact of rotation resistance on diffuse failure of granular materials.Rock&Soil Mechanics,2017,38(5):1472-1480(in Chinese))
16刘嘉英,马刚,周伟等.基于离散元的颗粒材料三维临界状态与剪胀特性研究.水利学报,2017,48(9):1107-1117(Liu Jiaying,Ma Gang,Zhou Wei,et al.Three-dimensional critical state and dilatancy of granular materials based on DEM.Journal of Hydraulic Engineering,2017,48(9):1107-1117(in Chinese))
17周伟,刘东,马刚等.基于随机散粒体模型的堆石体真三轴数值试验研究.岩土工程学报,2012,34(4):748-755(Zhou Wei,Liu Dong,Ma Gang,et al.Numerical simulation of true triaxial tests on mechanical behaviors of rockfill based on stochastic granule model.Chinese Journal of Geotechnical Engineering,2012,34(4):748-755(in Chinese))
18 Zhou W,Ma G,Chang X,et al.Influence of particle shape on behavior of rockfill using a three-dimensional deformable DEM.Journal of Engineering Mechanics,2013,139(12):1868-1873
19 Ma G,Zhou W,Ng TT,et al.Microscopic modeling of the creep behavior of rockfills with a delayed particle breakage model.Acta Geotechnica,2015,10(4):481-496
20 Ma G,Regueiro RA,Zhou W,et al.Role of particle crushing on particle kinematics and shear banding in granular materials.Acta Geotechnica,2018(6):1-18
21 Rothenburg L,Bathurst RJ.Analytical study of induced anisotropy in idealized granular materials.G′eotechnique,1989,39(4):601-614
22 Chantawarangul K.Numerical simulations of three-dimensional granular assemblies.[Ph D Thesis].University,of Waterloo,1993
23 Zhao J,Guo N.Unique critical state characteristics in granular media considering fabric anisotropy.Geotechnique,2013,63(8):695-704
24 Radjai F,Jean M,Moreau JJ,et al.Force Distributions in Dense Two-Dimensional Granular Systems.Physical Review Letters,1996,77(2):274-277
25 Radjai F,Wolf DE,Jean M,et al.Bimodal character of stress transmission in granular packings.Physical Review Letters,1998,80(1):61-64
26张敏,许成顺,杜修力等.中主应力系数及应力路径对砂土剪切特性影响的真三轴试验研究.水利学报,2015,46(9):1072-1079(Zhang Min,Xu Chengshun,Du Xiuli,et al.True triaxial experimental research on shear behaviors of sand under different intermediate principal stresses and different stress paths.Journal of Hydraulic Engineering,2015,46(9):1072-1079(in Chinese))
27 Huang X,Hanley KJ,O’Sullivan C,et al.DEM analysis of the influence of the intermediate stress ratio on the critical-state behaviour of granular materials.Granular Matter,2014,16(5):641-655
28 Ma G,Chang X L,Zhou W,et al.Mechanical response of rockfills in a simulated true triaxial test:A combined FDEM study.Geomechanics&Engineering,2014,7(3):317-333
29 Zhou W,Liu J,Ma G,et al.Three-dimensional DEM investigation of critical state and dilatancy behaviors of granular materials.Acta Geotechnica,2017,12(3):1-14
30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))
31 Li X S,Dafalias Y F.Anisotropic critical state theory:Role of fabric.Journal of Engineering Mechanics,2012,138(3):263-275
32白冰,周健.扫描电子显微镜测试技术在岩土工程中的应用与进展.电子显微学报,2001,20(2):154-160(Bai Bing,Zhou Jian.Application and progress of scanning electron microscopy testing technology in geotechnical engineering.Journal of Chinese Electron Microscopy Society,2001,20(2):154-160(in Chinese))
33 Yang J,Yang ZX,Li XS.Quantifying and modelling fabric anisotropy of granular soils.G′eotechnique,2008,58(4):237-248
34 Hall SA,Bornert M,Desrues J,et al.Discrete and continuum analysis of localised deformation in sand using X-ray CT and volumetric digital image correlation.G′eotechnique,2010,60(5):11-20
35程展林,左永振,丁红顺.CT技术在岩土试验中的应用研究.长江科学院院报,2011,28(3):33-38(Chen Zhanlin,Zuo Yongzhen,Ding Hongshun.Application research of CT technology in geotechnical experiment.Journal of Yangtze River Scientific Research Institute,2011,28(3):33-38(in Chinese))
36姜景山,程展林,左永振等.粗粒土CT三轴流变试验研究.岩土力学,2014(9):2507-2514(Jiang Jinshan,Cheng Zhanlin,Zuo Youzhen,et al.CT triaxial rheological test on coarse-grained soils.Rock&Soil Mechanics,2014(9):2507-2514(in Chinese))
37徐小敏.砂土液化及其判别的微观机理研究.[博士论文].杭州:浙江大学,2012(Xu Xiaomin.Study on the micromechanism of sand liquefaction and its evalution.[PhD Thesis].Hangzhou:Zhejiang University,2012(in Chinese))
38戴北冰,杨峻,周翠英.松砂不稳定行为的数值模拟研究.岩土工程学报,2013,35(9):1737-1745(Dai Beibing,Yang Jun,Zhou Cuiying.Numerical study on instability behavior of sand.Chinese Journal of Geotechnical Engineering,2013,35(9):1737-1745(in Chinese))
39 Sibille L,Hadda N,Nicot F,et al.Granular plasticity,a contribution from discrete mechanics.Journal of the Mechanics&Physics of Solids,2015,75:119-139
40 Latham JP,Munjiza A,Garcia X,et al.Three-dimensional particle shape acquisition and use of shape library for DEM and FEM/DEMsimulation.Minerals Engineering,2008,21(11):797-805
41 Zhou W,Yang L,Ma G,et al.Macro-micro responses of crushable granular materials in simulated true triaxial tests.Granular Matter,2015,17(4):497-509
42 Alaei E,Mahboubi A.A discrete model for simulating shear strength and deformation behaviour of rockfill material,considering the particle breakage phenomenon.Granular Matter,2012,14(6):707-717
43 Yuan C,Chareyre B,Darve F.Pore-scale simulations of drainage in granular materials:Finite size effects and the representative elementary volume.Advances in Water Resources,2015,95:109-124
44 Lade PV,Duncan JM.Elasto-plastic stress-strain theory for cohesionless soil.ASCE Journal of the Geotechnical Engineering Division,1975,101(1):1037-1053
45 Matsuoka H,Nakai T.Relationship among Tresca,Mises,MohrCoulomb and Matsuoka-Nakai failure criteria.Soils&Foundations,2008,25(4):123-128
46 Kanatani K I.Stereological determination of structural anisotropy.International Journal of Engineering Science,1984,22(5):531-546
47 Oda M.Fabric tensor for discontinuous geological materials.Soils and Foundations,1982,22(4):96-108
49 Li XS,Dafalias YF.Dissipation consistent fabric tensor definition from DEM to continuum for granular media.Journal of the Mechanics and Physics of Solids,2015,78:141-153
2程展林,丁红顺,吴良平.粗粒土试验研究.岩土工程学报,2007,29(8):1151-1158(Cheng Zhanlin,Ding Hongshun,Wu Liangping.Experimental study on mechanical behaviour of granular material.Chinese Journal of Geotechnical Engineering,2007,29(8):1151-1158(in Chinese))
3黄茂松,姚仰平,尹振宇等.土的基本特性及本构关系与强度理论研究进展//中国土木工程学会全国土力学及岩土工程学术大会,2015(Huang Maosong,Yao Yangping,Yin Zhenyu,et al.Progress in the study of elementary mechanical behaviors,constitutive modeling and failure criterion of soils//The 12th National Conference on Soil Mechanics and Geotechnical Engineering of China Civil Engineering Society,2015(in Chinese))
4 Darve F,Laouafa F.Instabilities in granular materials and application to landslides.Mechanics of Cohesive-frictional Materials,2000,5(8):627-652
5 Nicot F,Darve F.A micro-mechanical investigation of bifurcation in granular materials.International Journal of Solids&Structures,2007,44(20):6630-6652
6 Nicot F,Darve F.The H-microdirectional model:Accounting for a mesoscopic scale.Mechanics of Materials,2011,43(12):918-929
7 Small M,Walker D M,Tordesillas A,et al.Characterizing chaotic dynamics from simulations of large strain behavior of a granular material under biaxial compression.Chaos:An Interdisciplinary Journal of Nonlinear Science,2013,23(1):013113
8 Zhou W,Liu J,Ma G,et al.Macroscopic and microscopic behaviors of granular materials under proportional strain path:A DEMstudy.International Journal for Numerical and Analytical Methods in Geomechanics,2016,40(18):2450-2467
9钱建固,黄茂松.轴对称状态下土体剪切带触发形成的分叉理论.岩土工程学报,2003,25(4):400-404(Qian Jiangu,Huang Maosong.Bifurcation of soils at inception of shear band under axisymmetric conditions.Chinese Jounal of Geotechnical Engineering,2003,25(4):400-404(in Chinese))
10 Drescher A,Jong GDJD.Photoelastic verification of a mechanical model for the flow of a granular material.Journal of the Mechanics&Physics of Solids,1972,20(5):337-340
11王雨婷.摩擦特性对颗粒材料宏细观力学特征的影响.[硕士论文].武汉:武汉大学,2017(Wang Yuting.The influence of friction properties on macro-mechanical characteristics of granular materials.[Master Thesis].Wuhan:Wuhan University,2017(in Chinese))
12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))
13熊迅,李天密,马棋棋等.石英玻璃圆环高速膨胀碎裂过程的离散元模拟.力学学报,2018,50(3):622-632(Xiong Xun,Li Tianmi,Ma Qiqi,et al.Discrete element simulations of the high velocity expension and fragmentation of qartz glass rings.Chinese Journal of Theoretical and Applied Mechanics,2018,50(3):622-632(in Chinese))
14周博,黄润秋,汪华斌等.基于离散元法的砂土破碎演化规律研究.岩土力学,2014,35(9):2709-2716(Zhou Bo,Huang Ruiqiu,Wang Huabin,et al.Study of evolution of sand crushability based on discrete elements method.Rock&Soil Mechanics,2014,35(9):2709-2716(in Chinese))
15刘嘉英,马刚,周伟等.抗转动特性对颗粒材料分散性失稳的影响研究.岩土力学,2017,38(5):1472-1480(Liu Jiaying,Ma Gang,Zhou Wei,et al.Impact of rotation resistance on diffuse failure of granular materials.Rock&Soil Mechanics,2017,38(5):1472-1480(in Chinese))
16刘嘉英,马刚,周伟等.基于离散元的颗粒材料三维临界状态与剪胀特性研究.水利学报,2017,48(9):1107-1117(Liu Jiaying,Ma Gang,Zhou Wei,et al.Three-dimensional critical state and dilatancy of granular materials based on DEM.Journal of Hydraulic Engineering,2017,48(9):1107-1117(in Chinese))
17周伟,刘东,马刚等.基于随机散粒体模型的堆石体真三轴数值试验研究.岩土工程学报,2012,34(4):748-755(Zhou Wei,Liu Dong,Ma Gang,et al.Numerical simulation of true triaxial tests on mechanical behaviors of rockfill based on stochastic granule model.Chinese Journal of Geotechnical Engineering,2012,34(4):748-755(in Chinese))
18 Zhou W,Ma G,Chang X,et al.Influence of particle shape on behavior of rockfill using a three-dimensional deformable DEM.Journal of Engineering Mechanics,2013,139(12):1868-1873
19 Ma G,Zhou W,Ng TT,et al.Microscopic modeling of the creep behavior of rockfills with a delayed particle breakage model.Acta Geotechnica,2015,10(4):481-496
20 Ma G,Regueiro RA,Zhou W,et al.Role of particle crushing on particle kinematics and shear banding in granular materials.Acta Geotechnica,2018(6):1-18
21 Rothenburg L,Bathurst RJ.Analytical study of induced anisotropy in idealized granular materials.G′eotechnique,1989,39(4):601-614
22 Chantawarangul K.Numerical simulations of three-dimensional granular assemblies.[Ph D Thesis].University,of Waterloo,1993
23 Zhao J,Guo N.Unique critical state characteristics in granular media considering fabric anisotropy.Geotechnique,2013,63(8):695-704
24 Radjai F,Jean M,Moreau JJ,et al.Force Distributions in Dense Two-Dimensional Granular Systems.Physical Review Letters,1996,77(2):274-277
25 Radjai F,Wolf DE,Jean M,et al.Bimodal character of stress transmission in granular packings.Physical Review Letters,1998,80(1):61-64
26张敏,许成顺,杜修力等.中主应力系数及应力路径对砂土剪切特性影响的真三轴试验研究.水利学报,2015,46(9):1072-1079(Zhang Min,Xu Chengshun,Du Xiuli,et al.True triaxial experimental research on shear behaviors of sand under different intermediate principal stresses and different stress paths.Journal of Hydraulic Engineering,2015,46(9):1072-1079(in Chinese))
27 Huang X,Hanley KJ,O’Sullivan C,et al.DEM analysis of the influence of the intermediate stress ratio on the critical-state behaviour of granular materials.Granular Matter,2014,16(5):641-655
28 Ma G,Chang X L,Zhou W,et al.Mechanical response of rockfills in a simulated true triaxial test:A combined FDEM study.Geomechanics&Engineering,2014,7(3):317-333
29 Zhou W,Liu J,Ma G,et al.Three-dimensional DEM investigation of critical state and dilatancy behaviors of granular materials.Acta Geotechnica,2017,12(3):1-14
30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))
31 Li X S,Dafalias Y F.Anisotropic critical state theory:Role of fabric.Journal of Engineering Mechanics,2012,138(3):263-275
32白冰,周健.扫描电子显微镜测试技术在岩土工程中的应用与进展.电子显微学报,2001,20(2):154-160(Bai Bing,Zhou Jian.Application and progress of scanning electron microscopy testing technology in geotechnical engineering.Journal of Chinese Electron Microscopy Society,2001,20(2):154-160(in Chinese))
33 Yang J,Yang ZX,Li XS.Quantifying and modelling fabric anisotropy of granular soils.G′eotechnique,2008,58(4):237-248
34 Hall SA,Bornert M,Desrues J,et al.Discrete and continuum analysis of localised deformation in sand using X-ray CT and volumetric digital image correlation.G′eotechnique,2010,60(5):11-20
35程展林,左永振,丁红顺.CT技术在岩土试验中的应用研究.长江科学院院报,2011,28(3):33-38(Chen Zhanlin,Zuo Yongzhen,Ding Hongshun.Application research of CT technology in geotechnical experiment.Journal of Yangtze River Scientific Research Institute,2011,28(3):33-38(in Chinese))
36姜景山,程展林,左永振等.粗粒土CT三轴流变试验研究.岩土力学,2014(9):2507-2514(Jiang Jinshan,Cheng Zhanlin,Zuo Youzhen,et al.CT triaxial rheological test on coarse-grained soils.Rock&Soil Mechanics,2014(9):2507-2514(in Chinese))
37徐小敏.砂土液化及其判别的微观机理研究.[博士论文].杭州:浙江大学,2012(Xu Xiaomin.Study on the micromechanism of sand liquefaction and its evalution.[PhD Thesis].Hangzhou:Zhejiang University,2012(in Chinese))
38戴北冰,杨峻,周翠英.松砂不稳定行为的数值模拟研究.岩土工程学报,2013,35(9):1737-1745(Dai Beibing,Yang Jun,Zhou Cuiying.Numerical study on instability behavior of sand.Chinese Journal of Geotechnical Engineering,2013,35(9):1737-1745(in Chinese))
39 Sibille L,Hadda N,Nicot F,et al.Granular plasticity,a contribution from discrete mechanics.Journal of the Mechanics&Physics of Solids,2015,75:119-139
40 Latham JP,Munjiza A,Garcia X,et al.Three-dimensional particle shape acquisition and use of shape library for DEM and FEM/DEMsimulation.Minerals Engineering,2008,21(11):797-805
41 Zhou W,Yang L,Ma G,et al.Macro-micro responses of crushable granular materials in simulated true triaxial tests.Granular Matter,2015,17(4):497-509
42 Alaei E,Mahboubi A.A discrete model for simulating shear strength and deformation behaviour of rockfill material,considering the particle breakage phenomenon.Granular Matter,2012,14(6):707-717
43 Yuan C,Chareyre B,Darve F.Pore-scale simulations of drainage in granular materials:Finite size effects and the representative elementary volume.Advances in Water Resources,2015,95:109-124
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