Review of particle breakage simulation based on DEM
XU Kun1, 2, ZHOU Wei1, 2, MA Gang1, 2, CHANG Xiao-lin1, 2, YANG Li-fu1, 2
1. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China; 2. Key Laboratory of Rock Mechanics in Hydraulic Structural Engineering, Wuhan University, Ministry of Education, Wuhan 430072, China
Abstract:Particle breakage has a significant effect on the macro- and micro-mechanical behaviors of granular assemblies. The development of micro-scale researches on particle breakage based on physical experiments is limited by the current experimental techniques. An efficient way is provided to investigate the effect of particle breakage on the behavior of granular assemblies from different scales with the proposed discrete element method (DEM). The worldwide researches are reviewed, and two kinds of particle breakage simulation methods based on DEM are introduced, namely the particle breakage simulation methods based on the bonded-particle model (BPM) and based on the fragment replacement method (FRM). The distinct problems for the particle breakage simulation method based on BPM are that it is not suitable for a large-scale numerical simulation and has a limited breakage level. Two key points, the fragment replacement mode and the particle breakage criterion, should be considered when using the particle breakage simulation method based on FRM. The fragment number, size distribution and law of mass conservation strategies of fragment replacement mode are discussed as well as the stress criterion and force criterion for particle breakage. The possible research emphasis in the field of particle breakage simulation method based on DEM is proposed.
徐琨, 周伟, 马刚, 常晓林, 杨利福. 基于离散元法的颗粒破碎模拟研究进展[J]. 岩土工程学报, 2018, 40(5): 880-889.
XU Kun, ZHOU Wei, MA Gang, CHANG Xiao-lin, YANG Li-fu. Review of particle breakage simulation based on DEM. Chinese J. Geot. Eng., 2018, 40(5): 880-889.
[1] HARDIN B O. Crushing of soil particles[J]. Journal of Geotechnical Engineering, 1985, 111(10): 1177-1192. [2] BOLTON M D. The strength and dilatancy of sands[J]. Géotechnique, 1986, 36(1): 65-78. [3] 郭熙灵, 胡 辉, 包承纲. 堆石料颗粒破碎对剪胀性及抗剪强度的影响[J]. 岩土工程学报, 1997, 19(3): 86-91. (GUO Xi-ling, HU Hui, BAO Cheng-gang. Experimental studies of the effects of grain breakage on the dilatancy and shear strength of rock fill[J]. Chinese Journal of Geotechnical Engineering, 1997, 19(3): 86-91. (in Chinese)) [4] 汪 稔, 孙吉主. 钙质砂不排水性状的损伤-滑移耦合作用分析[J]. 水利学报, 2002, 7(7): 75-78. (WANG Ren, SUN Ji-zhu. Damage-slide coupled interaction behavior of undrained calcareous sand[J]. Journal of Hydraulic Engineering, 2002, 7(7): 75-78. (in Chinese)) [5] 刘汉龙, 秦红玉, 高玉峰, 等. 堆石粗粒料颗粒破碎试验研究[J]. 岩土力学, 2005, 26(4): 562-566. (LIU Han-long, QIN Hong-yu, GAO Yu-feng, et al. Experimental study on particle breakage of rockfill and coarse aggregates[J]. Rock and Soil Mechanics, 2005, 26(4): 562-566. (in Chinese)) [6] 魏 松, 朱俊高. 粗粒料三轴湿化颗粒破碎试验研究[J]. 岩石力学与工程学报, 2006, 25(6): 1252-1258. (WEI Song, ZHU Jun-gao. Study on wetting breakage of coarse-grained materials in triaxial test[J]. Chinese Journal of Rock Mechanics and Engineering, 2006, 25(6): 1252-1258. (in Chinese)) [7] 井国庆, 封 坤, 高 亮, 等. 循环荷载作用下道砟破碎老化的离散元仿真[J]. 西南交通大学学报, 2012, 47(2): 187-191. (JING Guo-qing, FENG Kun, GAO Liang, et al. DEM simulation of ballast degradation and breakage under cyclic loading[J]. Journal of Southwest Jiaotong University, 2012, 47(2): 187-191. (in Chinese)) [8] INDRARATNA B, LACKENBY J, CHRISTIE D. Effect of confining pressure on the degradation of ballast under cyclic loading[J]. Géotechnique, 2005, 55(4): 325-328. [9] 陈生水, 霍家平, 章为民. “ 5.12”汶川地震对紫坪铺混凝土面板坝的影响及原因分析[J]. 岩土工程学报, 2008, 30(6): 795-801. (CHEN Sheng-shui, HUO Jia-ping, ZHANG Wei-min. Analysis of effects of “5.12” Wenchuan Earthquake on Zipingpu Concrete Face Rock-fill Dam[J]. Chinese Journal of Geotechnical Engineering , 2008, 30(6): 795-801. (in Chinese)) [10] COOP M R, LEE I K. The behaviour of granular soils at elevated stresses: predictive soil mechanics[C]// Proceedings of Wroth Memorial Symposium. London, 1993: 186-198. [11] MCDOWELL G R, BOLTON M D. On the micromechanics of crushable aggregates[J]. Géotechnique, 1998, 48(5): 667-679. [12] 张家铭, 汪 稔, 张阳明, 等. 土体颗粒破碎研究进展[J] .岩土力学, 2003, 24(增刊1): 661-665. (ZHANG Jia-ming, WANG Ren, ZHANG Yang-ming, et al. Advance in studies of soil grain crush[J]. Rock and Soil Mechanics, 2003, 24(S1): 661-665. (in Chinese)) [13] 刘汉龙, 孙逸飞, 杨 贵, 等. 粗粒料颗粒破碎特性研究述评[J]. 河海大学学报: 自然科学版, 2012, 40(4): 361-369. (LIU Han-long, SUN Yi-fei, YANG Gui, et al. A review of particle breakage characteristics of coarse aggregates[J]. Journal of Hohai University: Natural Sciences, 2012, 40(4): 361-369. (in Chinese)) [14] KH A B, MIRGHASEMI A A, MOHAMMADI S. Numerical simulation of particle breakage of angular particles using combined DEM and FEM[J]. Powder Technology, 2011, 205(1): 15-29. [15] MA G, ZHOU W, CHANG X L, et al. A hybrid approach for modeling of breakable granular materials using combined finite-discrete element method[J]. Granular Matter, 2016, 18(1): 1-17. [16] MA G, ZHOU W, CHANG X L. Modeling the particle breakage of rockfill materials with the cohesive crack model[J]. Computers and Geotechnics, 2014, 61: 132-143. [17] LOBO-GUERRERO S, VALLEJO L E. Discrete element method analysis of railtrack ballast degradation during cyclic loading[J]. Granular Matter, 2006, 8(3/4): 195-204. [18] MCDOWELL G R, DE BONO J P. On the micro mechanics of one-dimensional normal compression[J]. Géotechnique, 2013, 63(11): 895-908. [19] 刘 君, 刘福海, 孔宪京. 考虑破碎的堆石料颗粒流数值模拟[J]. 岩土力学, 2008, 29(增刊): 107-112. (LIU Jun, LIU Fu-hai, KONG Xian-jing. Particle flow code numerical simulation of particle breakage of rockfill[J]. Rock and Soil Mechanics, 2008, 29(S0): 107-112. (in Chinese)) [20] 姜 浩, 徐 明. 碎石料应力路径大型三轴试验的离散元模拟研究[J]. 工程力学, 2014, 31(10): 151-157. (JIANG Hao, XU Ming. Study of stress-path-dependent behavior of rockfills using discrete element method[J]. Engineering Mechanics, 2014, 31(10): 151-157. (in Chinese)) [21] 邵 磊, 迟世春, 张 勇, 等. 基于颗粒流的堆石料三轴剪切试验研究[J]. 岩土力学, 2013, 34(3): 711-720. (SHAO Lei, CHI Shi-chun, ZHANG Yong, et al. Study of triaxial shear tests for rockfill based on particle flow code[J]. Rock and Soil Mechanics, 2013, 34(3): 711-720. (in Chinese)) [22] ZHOU W, YANG L, MA G, et al. DEM analysis of the size effects on the behavior of crushable granular materials[J]. Granular Matter, 2016, 18(3): 1-11. [23] CIL M B, ALSHIBLI K A. 3D evolution of sand fracture under 1D compression[J]. Géotechnique, 2014, 64(5): 351-364. [24] CIL M B, BUSCARNERA G. DEM assessment of scaling laws capturing the grain size dependence of yielding in granular soils[J]. Granular Matter, 2016, 18(3): 1-15. [25] DRUCKREY A M, ALSHIBLI K A. 3D finite element modeling of sand particle fracture based on in situ X‐Ray synchrotron imaging[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2016, 40(1): 105-116. [26] 罗 滔, OOI E T, CHAN A H C, 等. 一种模拟堆石料颗粒破碎的离散元-比例边界有限元结合法[J]. 岩土力学, 2017(5): 883-892. (LUO Tao, OOI E T, CHAN A H C, et al. A combined DEM-SBFEM for particle breakage modelling of rock-fill materials[J]. Rock and Soil Mechanics, 2017(5): 883-892. (in Chinese)) [27] MCDOWELL G R, HARIRECHE O. Discrete element modelling of soil particle fracture[J]. Géotechnique, 2002, 52(2): 131-136. [28] MCDOWELL G R, HARIRECHE O. Discrete element modelling of yielding and normal compression of sand[J]. Géotechnique, 2002, 52(4): 299-304. [29] CHENG Y P, NAKATA Y, BOLTON M D. Discrete element simulation of crushable soil[J]. Géotechnique, 2003, 53(7): 633-642. [30] CHENG Y P, BOLTON M D, NAKATA Y. Grain crushing and critical states observed in DEM simulations[C]// Proceedings of the 5th International Conference on Micromecnanics of Granular Media. Stuttgart, 2005, 2: 1393-1397. [31] LIM W L, MCDOWELL G R. Discrete element modelling of railway ballast[J]. Granular Matter, 2005, 7(1): 19-29. [32] LU M, MCDOWELL G R. Discrete element modelling of ballast abrasion[J]. Géotechnique, 2006, 56(9): 651-655. [33] LU M, MCDOWELL G R. Discrete element modelling of railway ballast under triaxial conditions[J]. Geomechanics and Geoengineering: An International Journal, 2008, 3(4): 257-270. [34] 史旦达, 周 健, 贾敏才, 等. 考虑颗粒破碎的砂土高应力一维压缩特性颗粒流模拟[J]. 岩土工程学报, 2007, 29(5): 736-742. (SHI Dan-da, ZHOU Jian, JIA Min-cai, et al. Numerical simulations of particle breakage property of sand under high pressure 1D compression condition by use of particle flow code[J]. Chinese Journal of Geotechnical Engineering, 2007, 29(5): 736-742. (in Chinese)) [35] BOLTON M D, NAKATA Y, CHENG Y P. Micro-and macro-mechanical behaviour of DEM crushable materials[J]. Géotechnique, 2008, 58(6): 471-480. [36] CIL M B, ALSHIBLI K A. 3D assessment of fracture of sand particles using discrete element method[J]. Géotechnique Letters, 2012, 2(3): 161-166. [37] ALONSO E E, TAPIAS M, GILI J. Scale effects in rockfill behaviour[J]. Géotechnique Letters, 2012, 2(3): 155-160. [38] WANG J, YAN H. On the role of particle breakage in the shear failure behavior of granular soils by DEM[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(8): 832-854. [39] ÅSTRÖM J A, HERRMANN H J. Fragmentation of grains in a two-dimensional packing[J]. The European Physical Journal B-Condensed Matter and Complex Systems, 1998, 5(3): 551-554. [40] TSOUNGUI O, VALLET D, CHARMET J C. Numerical model of crushing of grains inside two-dimensional granular materials[J]. Powder Technology, 1999, 105(1): 190-198. [41] MARKETOS G, BOLTON M D. Compaction bands simulated in discrete element models[J]. Journal of Structural Geology, 2009, 31(5): 479-490. [42] BEN-NUN O, EINAV I. The role of self-organization during confined comminution of granular materials[J]. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 2010, 368(1910): 231-247. [43] BROSH T, KALMAN H, LEVY A. Fragments spawning and interaction models for DEM breakage simulation[J]. Granular Matter, 2011, 13(6): 765-776. [44] DE BONO J P, MCDOWELL G R. DEM of triaxial tests on crushable sand[J]. Granular Matter, 2014, 16(4): 551-562. [45] ZHOU W, YANG L, MA G, et al. Macro-micro responses of crushable granular materials in simulated true triaxial tests[J]. Granular Matter, 2015, 17(4): 497-509. [46] CIANTIA M, ARROYO ALVAREZ DE TOLEDO M, CALVETTI F, et al. An approach to enhance efficiency of DEM modelling of soils with crushable grains[J]. Géotechnique, 2015, 65(2): 91-110. [47] 杨 贵, 许建宝, 刘昆林. 粗粒料颗粒破碎数值模拟研究[J]. 岩土力学, 2015, 36(11): 3301-3306. (YANG Gui, XU Jian-bao, LIU Kun-lin. Numerical simulation of particle breakage of coarse aggregates[J]. Rock and Soil Mechanics, 2015, 36(11): 3301-3306. (in Chinese)) [48] THORNTON C, YIN K K, ADAMS M J. Numerical simulation of the impact fracture and fragmentation of agglomerates[J]. Journal of Physics D: Applied Physics, 1996, 29(2): 424-435. [49] POTYONDY D O, CUNDALL P A. A bonded-particle model for rock[J]. International Journal of Rock Mechanics and Mining Sciences, 2004, 41(8): 1329-1364. [50] DE BONO J P, MCDOWELL G R. Investigating the effects of particle shape on normal compression and over consolidation using DEM[J]. Granular Matter, 2016, 18(3): 1-10. [51] CLARKE D R, FABER K T. Fracture of ceramics and glasses[J]. Journal of Physics and Chemistry of Solids, 1987, 48(11): 1115-1157. [52] LI Y S, DUXBURY P M. From moduli scaling to breakdown scaling: A moment-spectrum analysis[J]. Physical Review B, 1989, 40(7): 4889. [53] LOBO-GUERRERO S, VALLEJO L E. Analysis of crushing of granular material under isotropic and biaxial stress conditions[J]. Soils and Foundations, 2005, 45(4): 79-87. [54] LOBO-GUERRERO S, VALLEJO L E. Crushing a weak granular material: experimental numerical analyses[J]. Géotechnique, 2005, 55(3): 245-249. [55] TSOUNGUI O, VALLET D, CHARMET J C. Numerical model of crushing of grains inside two-dimensional granular materials[J]. Powder Technology, 1999, 105(1): 190-198. [56] NAKATA Y, HYODO M, HYDE A F L, et al. Microscopic particle crushing of sand subjected to high pressure one-dimensional compression[J]. Soils and Foundations, 2001, 41(1): 69-82. [57] BEN-NUN O, EINAV I. A refined DEM study of grain size reduction in uniaxial compression[C]// Proceedings of the 12th International Conference of the International Association for Computer Methods and Advances in Geomechanics (IACMAG). Goa, 2008: 702-708. [58] RUSSELL A R, WOOD D M. Point load tests and strength measurements for brittle spheres[J]. International Journal of Rock Mechanics and Mining Sciences, 2009, 46(2): 272-280. [59] RUSSELL A R, WOOD D M, KIKUMOTO M. Crushing of particles in idealised granular assemblies[J]. Journal of the Mechanics and Physics of Solids, 2009, 57(8): 1293-1313. [60] DE BONO J P, MCDOWELL G R. Particle breakage criteria in discrete element modelling[J]. Géotechnique, 2016. doi:10.1680/jgeot.15.P.280 [61] SUKUMARAN B, EINAV I. DYSKIN A V. Qualitative assessment of the influence of coordination number on crushing strength using DEM[C]// Proceeding of the Fifth World Congress on Particle Technology. Florida, 2006. [62] TAKEI M, KUSAKABE O, HAYASHI T. Time-dependent behavior of crushable materials in one-dimensional compression tests[J]. Soils and Foundations, 2001, 41(1): 97-121.