级配颗粒堆积体密度估算方法研究
|
摘要
颗粒堆积密度是反映颗粒介质内部构造的一个基本指标,是土木工程中的一项必不可少的设计参数,也是研究许多颗粒力学问题的切入点。鉴于颗粒堆积密度的重要性,本文结合水利围堰中密度参数确定问题,基于PFC3D数值平台,开展了颗粒材料堆积密度的数值试验,研究影响颗粒堆积密度的相关因素,建立了堆积密度计算公式。同时进行了物理模型试验和离心机模型试验验证计算结果的可靠性。研究内容与研究成果如下：
1.建立了颗粒堆积密度的计算公式。基于颗粒的“填隙”和“替换”机制,从单粒径颗粒、二元颗粒的堆积密度,推广到级配颗粒的密度计算模式。通过数值试验研究计算公式中参数的影响,针对容器中颗粒堆积以及无侧向边界限制的颗粒堆积,分别建立了一整套估算级配颗粒堆积体密度的方法及计算公式。
2.基于Matlab的图像处理功能,进行颗粒形状信息提取和颗粒形状重建。从颗粒的三视图图像中提取圆度信息并对其进行加权平均,得到加权圆度作为反映颗粒三维形状特征的指标。在Matlab中创建具有指定加权圆度的三维凸包,对凸包进行体素化和骨架化处理,提取颗粒的三维空间信息,从而在PFC3D中重建具有特定形状的clump块体,为形状颗粒的堆积试验提供基础。
3.研究了颗粒材料特性对颗粒堆积密度的影响。针对颗粒的摩擦系数、颗粒形状、颗粒级配等颗粒材料特性,设计了相关的数值试验,得到各因素与颗粒堆积密度的影响关系。讨论了颗粒试样宏观摩擦角与颗粒间摩擦系数之间的联系,提出了反映颗粒级配情况的粒度分布宽度的计算方法。
4.研究了静水条件下颗粒堆积密度的变化规律。颗粒在水中的堆积受到重力、浮力、阻力等作用,也受到颗粒与颗粒之间相互干扰的影响,这些外力作用和影响最终反映在堆积密度的变化上。本文设计了级配颗粒在流体中的堆积试验,得出了在静水中颗粒堆积密度与级配之间的关系。
5.研究了颗粒堆积深度与密度的关系。基于数值试验结果,根据Janssen压力公式拟合得到随深度变化的孔隙比计算公式。在PFC3D中进行了不同摩擦系数的颗粒侧限压缩试验,将试验成果作为上覆荷载作用下颗粒孔隙比变化的依据,对建立的孔隙比随深度变化的公式进行扩充和完善。
6.进行了物理模型试验以及离心机模型试验,对建立的估算公式的有效性进行判断。在不同高度的圆柱筒容器中进行玻璃球和风化砂的抛填试验,对级配风化砂进行不同加速度的离心机试验,模拟不同深度的风化砂自重压密效果。将估算值与模型试验值进行对比,两者具有较好的一致性。
Particle packing density is one of the most basic parameters which reflect the internalstructure of granules medium. It is one of the key design parameters in civil engineering andis a point of penetration of many particle mechanics problems. In view of the importance ofstudying particle packing density, numerical test is carried out in PFC3D numerical platformbased on the deep water cofferdam project. Relevant factors of particle packing density arestudied and computational formula of particle packing density is established in thisdissertation. Meanwhile, physical model test and centrifugal model test are also carried out tocheck the result of computation. The research contents and results are as follows.
1The computational formula of particle packing density.is set up. Based on the mechanism ofparticle "filling" and particle "replacing", the estimation model of particle density is extendedfrom mono-size particle and binary particle to multiple size particles. The influence of theparameters in computational formula is studied by the numerical test. A whole set of methodand computational formula estimating particle packing density is set up respectively for thedifferent situations
2. Particle shape information is extracted and its shape is reconstructed based on the imageprocessing in Matlab.Weighted roundness of the particle is defined as shape indices. Thereconstruction process can be state as follows: fetching roundness information from threeviews of particles which are shooted by digital camera firstly, then calculate the averageroundness is weighted by the areas.3D convex hulls which have certain weighted roundnessare created in Matlab and then extract three-dimensional information by means ofvoxelization and skeletonizing. The clumps are created according to the three-dimensionalspace coordinate information in PFC3D.
3. The influence of particles characteristics on packing densityis studied. Knowing thatpacking density are influenced by factors such as friction coefficient between particlesparticle shape and gradation of particles, correlative numerical test are carried out and therelationship between the packing density and factors is clear. The relationship between macro-frictional angle of granular media and micro-friction coefficient between particles isdiscussed and defined the calculative process of width of size distributions.
4. The packing density in the condition of fluid-structure interaction studied. The particlesyielded force such as gravity, buoyancy, resistance and disturbing force between particles inthe fluid. Packing density will be modified due to the external force. Numerical tests ofgradation particles were designed to study the influence of still water on packing density.
5. The influence of packing depth and vertical press on the packing density is studied. Fittingformula of void ratio varied with depth and vertical press is established according to Janssenformulas and numerical experimental results. Meantime, the confined compression numericaltest is carried out by PFC3D and its results can be the basis of variation of void ratio with theimpact on cover load. Also the fitting formula whose void ratio varied with depth and verticalpress is improved.
6. Physical model and centrifuge model testing are designed to verify the validity of packingdensity estimation model. Glass marble and weathered sand are poured to cylinder in differentheight and weathered sand with graduation are packed in centrifugal machine in the conditionof different acceleration to simulate self-weight compression. The calculated results agreewell with those of the physical model testing and centrifuge model test.
1.建立了颗粒堆积密度的计算公式。基于颗粒的“填隙”和“替换”机制,从单粒径颗粒、二元颗粒的堆积密度,推广到级配颗粒的密度计算模式。通过数值试验研究计算公式中参数的影响,针对容器中颗粒堆积以及无侧向边界限制的颗粒堆积,分别建立了一整套估算级配颗粒堆积体密度的方法及计算公式。
2.基于Matlab的图像处理功能,进行颗粒形状信息提取和颗粒形状重建。从颗粒的三视图图像中提取圆度信息并对其进行加权平均,得到加权圆度作为反映颗粒三维形状特征的指标。在Matlab中创建具有指定加权圆度的三维凸包,对凸包进行体素化和骨架化处理,提取颗粒的三维空间信息,从而在PFC3D中重建具有特定形状的clump块体,为形状颗粒的堆积试验提供基础。
3.研究了颗粒材料特性对颗粒堆积密度的影响。针对颗粒的摩擦系数、颗粒形状、颗粒级配等颗粒材料特性,设计了相关的数值试验,得到各因素与颗粒堆积密度的影响关系。讨论了颗粒试样宏观摩擦角与颗粒间摩擦系数之间的联系,提出了反映颗粒级配情况的粒度分布宽度的计算方法。
4.研究了静水条件下颗粒堆积密度的变化规律。颗粒在水中的堆积受到重力、浮力、阻力等作用,也受到颗粒与颗粒之间相互干扰的影响,这些外力作用和影响最终反映在堆积密度的变化上。本文设计了级配颗粒在流体中的堆积试验,得出了在静水中颗粒堆积密度与级配之间的关系。
5.研究了颗粒堆积深度与密度的关系。基于数值试验结果,根据Janssen压力公式拟合得到随深度变化的孔隙比计算公式。在PFC3D中进行了不同摩擦系数的颗粒侧限压缩试验,将试验成果作为上覆荷载作用下颗粒孔隙比变化的依据,对建立的孔隙比随深度变化的公式进行扩充和完善。
6.进行了物理模型试验以及离心机模型试验,对建立的估算公式的有效性进行判断。在不同高度的圆柱筒容器中进行玻璃球和风化砂的抛填试验,对级配风化砂进行不同加速度的离心机试验,模拟不同深度的风化砂自重压密效果。将估算值与模型试验值进行对比,两者具有较好的一致性。
Particle packing density is one of the most basic parameters which reflect the internalstructure of granules medium. It is one of the key design parameters in civil engineering andis a point of penetration of many particle mechanics problems. In view of the importance ofstudying particle packing density, numerical test is carried out in PFC3D numerical platformbased on the deep water cofferdam project. Relevant factors of particle packing density arestudied and computational formula of particle packing density is established in thisdissertation. Meanwhile, physical model test and centrifugal model test are also carried out tocheck the result of computation. The research contents and results are as follows.
1The computational formula of particle packing density.is set up. Based on the mechanism ofparticle "filling" and particle "replacing", the estimation model of particle density is extendedfrom mono-size particle and binary particle to multiple size particles. The influence of theparameters in computational formula is studied by the numerical test. A whole set of methodand computational formula estimating particle packing density is set up respectively for thedifferent situations
2. Particle shape information is extracted and its shape is reconstructed based on the imageprocessing in Matlab.Weighted roundness of the particle is defined as shape indices. Thereconstruction process can be state as follows: fetching roundness information from threeviews of particles which are shooted by digital camera firstly, then calculate the averageroundness is weighted by the areas.3D convex hulls which have certain weighted roundnessare created in Matlab and then extract three-dimensional information by means ofvoxelization and skeletonizing. The clumps are created according to the three-dimensionalspace coordinate information in PFC3D.
3. The influence of particles characteristics on packing densityis studied. Knowing thatpacking density are influenced by factors such as friction coefficient between particlesparticle shape and gradation of particles, correlative numerical test are carried out and therelationship between the packing density and factors is clear. The relationship between macro-frictional angle of granular media and micro-friction coefficient between particles isdiscussed and defined the calculative process of width of size distributions.
4. The packing density in the condition of fluid-structure interaction studied. The particlesyielded force such as gravity, buoyancy, resistance and disturbing force between particles inthe fluid. Packing density will be modified due to the external force. Numerical tests ofgradation particles were designed to study the influence of still water on packing density.
5. The influence of packing depth and vertical press on the packing density is studied. Fittingformula of void ratio varied with depth and vertical press is established according to Janssenformulas and numerical experimental results. Meantime, the confined compression numericaltest is carried out by PFC3D and its results can be the basis of variation of void ratio with theimpact on cover load. Also the fitting formula whose void ratio varied with depth and verticalpress is improved.
6. Physical model and centrifuge model testing are designed to verify the validity of packingdensity estimation model. Glass marble and weathered sand are poured to cylinder in differentheight and weathered sand with graduation are packed in centrifugal machine in the conditionof different acceleration to simulate self-weight compression. The calculated results agreewell with those of the physical model testing and centrifuge model test.
引文
[1]陈生平,魏建雄.深水防波堤工程抛石断面成型控制[J].中国港湾建设.2005(03).
[2]阎宗岭.堆石体物理力学特性及其工程应用研究[D].重庆大学,2003.
[3]毛泽宇.地震作用下松散堆积体崩塌规模研究与应用[D].西南交通大学,2008.
[4]李增志,别社安,任增金.抛石防波堤稳定性的离散单元法分析[J].工程力学.2009(S1).
[5]张明鸣,徐卫亚,夏玉斌,等.抛石挤淤机理及其颗粒流数值模拟研究[J].中南大学学报(自然科学版).2010(01).
[6]李巍,俞良群,邢纪波.筒仓装卸料力学过程的数值模拟[J].煤炭工程.1992(01).
[7]张翠兵,邓志勇,高凌天,等.抛石散体振动密实过程的离散元数值模拟[J].岩石力学与工程学报.2004(01).
[8]张剑,金南国,金贤玉,等.混凝土多边形骨料分布的数值模拟方法[J].浙江大学学报(工学版).2004(05).
[9]杜成斌,孙立国.任意形状混凝土骨料的数值模拟及其应用[J].水利学报.2006(06).
[10]徐桂弘.干燥砂土堆积稳定性分析试验研究[J].路基工程.2007(6)：79-81.
[11]蒲传金.排土场松散堆积体特性及灾害研究现状[J].化工矿物与加工.2008,37(6)：34-37.
[12]Fazekas S, Torok J, Kertesz J. Critical packing in granular shear bands[J]. Phys.Rev.E.2007,75:011302.
[13]肖文波,胡林.颗粒物质的两个典型效应及其研究现状的分析[J].物理实验.2004,24(3)：44-46.
[14]Zuriguel I, Garcimartin A, Maza D, et al. Jamming during the discharge of granular matter from a silo[J]. Phys. Rev. E.2005,71:051303.
[15]Brauer K, Pfitzner M, Krimer D O, et al. Granular elasticity:Stress distributions in silos under point loads[J]. Phys.Rev.E.2006(74:061311).
[16]肖文波,胡林,蔡绍洪.颗粒物质中的坍塌现象[J].中国沙漠.2004,24(6)：798-801.
[17]Bak P, Tang C, Wiesenfeld K. Self-Organized criticality:An explanation of1/f noise[J]. Phys. Rev. Lett.1987,59:381-384.
[18]Lemieux P A, Durian D J. From avalanches to fluid flow:a continuous picture of grain dynamics down a heap [J]. Phys.Rev.Left.2000,85(20):4273-4276.
[19]De G P G. Granular matter:a tentative view.[J]. Reviews of Modeern Physics.1999,71(2): S374-S382.
[20]P K L. Theoretical ideas inspired by granular flows.[J]. Review of Modern Physics.1999,71(1):435-444.
[21]J H H, S. L, R. C. Dynamics of granular systems[J]. Physica A.2001,93-100(295).
[22]He D, Ekere N N, Cai L. Computer simulation of random packing of unequal particles[J]. Physical Review E.,60(6):7098-7104.
[23]张翠兵,邓志勇,高凌天,等.抛石散体振动密实过程的离散元数值模拟[J].岩石力学与工程学报.2004(01).
[24]包承纲.三峡工程二期深水围堰的建设和研究[J].水利水电科技进展.2001(04).
[25]蔡绍洪,周海平,王春香.颗粒堆积物在不同堆放方式下的占空比和分形维数的计算[J].贵州科学.2007(01).
[26]石雨亮,陆晶,詹义正,等.泥沙的水下休止角与干容重计算[J].武汉大学学报：工学版.2007,40(3)：14-17.
[27]梁春雨,徐金声.沥青混合料粗骨料形状指标研究[J].交通标准化.2007(7)：96-99.
[28]王家柱.二期横向围堰工程的几个主要技术问题[J].中国三峡建设.1999(3).
[29]李玫,龚壁卫.三峡深水围堰风化砂料水下抛填密度和坡角的离心模型试验研究报告[R].长江科学院,1989.
[30]孙永福.青藏铁路多年冻土工程的研究和实践[J].冰川冻土.2005,27(2)：153-162.
[31]乔龄山.水泥颗粒特性参数及其对水泥和混凝土性能的影响[J].水泥.2001(10).
[32]Johansen V, Andersen P J. Particle packing and concrete properties [A], eds J. Skalny and S. Mindess. Materials Science of Conctete Ⅱ[C][Z]. The American Ceramic Society, Westerville,OH,pp,1991111-148.
[33]Andersen P J. Control and Monitoring of Concrete Production[D]. Academy of Technical Sciences, The Technical University of Denmark,1990.
[34]Dewar. Computer modeling of Concrete Mixtures[Z]. London:1999.
[35]Furnas C C. U.S.Bureau of Mines Reports of Investigation[J]. NO.2894.1928.
[36]Hugill A R W A. J.Amer.Ceram.Soc[J].1930,13(11):767.
[37]Andreasen A M A J. Kolloid Z[J].1984,50(217).
[38]Berryman J G. random close packing of hard spheres and disks[J].1983.
[39]Suzuki M, Oshima T. Verification of a model for estimating the void fraction in a three-component randomly packed bed[J]. Powder Technology.1985,43(2):147-153.
[40]Marmur A. A thermodynamic approach to the packing of particle mixtures[J]. Powder Technology.1985,44(3):249-253.
[41]Leitzelement M, Lo C S, Dodds J. Porosity and permeability of ternary mixtures of particles[J]. Powder Technology.1985,41(2):159-164.
[42]Stovall T, de Larrard F, Buil M. Linear packing density model of grain mixtures[J]. Powder Technology.1986,48(1):1-12.
[43]Yu A B, Standish N. An analytical-parametric theory of the random packing of particles[J]. Powder Technology.1988,55(3):171-186.
[44]Liu J X, Davies T J. Coordination number/density relationships for random packing of spherical powders[J]. Metal Powder Report.1998,53(1):35.
[45]Rassouly S M K. The packing density of'perfect'binary mixtures[J]. powder technology.1999.
[46]王海兵,刘咏,黄伯云,等.粉末颗粒线性堆积密度模型的改进[J].粉末冶金技术.2001(04).
[47]Scott G D. packing of spheres[J]. Nature.1960(188):908-909.
[48]张红武,汪家寅.沙石及模型沙水下休止角试验研究[J].泥沙研究.1989(03).
[49]董麒,叶大年.颗粒的比重、形态与其任意堆积[J].科学通报.1993(01).
[50]Scott G. Radial distribution of the random close packing of equal spheres[J]. Nature.1962,194:956-957.
[51]B M, C. O, P B R. Stress Fluctuations for Continuously Sheared Granular Materials[J]. Phs. Rev. Lett.1996,77:3110.
[52]M M D, M J H, R N S. Force distribution in a granular medium[J]. Phy.Rev.E.1998,57:3164.
[53]M E J, W M N, M J H, et al. Force distributions in three-dimensional compressible granular packs[J]. Phys.Rev.E.2002,66:40301.
[54]M. G R. particle packing characteristics[J]. Princeton:Metal Powder Industries Federation.1989.
[55]K Y, I K. The particle size distribution for the highest relative density in a compexted body.[J]. Powder Technology.1990,63(3):241-246.
[56]Oger L, Troadec J P, Bideau D. Properties of disordered spheres packing Ⅰ. Geometric Structure:Statistical Model, Numerical Simulation and Experimental Results.[J]. Powder Technoligy.1986,46(2-3):121-131.
[57]J. R, H A C, M. C J. A computer method for random packing of spheres of unequal size[J]. Powder Technology.1986,47(1):25-33.
[58]Suzuki M, Oshima T. Comparison between the computer-simulated results and the model for estimating the Co-ordination number in a three-component random mixture of spheres.[J]. Powder Technology.1985,43(1):19-25.
[59]German R M. Particle packin characteristics[M]. New Jersey:Princeton Publication,1989.
[60]Visscher W M, Bolsterli M. Random packing of equal and unequal spheres in two and three dimension[J]. nature.1972,239:504-507.
[61]Meakin P, Jullien R. Restruction effects in the rain model for random deposition[J]. J. Physique.1987,48:1651-1687.
[62]Barker G C, Grimson M J. Sequential random close packing of binary disc mixtures[J]. J. Phy. Condens Matter.1989,1(2779-2789).
[63]Dobry R, Ng T T. Discrete modeling of stress-strain behavior of granular media at small and large strains[Z]. Golder. Co.:1989.
[64]D. G. Discrete Mechanics of Granular Matter[D]. The University of Calgary,1999.
[65]文玉华,朱如曾,周富信,等.分子动力学模拟的主要技术[J].力学进展.2003(3).
[66]M M, Hj H. DSMC-a stochastic algorithm for granular matter. In:Physics of dry granular media. Herrmann HJ, Hovi JP and Luding S, Eds. NATO advanced Study Institute, Kluwer.
[67]Cundall P, Strack O D L. A discrete numerical model for granular assemblies[J]. Geotechnique.1979,29:47-65.
[68]Cundall P A, Hart R D. Numerical Modeling of Discontinua[Z]. Golden. Co.:1989.
[69]Yu A B. Computer simulation of the packing of fine particles[J].2000.
[70]Cheng Y F, Guo S J, Lai H Y. Dynamic simulation of random packing of spherical particles[J]. Powder Technology.2000,107:123-130.
[71]王泳嘉,邢纪波.离散单元法及其在岩土力学中的应用[M].辽宁：东北工学院出版社,1991.
[72]王泳嘉,邢纪波.离散单元法同拉格朗日元法及其在岩土力学中的应用[J].岩土力学.1995(02).
[73]邢纪波,俞良群,张瑞丰,等.离散单元法的计算参数和求解方法选择[J].计算力学学报.1999(01).
[74]王泳嘉,刘连峰.三维离散单元法软件系统TRUDEC的研制[J].岩石力学与工程学报.1996(03).
[75]邢纪波,俞良群,张瑞丰,等.离散单元法的计算参数和求解方法选择[J].计算力学学报.1999(01).
[76]王泳嘉,邢纪波.离散单元法同拉格朗日元法及其在岩土力学中的应用[J].岩土力学.1995(02).
[77]李艳洁,徐泳.用离散元模拟颗粒堆积问题[J].农机化研究.2005(02).
[78]李艳洁.堆积问题的离散元模拟_实验研究[D].北京：中国农业大学,2004.
[79]黄晚清,陆阳.散粒体重力堆积的三维离散元模拟[J].岩土工程学报.2006,28(12).
[80]刘军,刘汉龙.用MonteCarlo方法模拟砂土的自然堆积过程[J].岩土力学.2005,26.
[81]郭培玺,林绍忠.粗粒料颗粒随机分布的数值模拟[J].长江科学院院报.2007(4)：50-52.
[82]陆厚根.粉体工程导论[M].同济大学出版社,1998.
[83]叶大年.颗粒堆积问题[J].地质科技情报.1988,7(4).
[84]Ashmawy A K, Sukumaran B, Hoang A V. Evaluating the influence of particle shape on liquefaction behavior using Discrete Element Method[Z]. Honolulu, Hawaii:2003.
[85]Sallam A M. Studies on Modeling Angular Soil Particles Using the Discrete Element Method[D]. Tampa, FL:University of South Florida,2004.
[86]Lin X, Ng T T. A three-dimensional discrete element model using arrays of ellipsoids[J]. Geotechnique.1997,47(2):319-329.
[87]Ghaboussi J, Barbosa R. Three-dimensional discrete element method for granularmaterials[J]. International Journal for Numerical and Analytical Methods in Geomechanics.1990,14:451-472.
[88] Matsushima T.3-D image-based discrete element modeling for irregularly-shapedgrains[Z]. Kyoto:2004.
[89] T F, C C, E M, et al. Aggregate Imaging System (AIMS) for characterizing the shape offine and coarse aggregates[Z]. Washington, DC: Transportation Research Board, NationalResearch Council,2003.
[90] E. M. Review of imaging techniques for characterizing the shape of aggregates used inasphalt mixes.[Z]. Austin, TX.:2001.
[91] D J. Evaluation of aggregate particle shapes through multiple ratio analysis[Z]. Denver,CO.:2000.
[92] H K, C H, A R, et al. A prototype laser scanner for characterizing size and shape propertiesin aggregates[Z]. Austin, TX.:2000.
[93] Wc K. Measurement and geological significance of shape and roundness of sedimentaryparticles[J]. J Sediment petrol.1941,11(2):64-72.
[94] Powers M C. A new roundness scale for sedimentary particles[J]. Journal of SedimentaryPetrology.1953(23):117-119.
[95] Barret P J. The shape of rock particles, a critical review[J]. Sedimentology.1980(27):291-303.
[96] Wadell H. shape&roundness of rock particles[J]. J. of Geology.1932(40):443-451.
[97] Sukumaran B, Ashmawy A K. Quantitative characterization of the geometry of discreteparticles[J]. Geotechnique.2001,51(7):619-627.
[98] Wadell H. Sphericity and roundness of rock particles[J]. The Journal of Geology.1933,41(3):310-331.
[99] Sukumaran B, Ashmawy A K. Influence of inherent particle characteristics on the strengthparoperties of Particulate materials[Z]. Oslo, Norway:2001.
[100] Ehrlich R, Weinberg B. An exact method for characterization of grain shape[J]. J.Sediment.Petrol.1970,40(1):205-212.
[101] Bowman E T, Soga K. Particle shape characterization using Fourier descriptor analysis[J].Geotechnique.2001,51(6):545-554.
[102] Yudhbir, Abedinzadeh R. Quantification of particle shape and angularity using image analyzer[J]. Geotechnical Testing Journal.1991,14(3):296-308.
[103]Cho G, Dodds J, Santamarina J C. Particle shape effects on packing density, stiffness, and strength:natural and crushed sands[J]. Journal of Geotechnical and Geoenvironmental Engineering.2006,132(5):591-602.
[104]Rao C, Tutumluer E, Kim I T. Quantification of coarse aggregate angularity based on image analysis[Z]. Washington DC:2002:1787,117-124.
[105]Masad E, Button J W. Unified imaging approach for measuring aggregate angularity[J]. The International Journal of Computer-Aided Civil and Infrastructure Engineering.2000,15(4):273-280.
[106]Reschke T. Schriftenreihe der Zementindustrie[J]. Dusseldorf:Verlag Baut Technik Gmbh.2000,2006(62).
[107]R Y D, V H. Skeletonization of volumetric angiorams for display[J]. Computer Methods in Biomethanics and Biomedical Engineering.2002,5(5):329-341.
[108]樊雅萍,黄生学,温佩芝,等.基于数字距离变换的3D模型骨架提取算法[J].信息与控制.2004,33(6).
[109]牛立聪,孙香花,左晓宝.基于Matlab图像处理的砂石颗粒圆形度计算方法[J].混凝土.2012(2).
[110]吴威,谢步瀛.基于三角形的三维点集凸包快速求取算法[J].东华大学学报(自然科学版).2008(3)：311-314.
[111]李志,李儒琼.一种改进的快速三维凸包生成算法及实现[J].计算机工程与科学.2011(2)：129-132.
[112]Barber C B, Dobkin D P, Huhdanpaa H T. The Quickhull Algorithm for Convex Hulls[J]. ACM Transactions on Mathematical Software.1996,22(4):469-483.
[113]Kroon D. Segmentation of the mandibular canal in cone-beam CT data[D]. Enschede, the Netherlands:University of Twente,2011.
[114]芦鸿雁.基于层次包围盒的碰撞检测算法研究[J].计算机与数字工程.2008,36(2)：23-25.
[115]朱响斌,唐敏,董金祥.一种基于八叉树的三维实体内部可视化技术[J].中国图像图形学报.2002(3).
[116]L. O R, O. K. Hierarchic Voronoi skeletons[J]. Pattern Recognition.1995,28(3):343-359.
[117]Palagyi K, Kuba A. Directional3D Thinning Using8Subiterations[J]. Lecture Notes in Computer Science.1999,1568:325-336.
[118]Blum H. A transformation for extracting descriptors of shape[C]. MIT Press,1967.
[119]Bitter I, Kaufman A E, Sato M. Penalized-Distance Volumetric Skeleton Algorithm[J]. IEEE Trans, on Visualization and Computer Graphics.2001,7(3):195-206.
[120]Das N. Modeling three-dimensional shape of sand grains using discrete element method[D]. University of South Florida,2007.
[121]钟文镇,何克晶,周照耀,等.颗粒离散元模拟中的阻尼系数标定[J].物理学报.2009(8)：5155-5161.
[122]钟文镇,何克晶,夏伟,等.球形颗粒堆积过程中的能量转换研究(英文)[J].科学技术与工程.2009(07).
[123]Bishop A W. Correspondence on shear characteristics of a saturated silt, measured in triaxial compression[J]. Geotechnique.1954,4(1):43-45.
[124]Tsuji Y, Kawaguchi T, Tanata T. Discrete Particle Simulation of Two-Dimensional Fluidized Bed[J]. Powder Tech.1993(77):79-87.
[125]Kawaguchi T, Tanata T, Tsuji Y. Numerical Simulation of Fluidized Bed Using the Discrete Element Method[J]. JSME (B).1992,58(551):79-85.
[126]陆厚根.粉体技术导论[M].同济大学出版社,1992.
[127]程展林,包承纲.三峡工程二期围堰填料特性试验研究[J].长江科学院院报.1997(04).
[128]张小平,包承纲,施斌.三峡二期围堰填料参数的反分析[J].岩石力学与工程学报.2001(05).
[129]程永辉,李青云,饶锡保,等.长江科学院土工离心机的应用与发展[J].长江科学院院报.2011(5).
[2]阎宗岭.堆石体物理力学特性及其工程应用研究[D].重庆大学,2003.
[3]毛泽宇.地震作用下松散堆积体崩塌规模研究与应用[D].西南交通大学,2008.
[4]李增志,别社安,任增金.抛石防波堤稳定性的离散单元法分析[J].工程力学.2009(S1).
[5]张明鸣,徐卫亚,夏玉斌,等.抛石挤淤机理及其颗粒流数值模拟研究[J].中南大学学报(自然科学版).2010(01).
[6]李巍,俞良群,邢纪波.筒仓装卸料力学过程的数值模拟[J].煤炭工程.1992(01).
[7]张翠兵,邓志勇,高凌天,等.抛石散体振动密实过程的离散元数值模拟[J].岩石力学与工程学报.2004(01).
[8]张剑,金南国,金贤玉,等.混凝土多边形骨料分布的数值模拟方法[J].浙江大学学报(工学版).2004(05).
[9]杜成斌,孙立国.任意形状混凝土骨料的数值模拟及其应用[J].水利学报.2006(06).
[10]徐桂弘.干燥砂土堆积稳定性分析试验研究[J].路基工程.2007(6)：79-81.
[11]蒲传金.排土场松散堆积体特性及灾害研究现状[J].化工矿物与加工.2008,37(6)：34-37.
[12]Fazekas S, Torok J, Kertesz J. Critical packing in granular shear bands[J]. Phys.Rev.E.2007,75:011302.
[13]肖文波,胡林.颗粒物质的两个典型效应及其研究现状的分析[J].物理实验.2004,24(3)：44-46.
[14]Zuriguel I, Garcimartin A, Maza D, et al. Jamming during the discharge of granular matter from a silo[J]. Phys. Rev. E.2005,71:051303.
[15]Brauer K, Pfitzner M, Krimer D O, et al. Granular elasticity:Stress distributions in silos under point loads[J]. Phys.Rev.E.2006(74:061311).
[16]肖文波,胡林,蔡绍洪.颗粒物质中的坍塌现象[J].中国沙漠.2004,24(6)：798-801.
[17]Bak P, Tang C, Wiesenfeld K. Self-Organized criticality:An explanation of1/f noise[J]. Phys. Rev. Lett.1987,59:381-384.
[18]Lemieux P A, Durian D J. From avalanches to fluid flow:a continuous picture of grain dynamics down a heap [J]. Phys.Rev.Left.2000,85(20):4273-4276.
[19]De G P G. Granular matter:a tentative view.[J]. Reviews of Modeern Physics.1999,71(2): S374-S382.
[20]P K L. Theoretical ideas inspired by granular flows.[J]. Review of Modern Physics.1999,71(1):435-444.
[21]J H H, S. L, R. C. Dynamics of granular systems[J]. Physica A.2001,93-100(295).
[22]He D, Ekere N N, Cai L. Computer simulation of random packing of unequal particles[J]. Physical Review E.,60(6):7098-7104.
[23]张翠兵,邓志勇,高凌天,等.抛石散体振动密实过程的离散元数值模拟[J].岩石力学与工程学报.2004(01).
[24]包承纲.三峡工程二期深水围堰的建设和研究[J].水利水电科技进展.2001(04).
[25]蔡绍洪,周海平,王春香.颗粒堆积物在不同堆放方式下的占空比和分形维数的计算[J].贵州科学.2007(01).
[26]石雨亮,陆晶,詹义正,等.泥沙的水下休止角与干容重计算[J].武汉大学学报：工学版.2007,40(3)：14-17.
[27]梁春雨,徐金声.沥青混合料粗骨料形状指标研究[J].交通标准化.2007(7)：96-99.
[28]王家柱.二期横向围堰工程的几个主要技术问题[J].中国三峡建设.1999(3).
[29]李玫,龚壁卫.三峡深水围堰风化砂料水下抛填密度和坡角的离心模型试验研究报告[R].长江科学院,1989.
[30]孙永福.青藏铁路多年冻土工程的研究和实践[J].冰川冻土.2005,27(2)：153-162.
[31]乔龄山.水泥颗粒特性参数及其对水泥和混凝土性能的影响[J].水泥.2001(10).
[32]Johansen V, Andersen P J. Particle packing and concrete properties [A], eds J. Skalny and S. Mindess. Materials Science of Conctete Ⅱ[C][Z]. The American Ceramic Society, Westerville,OH,pp,1991111-148.
[33]Andersen P J. Control and Monitoring of Concrete Production[D]. Academy of Technical Sciences, The Technical University of Denmark,1990.
[34]Dewar. Computer modeling of Concrete Mixtures[Z]. London:1999.
[35]Furnas C C. U.S.Bureau of Mines Reports of Investigation[J]. NO.2894.1928.
[36]Hugill A R W A. J.Amer.Ceram.Soc[J].1930,13(11):767.
[37]Andreasen A M A J. Kolloid Z[J].1984,50(217).
[38]Berryman J G. random close packing of hard spheres and disks[J].1983.
[39]Suzuki M, Oshima T. Verification of a model for estimating the void fraction in a three-component randomly packed bed[J]. Powder Technology.1985,43(2):147-153.
[40]Marmur A. A thermodynamic approach to the packing of particle mixtures[J]. Powder Technology.1985,44(3):249-253.
[41]Leitzelement M, Lo C S, Dodds J. Porosity and permeability of ternary mixtures of particles[J]. Powder Technology.1985,41(2):159-164.
[42]Stovall T, de Larrard F, Buil M. Linear packing density model of grain mixtures[J]. Powder Technology.1986,48(1):1-12.
[43]Yu A B, Standish N. An analytical-parametric theory of the random packing of particles[J]. Powder Technology.1988,55(3):171-186.
[44]Liu J X, Davies T J. Coordination number/density relationships for random packing of spherical powders[J]. Metal Powder Report.1998,53(1):35.
[45]Rassouly S M K. The packing density of'perfect'binary mixtures[J]. powder technology.1999.
[46]王海兵,刘咏,黄伯云,等.粉末颗粒线性堆积密度模型的改进[J].粉末冶金技术.2001(04).
[47]Scott G D. packing of spheres[J]. Nature.1960(188):908-909.
[48]张红武,汪家寅.沙石及模型沙水下休止角试验研究[J].泥沙研究.1989(03).
[49]董麒,叶大年.颗粒的比重、形态与其任意堆积[J].科学通报.1993(01).
[50]Scott G. Radial distribution of the random close packing of equal spheres[J]. Nature.1962,194:956-957.
[51]B M, C. O, P B R. Stress Fluctuations for Continuously Sheared Granular Materials[J]. Phs. Rev. Lett.1996,77:3110.
[52]M M D, M J H, R N S. Force distribution in a granular medium[J]. Phy.Rev.E.1998,57:3164.
[53]M E J, W M N, M J H, et al. Force distributions in three-dimensional compressible granular packs[J]. Phys.Rev.E.2002,66:40301.
[54]M. G R. particle packing characteristics[J]. Princeton:Metal Powder Industries Federation.1989.
[55]K Y, I K. The particle size distribution for the highest relative density in a compexted body.[J]. Powder Technology.1990,63(3):241-246.
[56]Oger L, Troadec J P, Bideau D. Properties of disordered spheres packing Ⅰ. Geometric Structure:Statistical Model, Numerical Simulation and Experimental Results.[J]. Powder Technoligy.1986,46(2-3):121-131.
[57]J. R, H A C, M. C J. A computer method for random packing of spheres of unequal size[J]. Powder Technology.1986,47(1):25-33.
[58]Suzuki M, Oshima T. Comparison between the computer-simulated results and the model for estimating the Co-ordination number in a three-component random mixture of spheres.[J]. Powder Technology.1985,43(1):19-25.
[59]German R M. Particle packin characteristics[M]. New Jersey:Princeton Publication,1989.
[60]Visscher W M, Bolsterli M. Random packing of equal and unequal spheres in two and three dimension[J]. nature.1972,239:504-507.
[61]Meakin P, Jullien R. Restruction effects in the rain model for random deposition[J]. J. Physique.1987,48:1651-1687.
[62]Barker G C, Grimson M J. Sequential random close packing of binary disc mixtures[J]. J. Phy. Condens Matter.1989,1(2779-2789).
[63]Dobry R, Ng T T. Discrete modeling of stress-strain behavior of granular media at small and large strains[Z]. Golder. Co.:1989.
[64]D. G. Discrete Mechanics of Granular Matter[D]. The University of Calgary,1999.
[65]文玉华,朱如曾,周富信,等.分子动力学模拟的主要技术[J].力学进展.2003(3).
[66]M M, Hj H. DSMC-a stochastic algorithm for granular matter. In:Physics of dry granular media. Herrmann HJ, Hovi JP and Luding S, Eds. NATO advanced Study Institute, Kluwer.
[67]Cundall P, Strack O D L. A discrete numerical model for granular assemblies[J]. Geotechnique.1979,29:47-65.
[68]Cundall P A, Hart R D. Numerical Modeling of Discontinua[Z]. Golden. Co.:1989.
[69]Yu A B. Computer simulation of the packing of fine particles[J].2000.
[70]Cheng Y F, Guo S J, Lai H Y. Dynamic simulation of random packing of spherical particles[J]. Powder Technology.2000,107:123-130.
[71]王泳嘉,邢纪波.离散单元法及其在岩土力学中的应用[M].辽宁：东北工学院出版社,1991.
[72]王泳嘉,邢纪波.离散单元法同拉格朗日元法及其在岩土力学中的应用[J].岩土力学.1995(02).
[73]邢纪波,俞良群,张瑞丰,等.离散单元法的计算参数和求解方法选择[J].计算力学学报.1999(01).
[74]王泳嘉,刘连峰.三维离散单元法软件系统TRUDEC的研制[J].岩石力学与工程学报.1996(03).
[75]邢纪波,俞良群,张瑞丰,等.离散单元法的计算参数和求解方法选择[J].计算力学学报.1999(01).
[76]王泳嘉,邢纪波.离散单元法同拉格朗日元法及其在岩土力学中的应用[J].岩土力学.1995(02).
[77]李艳洁,徐泳.用离散元模拟颗粒堆积问题[J].农机化研究.2005(02).
[78]李艳洁.堆积问题的离散元模拟_实验研究[D].北京：中国农业大学,2004.
[79]黄晚清,陆阳.散粒体重力堆积的三维离散元模拟[J].岩土工程学报.2006,28(12).
[80]刘军,刘汉龙.用MonteCarlo方法模拟砂土的自然堆积过程[J].岩土力学.2005,26.
[81]郭培玺,林绍忠.粗粒料颗粒随机分布的数值模拟[J].长江科学院院报.2007(4)：50-52.
[82]陆厚根.粉体工程导论[M].同济大学出版社,1998.
[83]叶大年.颗粒堆积问题[J].地质科技情报.1988,7(4).
[84]Ashmawy A K, Sukumaran B, Hoang A V. Evaluating the influence of particle shape on liquefaction behavior using Discrete Element Method[Z]. Honolulu, Hawaii:2003.
[85]Sallam A M. Studies on Modeling Angular Soil Particles Using the Discrete Element Method[D]. Tampa, FL:University of South Florida,2004.
[86]Lin X, Ng T T. A three-dimensional discrete element model using arrays of ellipsoids[J]. Geotechnique.1997,47(2):319-329.
[87]Ghaboussi J, Barbosa R. Three-dimensional discrete element method for granularmaterials[J]. International Journal for Numerical and Analytical Methods in Geomechanics.1990,14:451-472.
[88] Matsushima T.3-D image-based discrete element modeling for irregularly-shapedgrains[Z]. Kyoto:2004.
[89] T F, C C, E M, et al. Aggregate Imaging System (AIMS) for characterizing the shape offine and coarse aggregates[Z]. Washington, DC: Transportation Research Board, NationalResearch Council,2003.
[90] E. M. Review of imaging techniques for characterizing the shape of aggregates used inasphalt mixes.[Z]. Austin, TX.:2001.
[91] D J. Evaluation of aggregate particle shapes through multiple ratio analysis[Z]. Denver,CO.:2000.
[92] H K, C H, A R, et al. A prototype laser scanner for characterizing size and shape propertiesin aggregates[Z]. Austin, TX.:2000.
[93] Wc K. Measurement and geological significance of shape and roundness of sedimentaryparticles[J]. J Sediment petrol.1941,11(2):64-72.
[94] Powers M C. A new roundness scale for sedimentary particles[J]. Journal of SedimentaryPetrology.1953(23):117-119.
[95] Barret P J. The shape of rock particles, a critical review[J]. Sedimentology.1980(27):291-303.
[96] Wadell H. shape&roundness of rock particles[J]. J. of Geology.1932(40):443-451.
[97] Sukumaran B, Ashmawy A K. Quantitative characterization of the geometry of discreteparticles[J]. Geotechnique.2001,51(7):619-627.
[98] Wadell H. Sphericity and roundness of rock particles[J]. The Journal of Geology.1933,41(3):310-331.
[99] Sukumaran B, Ashmawy A K. Influence of inherent particle characteristics on the strengthparoperties of Particulate materials[Z]. Oslo, Norway:2001.
[100] Ehrlich R, Weinberg B. An exact method for characterization of grain shape[J]. J.Sediment.Petrol.1970,40(1):205-212.
[101] Bowman E T, Soga K. Particle shape characterization using Fourier descriptor analysis[J].Geotechnique.2001,51(6):545-554.
[102] Yudhbir, Abedinzadeh R. Quantification of particle shape and angularity using image analyzer[J]. Geotechnical Testing Journal.1991,14(3):296-308.
[103]Cho G, Dodds J, Santamarina J C. Particle shape effects on packing density, stiffness, and strength:natural and crushed sands[J]. Journal of Geotechnical and Geoenvironmental Engineering.2006,132(5):591-602.
[104]Rao C, Tutumluer E, Kim I T. Quantification of coarse aggregate angularity based on image analysis[Z]. Washington DC:2002:1787,117-124.
[105]Masad E, Button J W. Unified imaging approach for measuring aggregate angularity[J]. The International Journal of Computer-Aided Civil and Infrastructure Engineering.2000,15(4):273-280.
[106]Reschke T. Schriftenreihe der Zementindustrie[J]. Dusseldorf:Verlag Baut Technik Gmbh.2000,2006(62).
[107]R Y D, V H. Skeletonization of volumetric angiorams for display[J]. Computer Methods in Biomethanics and Biomedical Engineering.2002,5(5):329-341.
[108]樊雅萍,黄生学,温佩芝,等.基于数字距离变换的3D模型骨架提取算法[J].信息与控制.2004,33(6).
[109]牛立聪,孙香花,左晓宝.基于Matlab图像处理的砂石颗粒圆形度计算方法[J].混凝土.2012(2).
[110]吴威,谢步瀛.基于三角形的三维点集凸包快速求取算法[J].东华大学学报(自然科学版).2008(3)：311-314.
[111]李志,李儒琼.一种改进的快速三维凸包生成算法及实现[J].计算机工程与科学.2011(2)：129-132.
[112]Barber C B, Dobkin D P, Huhdanpaa H T. The Quickhull Algorithm for Convex Hulls[J]. ACM Transactions on Mathematical Software.1996,22(4):469-483.
[113]Kroon D. Segmentation of the mandibular canal in cone-beam CT data[D]. Enschede, the Netherlands:University of Twente,2011.
[114]芦鸿雁.基于层次包围盒的碰撞检测算法研究[J].计算机与数字工程.2008,36(2)：23-25.
[115]朱响斌,唐敏,董金祥.一种基于八叉树的三维实体内部可视化技术[J].中国图像图形学报.2002(3).
[116]L. O R, O. K. Hierarchic Voronoi skeletons[J]. Pattern Recognition.1995,28(3):343-359.
[117]Palagyi K, Kuba A. Directional3D Thinning Using8Subiterations[J]. Lecture Notes in Computer Science.1999,1568:325-336.
[118]Blum H. A transformation for extracting descriptors of shape[C]. MIT Press,1967.
[119]Bitter I, Kaufman A E, Sato M. Penalized-Distance Volumetric Skeleton Algorithm[J]. IEEE Trans, on Visualization and Computer Graphics.2001,7(3):195-206.
[120]Das N. Modeling three-dimensional shape of sand grains using discrete element method[D]. University of South Florida,2007.
[121]钟文镇,何克晶,周照耀,等.颗粒离散元模拟中的阻尼系数标定[J].物理学报.2009(8)：5155-5161.
[122]钟文镇,何克晶,夏伟,等.球形颗粒堆积过程中的能量转换研究(英文)[J].科学技术与工程.2009(07).
[123]Bishop A W. Correspondence on shear characteristics of a saturated silt, measured in triaxial compression[J]. Geotechnique.1954,4(1):43-45.
[124]Tsuji Y, Kawaguchi T, Tanata T. Discrete Particle Simulation of Two-Dimensional Fluidized Bed[J]. Powder Tech.1993(77):79-87.
[125]Kawaguchi T, Tanata T, Tsuji Y. Numerical Simulation of Fluidized Bed Using the Discrete Element Method[J]. JSME (B).1992,58(551):79-85.
[126]陆厚根.粉体技术导论[M].同济大学出版社,1992.
[127]程展林,包承纲.三峡工程二期围堰填料特性试验研究[J].长江科学院院报.1997(04).
[128]张小平,包承纲,施斌.三峡二期围堰填料参数的反分析[J].岩石力学与工程学报.2001(05).
[129]程永辉,李青云,饶锡保,等.长江科学院土工离心机的应用与发展[J].长江科学院院报.2011(5).
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |