硕士论文开题报告-基于真实形态的颗粒材料细观力学研究

攻读硕士学位论文选题报告题目：基于真实形态的颗粒材料细观力学研究院系：水利水电工程系专业：土木工程2014年5月22日1研究背景颗粒材料是自然界中最常见的一种材料，在泥石流、滑坡等工程地质灾害中，其主要成分是颗粒材料。REF_Ref420263062\h图1是四川地震中小岗剑堰塞湖现场照片，REF_Ref420263065\h图2是亚洲第一大、世界第二大的易贡大滑坡，图中显示这两个地质灾害现场的主要成分是颗粒材料。颗粒材料在岩土工程、水利工程中被广泛使用，在糯扎渡高土石坝中，其使用的土石混合体是一种岩土领域最典型的颗粒材料，西恒山水库中所使用的堆石，其粗骨料也是大量颗粒材料构成。在工业生产，如化工、制药、冶金以及核工业中，都涉及到大量的颗粒材料，在炼铁工业中，铁矿石和煤炭都是颗粒材料，而新型的核反应堆设计，也将核燃料设计成球形的颗粒材料，研究颗粒材料与流体之间的热交换是新型核反应堆的一个重要课题。图SEQ图\*ARABIC1小岗剑堰塞湖图SEQ图\*ARABIC2易贡大滑坡图SEQ图\*ARABIC3糯扎渡高土石坝图SEQ图\*ARABIC4西恒山水电站2研究现状与不足颗粒材料十分复杂，2005年，在杂志创刊125周年之际，Science将“发展动态湍流理论以及颗粒材料的运动理论”列为重要的125个基础性问题之一，可见，颗粒材料的研究是一个基础性的研究，其研究成果将能够应用到实际工业生产中的各个领域，颗粒材料运动理论的研究也是一个十分具有挑战性的工作。本文将从以下五个部分进行研究：颗粒形态获取；三维模型建立；几何形态性质研究；颗粒形状表征；力学特性研究。2.1颗粒形态的获取过去十余年时间，国外学者尝试了使用激光、X光以及结构光对颗粒进行三维扫描。LanaroADDINEN.CITE<EndNote><Cite><Author>Lanaro</Author><Year>1998</Year><RecNum>258</RecNum><DisplayText><styleface="superscript">[1]</style></DisplayText><record><rec-number>258</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1426558522">258</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Lanaro,F</author><author>Jing,L</author><author>Stephansson,O</author></authors></contributors><titles><title>3-D-lasermeasurementsandrepresentationofroughnessofrockfractures</title><secondary-title>Proc.MechanicsofJointedandFaultedRock,Vienna.AABalkema,Rotterdam</secondary-title></titles><periodical><full-title>Proc.MechanicsofJointedandFaultedRock,Vienna.AABalkema,Rotterdam</full-title></periodical><pages>185-189</pages><dates><year>1998</year></dates><urls></urls></record></Cite></EndNote>[1]和TolppanenADDINEN.CITE<EndNote><Cite><Author>Lanaro</Author><Year>2002</Year><RecNum>257</RecNum><DisplayText><styleface="superscript">[2]</style></DisplayText><record><rec-number>257</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1426558404">257</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Lanaro,F</author><author>Tolppanen,P</author></authors></contributors><titles><title>3Dcharacterizationofcoarseaggregates</title><secondary-title>EngineeringGeology</secondary-title></titles><periodical><full-title>EngineeringGeology</full-title></periodical><pages>17-30</pages><volume>65</volume><number>1</number><dates><year>2002</year></dates><isbn>0013-7952</isbn><urls><related-urls><url>/S0013795201001338/1-s2.0-S0013795201001338-main.pdf?_tid=fc6854ee-cc4a-11e4-acd7-00000aacb35d&acdnat=1426558496_d69265aaea2f835949ab454d8f514e24</url></related-urls></urls></record></Cite></EndNote>[2]教授分别于1998年和2002年使用三维激光对粗骨料进行三维扫描；GarbocziADDINEN.CITE<EndNote><Cite><Author>Garboczi</Author><Year>2002</Year><RecNum>210</RecNum><DisplayText><styleface="superscript">[3]</style></DisplayText><record><rec-number>210</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1423642699">210</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>E.J.Garboczi</author></authors></contributors><titles><title>Three-dimensionalmathematicalanalysisofparticleshapeusingX-raytomographyandsphericalharmonics:Applicationtoaggregatesusedinconcrete</title><secondary-title>CementandConcreteResearch</secondary-title></titles><periodical><full-title>CementandConcreteResearch</full-title></periodical><pages>1621–1638</pages><volume>32</volume><number>10</number><dates><year>2002</year></dates><urls></urls></record></Cite></EndNote>[3]和TaylorADDINEN.CITE<EndNote><Cite><Author>Taylor</Author><Year>2006</Year><RecNum>274</RecNum><DisplayText><styleface="superscript">[4]</style></DisplayText><record><rec-number>274</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1432110422">274</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>M.A.Taylor</author><author>E.J.Garboczi</author><author>S.T.Erdogan</author><author>D.W.Fowler</author></authors></contributors><titles><title>Somepropertiesofirregular3-Dparticles</title><secondary-title>PowderTechnology</secondary-title></titles><periodical><full-title>PowderTechnology</full-title></periodical><pages>1–15</pages><volume>162</volume><number>1</number><dates><year>2006</year></dates><urls></urls></record></Cite></EndNote>[4]教授分别与2002年和2006年使用X光对块石进行三维扫描，并且分析其三维几何形态性质；RocchiniADDINEN.CITE<EndNote><Cite><Author>Rocchini</Author><Year>2001</Year><RecNum>261</RecNum><DisplayText><styleface="superscript">[5]</style></DisplayText><record><rec-number>261</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1426560427">261</key></foreign-keys><ref-typename="ConferenceProceedings">10</ref-type><contributors><authors><author>Rocchini,CMPPC</author><author>Cignoni,Paulo</author><author>Montani,Claudio</author><author>Pingi,Paolo</author><author>Scopigno,Roberto</author></authors></contributors><titles><title>Alowcost3Dscannerbasedonstructuredlight</title><secondary-title>ComputerGraphicsForum</secondary-title></titles><pages>299-308</pages><volume>20</volume><number>3</number><dates><year>2001</year></dates><publisher>WileyOnlineLibrary</publisher><isbn>1467-8659</isbn><urls></urls></record></Cite></EndNote>[5]和Hall-HoltADDINEN.CITE<EndNote><Cite><Author>Rocchini</Author><Year>2001</Year><RecNum>261</RecNum><DisplayText><styleface="superscript">[5]</style></DisplayText><record><rec-number>261</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1426560427">261</key></foreign-keys><ref-typename="ConferenceProceedings">10</ref-type><contributors><authors><author>Rocchini,CMPPC</author><author>Cignoni,Paulo</author><author>Montani,Claudio</author><author>Pingi,Paolo</author><author>Scopigno,Roberto</author></authors></contributors><titles><title>Alowcost3Dscannerbasedonstructuredlight</title><secondary-title>ComputerGraphicsForum</secondary-title></titles><pages>299-308</pages><volume>20</volume><number>3</number><dates><year>2001</year></dates><publisher>WileyOnlineLibrary</publisher><isbn>1467-8659</isbn><urls></urls></record></Cite></EndNote>[5]教授分别于2001年使用结构光对块石进行三维扫描。这三种扫描方式各有优势，我们课题组都有做过相关茶花女故事，激光三维扫描精度一般，使用成本较高，Leica系列三维扫描仪购置成本达到120万，其对使用环境不是很严苛，主要针对于地形进行扫描设计；X光CT三维扫描的成本十分高，但是其精度也很高，只能在室内使用，不具备便携性；结构光这些年的发展十分迅速，目前市面上流行的结构光三维扫描仪的精度一般，但是成本十分低廉，十分轻巧，便携性十分好。由于我们需要在滑坡、泥石流、施工现场、地质考察过程中对颗粒进行扫描，考虑到经济性和便携性，我们最终选取结构光对颗粒进行大规模扫描，采集大量颗粒三维几何信息，论文选取的结构光扫描设备是微软公司出品的Kinect。2.2三维模型的建立自从1995年以来，随着数字图像处理技术用于究竟系测量材料外观结合形态甚至是内部几何构造，其在沥青混凝土、水泥混凝土、土石混合体等研究的应用逐渐得到广泛应用。发展到目前，数字图像技术在该领域的应用主要集中于以下几个方面：利用数码相机对单个块石的表面几何参数进行分析；利用激光扫描技术，获取块石颗粒的精确三维尺寸，分析其菱角指数、纹理指数等；利用X-RayCT技术实现混凝土、土石混合体的内部构造成像，对其进行三维重建，生成数值计算模型；利用随机生成技术，生成土石混合体的技术模型ADDINEN.CITE<EndNote><Cite><Author>徐文杰</Author><Year>2007</Year><RecNum>287</RecNum><DisplayText><styleface="superscript">[6]</style></DisplayText><record><rec-number>287</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1432553432">287</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>徐文杰</author><author>岳中琦</author><author>胡瑞林</author></authors></contributors><titles><title>基于数字图像的土、岩和混凝土内部结构定量分析和力学数值计算的研究进展</title><secondary-title>工程地质学报</secondary-title></titles><periodical><full-title>工程地质学报</full-title></periodical><pages>289-313</pages><volume>15</volume><number>3</number><dates><year>2007</year></dates><urls></urls></record></Cite></EndNote>[6]。油新华ADDINEN.CITE<EndNote><Cite><Author>油新华</Author><Year>2001</Year><RecNum>289</RecNum><DisplayText><styleface="superscript">[7,8]</style></DisplayText><record><rec-number>289</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1432553563">289</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>油新华</author></authors></contributors><titles><title>土石混合体的随机结构模型及其应用研究</title><secondary-title>岩石力学与工程学报</secondary-title></titles><periodical><full-title>岩石力学与工程学报</full-title></periodical><dates><year>2001</year></dates><urls></urls></record></Cite><Cite><Author>油新华</Author><Year>2003</Year><RecNum>288</RecNum><record><rec-number>288</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1432553505">288</key></foreign-keys><ref-typename="ConferenceProceedings">10</ref-type><contributors><authors><author>油新华</author><author>李晓</author><author>何刚</author></authors></contributors><titles><title>土石混合体的随机结构模型及其生成技术研究</title><secondary-title>全国岩土与工程学术大会论文集（上册）</secondary-title></titles><dates><year>2003</year></dates><urls></urls></record></Cite></EndNote>[7,8]利用FORTRAN编写了AutoCAD、ANSYS、FLAC3D的接口程序，实现了土石混合体边坡数值建模；还根据土石混合体的结构特点，编了基于数码照片的建模程序，生成了土石混合体的二维结构模型。廖秋林ADDINEN.CITE<EndNote><Cite><Author>廖秋林</Author><Year>2010</Year><RecNum>290</RecNum><DisplayText><styleface="superscript">[9]</style></DisplayText><record><rec-number>290</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1432553641">290</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>廖秋林</author><author>李晓</author><author>朱万成</author><author>LIU</author><author>Jishan</author></authors></contributors><titles><title>基于数码图像土石混合体结构建模及其力学结构效应的数值分析</title><secondary-title>岩石力学与工程学报</secondary-title></titles><periodical><full-title>岩石力学与工程学报</full-title></periodical><pages>155-162</pages><volume>29</volume><number>1</number><dates><year>2010</year></dates><urls></urls></record></Cite></EndNote>[9]利用数码数字成像技术，利用土石混合体中块石和土体在颜色上的差异，实现了基于数码图像的土石混合体结构模型自动生成，并且建立了土石混合体的力学结构模型，利用有限元模拟系统实现了土石混合体数值计算。丁秀丽ADDINEN.CITE<EndNote><Cite><Author>丁秀丽</Author><Year>2010</Year><RecNum>291</RecNum><DisplayText><styleface="superscript">[10]</style></DisplayText><record><rec-number>291</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1432553689">291</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>丁秀丽</author><author>李耀旭</author><author>王新</author></authors></contributors><titles><title>基于数字图像的土石混合体力学性质的颗粒流模拟</title><secondary-title>岩石力学与工程学报</secondary-title></titles><periodical><full-title>岩石力学与工程学报</full-title></periodical><pages>477-484</pages><volume>29</volume><number>3</number><dates><year>2010</year></dates><urls></urls></record></Cite></EndNote>[10]等根据实际拍摄的数字图像，利用MATLAB的图像处理工具包，开发了图像处理系统，生成了二维的土石混合体数字模型，并且用PFC2D对模型进行了颗粒流模拟计算，研究了了细观角度土石混合体的力学特性。徐文杰ADDINEN.CITE<EndNote><Cite><Author>徐文杰</Author><Year>2007</Year><RecNum>287</RecNum><DisplayText><styleface="superscript">[6,11]</style></DisplayText><record><rec-number>287</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1432553432">287</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>徐文杰</author><author>岳中琦</author><author>胡瑞林</author></authors></contributors><titles><title>基于数字图像的土、岩和混凝土内部结构定量分析和力学数值计算的研究进展</title><secondary-title>工程地质学报</secondary-title></titles><periodical><full-title>工程地质学报</full-title></periodical><pages>289-313</pages><volume>15</volume><number>3</number><dates><year>2007</year></dates><urls></urls></record></Cite><Cite><Author>徐文杰</Author><Year>2008</Year><RecNum>292</RecNum><record><rec-number>292</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1432556710">292</key></foreign-keys><ref-typename="Thesis">32</ref-type><contributors><authors><author>徐文杰</author></authors></contributors><titles><title>土石混合体细观结构力学及其边坡稳定性研究</title></titles><dates><year>2008</year></dates><publisher>中国科学院地质与地球物理研究所</publisher><urls></urls></record></Cite></EndNote>[6,11]用随机生成技术实现了基于凸多边形块体的土石混合体二维细观结构生成系统，并且实现了三维土石混合体随机细观结构模型，并在此基础上进行了土石混合体的细观结构参数的研究，应用数值系统对下咱日土石混合体边坡进行稳定性分析。MollonADDINEN.CITE<EndNote><Cite><Author>Mollon</Author><Year>2012</Year><RecNum>293</RecNum><DisplayText><styleface="superscript">[12]</style></DisplayText><record><rec-number>293</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1432556739">293</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Mollon,Guilhem</author><author>Zhao,Jidong</author></authors></contributors><titles><title>Fourier–Voronoi-basedgenerationofrealisticsamplesfordiscretemodellingofgranularmaterials</title><secondary-title>GranularMatter</secondary-title></titles><periodical><full-title>GranularMatter</full-title></periodical><pages>621-638</pages><volume>14</volume><number>5</number><dates><year>2012</year></dates><urls></urls></record></Cite></EndNote>[12]等利用傅里叶描述因子和Voronoi棋盘法生成了任意形状的颗粒材料二维密实离散模型，并对该模型进行了数值试验研究。LeeSeungJaeADDINEN.CITE<EndNote><Cite><Author>Lee</Author><Year>2012</Year><RecNum>294</RecNum><DisplayText><styleface="superscript">[13]</style></DisplayText><record><rec-number>294</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1432556768">294</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Lee,SeungJae</author><author>Hashash,YoussefM.A.</author><author>Nezami,ErfanG.</author></authors></contributors><titles><title>Simulationoftriaxialcompressiontestswithpolyhedraldiscreteelements</title><secondary-title>Computers&Geotechnics</secondary-title></titles><periodical><full-title>Computers&Geotechnics</full-title></periodical><pages>92–100</pages><volume>43</volume><number>3</number><dates><year>2012</year></dates><urls></urls></record></Cite></EndNote>[13]等人利用多面体单元模拟土石混合体，并进行不同围压和初始孔隙率的三轴数值试验，证明了多面体单元用于数值模型试验的可行性。对土石混合体的研究已经进行了二十多年，尝试着用图像技术方法模拟真实的土石混合体也进行了十多年。最开始用照相机数码图像，分析土石混合体外观参数统计规律，后来利用照相机数码图像以及X-RayCT成像技术模拟土石混合体内部结构，到后来用多边形生成二维的土石混合体数值模型，以及用凸多面体生成三维的土石混合体数值模型。这些年土石混合体建模技术的发展是十分迅速的，但是这些技术有明显的缺陷。利用数码图像以及X-RayCT成像技术，其有三大缺点：一是成本昂贵；二是一次只能对一个模型进行扫描，数值模型生成过程太复杂，而且效率极其低下；三是不能够扫描真实情况下的土石混合体，依旧需要先制样，在扫描得到数值模型，实际价值不大，还不如做真实的物理试验。利用凸多边形生成二维的土石混合体数值模型，二维情况不能很好的模拟真实的三维模型，只能适用于侧限情况下的受力分析；而用凸多面体生成的三维土石混合体数值模型，虽然和实际情况十分接近，但是存在以下两大缺点：实际情况下的块石的形状各异，凸多面体的外形过于简单，与真实的块石相差太多；凸多面体的棱角过于分明，真实的块石并不是如此，在做数值计算时可能产生应力集中的现象，从而与实际情况相差较大，不能很好的揭示真实土石混合体内部的规律。本人于2014年本科毕业设计开发了基于真实形态的土石混合体精细结构生成系统，该系统可以生成基于真实块石形态的具有各种外观的土石混合体三维模型。但是该系统的含石量较低，只能达到15%-20%，因此在此基础上进行算法上的改进，以期达到更高含石量的土石混合体三维细观结构生成系统十分有必要。2.3几何形态性质研究关于颗粒几何形态的研究，加州大学戴维斯分校的Taylor教授和美国国家标准与技术研究所的Garboczi教授作了大量研究，GarbocziADDINEN.CITE<EndNote><Cite><Author>Garboczi</Author><Year>2002</Year><RecNum>210</RecNum><DisplayText><styleface="superscript">[3]</style></DisplayText><record><rec-number>210</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1423642699">210</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>E.J.Garboczi</author></authors></contributors><titles><title>Three-dimensionalmathematicalanalysisofparticleshapeusingX-raytomographyandsphericalharmonics:Applicationtoaggregatesusedinconcrete</title><secondary-title>CementandConcreteResearch</secondary-title></titles><periodical><full-title>CementandConcreteResearch</full-title></periodical><pages>1621–1638</pages><volume>32</volume><number>10</number><dates><year>2002</year></dates><urls></urls></record></Cite></EndNote>[3]教授研究了颗粒的球函数、体积、表面积、各阶惯性矩等参数，对颗粒表面形态性质有较为全面的研究，LanaroADDINEN.CITE<EndNote><Cite><Author>Lanaro</Author><Year>2002</Year><RecNum>257</RecNum><DisplayText><styleface="superscript">[2]</style></DisplayText><record><rec-number>257</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1426558404">257</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Lanaro,F</author><author>Tolppanen,P</author></authors></contributors><titles><title>3Dcharacterizationofcoarseaggregates</title><secondary-title>EngineeringGeology</secondary-title></titles><periodical><full-title>EngineeringGeology</full-title></periodical><pages>17-30</pages><volume>65</volume><number>1</number><dates><year>2002</year></dates><isbn>0013-7952</isbn><urls><related-urls><url>/S0013795201001338/1-s2.0-S0013795201001338-main.pdf?_tid=fc6854ee-cc4a-11e4-acd7-00000aacb35d&acdnat=1426558496_d69265aaea2f835949ab454d8f514e24</url></related-urls></urls></record></Cite></EndNote>[2]则对颗粒的长轴、中轴、短轴等表观参数进行相关分析和研究，TaylorADDINEN.CITE<EndNote><Cite><Author>Taylor</Author><Year>2006</Year><RecNum>274</RecNum><DisplayText><styleface="superscript">[4]</style></DisplayText><record><rec-number>274</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1432110422">274</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>M.A.Taylor</author><author>E.J.Garboczi</author><author>S.T.Erdogan</author><author>D.W.Fowler</author></authors></contributors><titles><title>Somepropertiesofirregular3-Dparticles</title><secondary-title>PowderTechnology</secondary-title></titles><periodical><full-title>PowderTechnology</full-title></periodical><pages>1–15</pages><volume>162</volume><number>1</number><dates><year>2006</year></dates><urls></urls></record></Cite></EndNote>[4]教授在Garboczi教授的基础上，对颗粒密度、尺寸、等效模型等进行研究。这些学者的研究对我们认识复杂颗粒的几何结构性质由重大推动作用，但是他们大都关注于单个颗粒，统计单个参数的规律，我将聚焦于颗粒堆积体的几何形态研究，并用实际模型进行验证，力求探索颗粒二维切片断面和三维堆积体之间的关系，从而可以在野外中通过观察某个地区裸露表面的颗粒统计参数，实现对该地区颗粒堆积体三维形态性质的推断。2.4颗粒形状表征CundallADDINEN.CITE<EndNote><Cite><Author>CUNDALL</Author><Year>1971</Year><RecNum>12</RecNum><DisplayText><styleface="superscript">[14,15]</style></DisplayText><record><rec-number>12</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1419007508">12</key></foreign-keys><ref-typename="ConferenceProceedings">10</ref-type><contributors><authors><author>CUNDALL,PA</author></authors></contributors><titles><title>Acomputermodelforsimulatingprogressive,large-scalemovementsinblockyrocksystems</title><secondary-title>Proc.Int.Symp.onRockFracture</secondary-title></titles><pages>11-8</pages><dates><year>1971</year></dates><urls></urls></record></Cite><Cite><Author>Cundall</Author><Year>1979</Year><RecNum>242</RecNum><record><rec-number>242</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1426317509">242</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Cundall,PeterA</author><author>Strack,OttoDL</author></authors></contributors><titles><title>Adiscretenumericalmodelforgranularassemblies</title><secondary-title>Geotechnique</secondary-title></titles><periodical><full-title>Geotechnique</full-title></periodical><pages>47-65</pages><volume>29</volume><number>1</number><dates><year>1979</year></dates><isbn>1751-7656</isbn><urls></urls></record></Cite></EndNote>[14,15]在1971年提出离散元的初期，使用二维圆盘和三维球体对颗粒材料进行模拟，其开发的PFC2D和PFC3D软件成为著名的颗粒流软件。RothenburgADDINEN.CITE<EndNote><Cite><Author>Rothenburg</Author><Year>1991</Year><RecNum>244</RecNum><DisplayText><styleface="superscript">[16]</style></DisplayText><record><rec-number>244</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1426317562">244</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Rothenburg,Leo</author><author>Bathurst,RichardJ</author></authors></contributors><titles><title>Numericalsimulationofidealizedgranularassemblieswithplaneellipticalparticles</title><secondary-title>Computersandgeotechnics</secondary-title></titles><periodical><full-title>Computersandgeotechnics</full-title></periodical><pages>315-329</pages><volume>11</volume><number>4</number><dates><year>1991</year></dates><isbn>0266-352X</isbn><urls></urls></record></Cite></EndNote>[16]和TingADDINEN.CITE<EndNote><Cite><Author>Ting</Author><Year>1995</Year><RecNum>245</RecNum><DisplayText><styleface="superscript">[17]</style></DisplayText><record><rec-number>245</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1426317764">245</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Ting,JohnM.</author><author>Meachum,Larry</author><author>Rowell,JeffreyD.</author></authors></contributors><titles><title>Effectofparticleshapeonthestrengthanddeformationmechanismsofellipse‐shapedgranularassemblages</title><secondary-title>EngineeringComputations</secondary-title></titles><periodical><full-title>EngineeringComputations</full-title></periodical><pages>99-108</pages><volume>12</volume><number>2</number><dates><year>1995</year></dates><isbn>0264-4401</isbn><urls></urls><electronic-resource-num>10.1108/02644409510799497</electronic-resource-num></record></Cite></EndNote>[17]分别与1991年和1993年实现了椭圆对颗粒材料的模拟，椭圆材料可以模拟不同长细比的颗粒材料，而LinXiaoshanADDINEN.CITE<EndNote><Cite><Author>Lin</Author><Year>1997</Year><RecNum>247</RecNum><DisplayText><styleface="superscript">[18]</style></DisplayText><record><rec-number>247</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1426318204">247</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Lin,Xiaoshan</author><author>Ng,T-T</author></authors></contributors><titles><title>Athree-dimensionaldiscreteelementmodelusingarraysofellipsoids</title><secondary-title>Geotechnique</secondary-title></titles><periodical><full-title>Geotechnique</full-title></periodical><pages>319-329</pages><volume>47</volume><number>2</number><dates><year>1997</year></dates><isbn>1751-7656</isbn><urls></urls></record></Cite></EndNote>[18]和Vu-quocLocADDINEN.CITE<EndNote><Cite><Author>Vu-Quoc</Author><Year>2000</Year><RecNum>246</RecNum><DisplayText><styleface="superscript">[19]</style></DisplayText><record><rec-number>246</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1426318187">246</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Vu-Quoc,Loc</author><author>Zhang,Xiang</author><author>Walton,OR</author></authors></contributors><titles><title>A3-Ddiscrete-elementmethodfordrygranularflowsofellipsoidalparticles</title><secondary-title>Computermethodsinappliedmechanicsandengineering</secondary-title></titles><periodical><full-title>ComputerMethodsinAppliedMechanicsandEngineering</full-title></periodical><pages>483-528</pages><volume>187</volume><number>3</number><dates><year>2000</year></dates><isbn>0045-7825</isbn><urls></urls></record></Cite></EndNote>[19]分别与1997年和2000年实现了用椭球对颗粒材料的模拟，极大地促进了颗粒材料研究的进展，对颗粒材料不同统计形状与其力学特性的关系有长足的进步。WaltonADDINEN.CITE<EndNote><Cite><Author>Walton</Author><Year>1993</Year><RecNum>253</RecNum><DisplayText><styleface="superscript">[20]</style></DisplayText><record><rec-number>253</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1426403840">253</key></foreign-keys><ref-typename="ConferenceProceedings">10</ref-type><contributors><authors><author>Walton,OR</author><author>Braun,RL</author></authors></contributors><titles><title>Simulationofrotary-drumandreposetestsforfrictionalspheresandrigidsphereclusters</title><secondary-title>JointDOE/NSFWorkshoponFlowofParticulatesandFluids,Ithaca,NY,Sept</secondary-title></titles><dates><year>1993</year></dates><urls></urls></record></Cite></EndNote>[20]和PotyondyADDINEN.CITE<EndNote><Cite><Author>Potyondy</Author><Year>1996</Year><RecNum>252</RecNum><DisplayText><styleface="superscript">[21]</style></DisplayText><record><rec-number>252</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1426403728">252</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Potyondy,DO</author><author>Cundall,PA</author><author>Lee,C</author></authors></contributors><titles><title>Modellingrockusingbondedassembliesofcircularparticles</title><secondary-title>RockMechanics</secondary-title></titles><periodical><full-title>RockMechanics</full-title></periodical><pages>1937-1944</pages><dates><year>1996</year></dates><urls></urls></record></Cite></EndNote>[21]分别与1993年和1996年用不嵌套的球对复杂颗粒进行表征，WangLinbingADDINEN.CITE<EndNote><Cite><Author>Wang</Author><Year>2007</Year><RecNum>202</RecNum><DisplayText><styleface="superscript">[22]</style></DisplayText><record><rec-number>202</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1422492260">202</key><keyapp="ENWeb"db-id="">0</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Wang,Linbing</author><author>Park,Jin-Young</author><author>Fu,Yanrong</author></authors></contributors><titles><title>RepresentationofrealparticlesforDEMsimulationusingX-raytomography</title><secondary-title>ConstructionandBuildingMaterials</secondary-title></titles><periodical><full-title>ConstructionandBuildingMaterials</full-title></periodical><pages>338-346</pages><volume>21</volume><number>2</number><dates><year>2007</year></dates><isbn>09500618</isbn><urls></urls><electronic-resource-num>10.1016/j.conbuildmat.2005.08.013</electronic-resource-num></record></Cite></EndNote>[22]提出燃烧算法，用不均匀不相互嵌套的球对复杂颗粒进行表征，该方法被运用于PFC3D中。HubbardADDINEN.CITE<EndNote><Cite><Author>Hubbard</Author><Year>1996</Year><RecNum>230</RecNum><DisplayText><styleface="superscript">[23]</style></DisplayText><record><rec-number>230</rec-number><foreign-keys><keyapp="EN"db-id="pdfpwfxa820av5evrs4vpv94tzazswfvx9ad"timestamp="1426035190">230</key></foreign-keys><ref-typename="JournalArticle">17</ref-type><contributors><authors><author>Hubbard,PhilipM</author></authors></contributors><titles><title>Approximatingpolyhedrawithspheresfortime-criticalcollisiondetection</title><secondary-title>ACMTransactionsonGraphics(TOG)</secondary-title></titles><periodical><full-title>ACMTransactionsonGraphics(TOG)</full-title></periodical><pages>179-210</pages><volume>15</volume><number>3</number><dates><year>1996</year></dates><isbn>0730-0301</isbn><urls><related-urls><url>/10.1145/240000/231732/p179-hubbard.pdf?ip=22&id=231732&acc=ACTIVE%20SERVICE&key=BF85BBA5741FDC6E%2E587F3204F5B62A59%2E4D4702B0C3E38B35%2E4D4702B0C3E38B35&CFID=637875122&CFTOKEN=76850678&__acm__=1426035477_856a85bc09077dfbae834aba2c0b27e2</url></related-urls></urls></record></Cite></EndNote>[23]教授实现了对复杂形状的表征，其采用的是多个不均匀