基于CT图像的混凝土细观三维有限元模型重建
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摘要
目前,混凝土材料力学行为的研究大都是建立在试验的基础上,需要花费大量的人力、物力,所得到的试验成果又往往受到试验条件、环境以及材料本身复杂性的影响,试验成果的离散性较大。在这种情况下,结合理论和试验的细观数值模拟是一种行之有效的方法。而在细观尺度上有限元模型的建立是数值模拟首要的一环。
随着混凝土力学性能研究的深入,学者们越来越重视其细观力学性能的研究,随之产生了各种各样的细观结构有限元模型,例如格构模型,梁—颗粒模型,随机骨料模型,随机力学特性模型。以上模型大多是基于随机抽样方法和统计学的知识,所建立的模型虽然在骨料的分布和形状上已越来越接近混凝土的真实结构,但不可避免的与混凝土的真实细观结构存在着差异。CT技术的出现,实现了在无损状态下将混凝土内部细观结构用数字化方法进行呈现。如果能利用CT平面图像的信息,建立真实或近似真实的细观结构有限元模型,将对混凝土数值模拟研究产生一定的作用。混凝土包括了骨料、水泥砂浆和孔隙三部分,从图像特征来看,骨料接近于白色,孔隙趋于黑色,水泥砂浆则介于两者之间。由于骨料、砂浆与孔隙具有相对明显的密度差异,通过CT扫描并转换成图像后,混凝土各个组分之间具有较好的对比度,能比较容易的观察和提取出骨料的轮廓。本文选用平滑滤波、阀值分割、形态学开闭运算等比较成熟的数字图像处理技术对混凝土圆柱试件的截面图像进行预处理,以获取准确的骨料几何与位置信息。利用这些信息,本文提出了两种三维重建的思路。第一种思路也就是本文第三章,基本步骤是利用处理好的图像,提取骨料的轮廓,基于矩理论对骨料的轮廓进行识别,将同一骨料在不同的层的轮廓提取出来,进行拓扑重构。对重构好的骨料数据进行处理,提取骨料的几何信息如长短轴长,长轴的倾角,圆度,矩形度等,并提取有限数量且能准确描述骨料结构的特征点,将这些特征点的位置信息导入ANSYS,连点成线,由线生成面,并利用ANSYS中的蒙皮技术利用同一骨料的不同面生成体,最后剖分网格,生成有限元模型。第二种方法也就是本文的第四章,基于混凝土的CT平面图像信息,用APDL语言生成的程序对混凝土的三维细观结构在大型商业有限元软件ANSYS中进行三维重建。重建过程没有生成点、线、面、体等几何元素,而是利用CT平面图像信息直接生成节点,连接节点生成单元,避免了网格无法剖分现象的出现。生成的单元形状规则,长宽比合理。第一种方法生成的模型忽略了小体积组分结构,由于特征点选取的有限,生成的较大体积的骨料与试件中骨料的圆形状也存在着差异,并且剖分后的一小部分网格质量不高。第二种方法直接对图像信息数据压缩,没有对不同的骨料进行区分,并且由于界面层的引入,使生成模型与原混凝土试件相比骨料率明显降低。但基于CT图像三维重建后的模型是以混凝土的真实细观结构信息为依据的,从而使生成的模型与真实模型差异更小,并且彻底解决了多级配骨料无法投放的难题。
Nowadays, researching on mechanical behavior of concrete is based on experiment, which takes plenty of manpower and material resources, and test results obtained from the experiments is largely discrete because of experimental conditions, circumstance an complexity of material of itself etx. In this case, numerical simulation in mesolevel, which combine experiment and theory together, is an effcctive way of researching concrete.
With the researching on concrete mechanical property, the scholar put more and mor focus on the micromechanical behaciors of the concrete. So many kings of meso-structure finite element model was been made, such as lattice model, beam—granular model, random aggregate model and random mechanics model. These methods were all based on the random sampling methods and the statistics knowledge. So the FEM models made by these methods were differert from the real concrete structure inevitablly. With the CT apperence, the meso-structure of concrete was seen non-destructivly by digital method. If we can use the message given by the CT images to constructed the more lifelike FEM model, it will be very meanful for the concrete digital simulation. The concrete was consist of aggregate, mortar and pore. In the images, the aggregates were white, the pores were black and the mortar was between of them. Because the density of the three materials were different apparenttly, the contrast between of the three was very well in the images transferred from the CT and we can get the contours easilly. In the article some digital image processing technics such as smooth filter, threshold dividing and the open and close on morphology were used to process the images of the concrete beam. The shape and location messages of the aggregates was got. In the article, two 3-D reconstruction methods were given. The first method was described by the third section in the article. Using the images processed, the contours were extracted, then these contours were identied based on the moment theory to reconstruction topologically. Processing the aggregate data to get the messages of the aggregate shapes such as length of the long and short axis, the pitch angle of the long axis, circularity and rectangular degree etc. a few number of characteristic points were extracted to describe the shape of the aggregate. the location of these characteristic points were loaded into ANSYS, then connecting these points to generate lines and generate areas by these lines, finally the volume was generated using envelope technology by areas. The FEM model was generated after the mesh divided. The second method described by the forth section in the article. Based on the CT images, the 3-D meso-structure of concrete was reconstructed using APDL language by ANSYS. In the reconstruction procession, the geometic constituents such as points, lines, areas and volumes had not been generated. Using the messages from the CT images, the nodes were generated directly, then the elements were generated by jointing the nodes. The phenomenons that the elements could not been divided was avoided. The shapes of elements were regular, and the aspect ratio was rationally. In The first method the small volume compoment constructions were ignored. Because the characteristic points chosen were finitly, the big aggregates generated in the FEM model was also a little different from the real aggregate shapes and the qualitity of some mesh was not very well. In the second method the images data was compressed directly, the specification between aggregates were not very well.The boundary layer was generated in this model, so the ratio of the aggregate was cuted down apperently contrast to the real concrete model. But the 3-D reconstruction FEM model generated from the real construction of the concrete beam. So the model was more likely with the real model and the problem that the different aggregate graded concrete can hardly be generated was ravel out rippingly.
随着混凝土力学性能研究的深入,学者们越来越重视其细观力学性能的研究,随之产生了各种各样的细观结构有限元模型,例如格构模型,梁—颗粒模型,随机骨料模型,随机力学特性模型。以上模型大多是基于随机抽样方法和统计学的知识,所建立的模型虽然在骨料的分布和形状上已越来越接近混凝土的真实结构,但不可避免的与混凝土的真实细观结构存在着差异。CT技术的出现,实现了在无损状态下将混凝土内部细观结构用数字化方法进行呈现。如果能利用CT平面图像的信息,建立真实或近似真实的细观结构有限元模型,将对混凝土数值模拟研究产生一定的作用。混凝土包括了骨料、水泥砂浆和孔隙三部分,从图像特征来看,骨料接近于白色,孔隙趋于黑色,水泥砂浆则介于两者之间。由于骨料、砂浆与孔隙具有相对明显的密度差异,通过CT扫描并转换成图像后,混凝土各个组分之间具有较好的对比度,能比较容易的观察和提取出骨料的轮廓。本文选用平滑滤波、阀值分割、形态学开闭运算等比较成熟的数字图像处理技术对混凝土圆柱试件的截面图像进行预处理,以获取准确的骨料几何与位置信息。利用这些信息,本文提出了两种三维重建的思路。第一种思路也就是本文第三章,基本步骤是利用处理好的图像,提取骨料的轮廓,基于矩理论对骨料的轮廓进行识别,将同一骨料在不同的层的轮廓提取出来,进行拓扑重构。对重构好的骨料数据进行处理,提取骨料的几何信息如长短轴长,长轴的倾角,圆度,矩形度等,并提取有限数量且能准确描述骨料结构的特征点,将这些特征点的位置信息导入ANSYS,连点成线,由线生成面,并利用ANSYS中的蒙皮技术利用同一骨料的不同面生成体,最后剖分网格,生成有限元模型。第二种方法也就是本文的第四章,基于混凝土的CT平面图像信息,用APDL语言生成的程序对混凝土的三维细观结构在大型商业有限元软件ANSYS中进行三维重建。重建过程没有生成点、线、面、体等几何元素,而是利用CT平面图像信息直接生成节点,连接节点生成单元,避免了网格无法剖分现象的出现。生成的单元形状规则,长宽比合理。第一种方法生成的模型忽略了小体积组分结构,由于特征点选取的有限,生成的较大体积的骨料与试件中骨料的圆形状也存在着差异,并且剖分后的一小部分网格质量不高。第二种方法直接对图像信息数据压缩,没有对不同的骨料进行区分,并且由于界面层的引入,使生成模型与原混凝土试件相比骨料率明显降低。但基于CT图像三维重建后的模型是以混凝土的真实细观结构信息为依据的,从而使生成的模型与真实模型差异更小,并且彻底解决了多级配骨料无法投放的难题。
Nowadays, researching on mechanical behavior of concrete is based on experiment, which takes plenty of manpower and material resources, and test results obtained from the experiments is largely discrete because of experimental conditions, circumstance an complexity of material of itself etx. In this case, numerical simulation in mesolevel, which combine experiment and theory together, is an effcctive way of researching concrete.
With the researching on concrete mechanical property, the scholar put more and mor focus on the micromechanical behaciors of the concrete. So many kings of meso-structure finite element model was been made, such as lattice model, beam—granular model, random aggregate model and random mechanics model. These methods were all based on the random sampling methods and the statistics knowledge. So the FEM models made by these methods were differert from the real concrete structure inevitablly. With the CT apperence, the meso-structure of concrete was seen non-destructivly by digital method. If we can use the message given by the CT images to constructed the more lifelike FEM model, it will be very meanful for the concrete digital simulation. The concrete was consist of aggregate, mortar and pore. In the images, the aggregates were white, the pores were black and the mortar was between of them. Because the density of the three materials were different apparenttly, the contrast between of the three was very well in the images transferred from the CT and we can get the contours easilly. In the article some digital image processing technics such as smooth filter, threshold dividing and the open and close on morphology were used to process the images of the concrete beam. The shape and location messages of the aggregates was got. In the article, two 3-D reconstruction methods were given. The first method was described by the third section in the article. Using the images processed, the contours were extracted, then these contours were identied based on the moment theory to reconstruction topologically. Processing the aggregate data to get the messages of the aggregate shapes such as length of the long and short axis, the pitch angle of the long axis, circularity and rectangular degree etc. a few number of characteristic points were extracted to describe the shape of the aggregate. the location of these characteristic points were loaded into ANSYS, then connecting these points to generate lines and generate areas by these lines, finally the volume was generated using envelope technology by areas. The FEM model was generated after the mesh divided. The second method described by the forth section in the article. Based on the CT images, the 3-D meso-structure of concrete was reconstructed using APDL language by ANSYS. In the reconstruction procession, the geometic constituents such as points, lines, areas and volumes had not been generated. Using the messages from the CT images, the nodes were generated directly, then the elements were generated by jointing the nodes. The phenomenons that the elements could not been divided was avoided. The shapes of elements were regular, and the aspect ratio was rationally. In The first method the small volume compoment constructions were ignored. Because the characteristic points chosen were finitly, the big aggregates generated in the FEM model was also a little different from the real aggregate shapes and the qualitity of some mesh was not very well. In the second method the images data was compressed directly, the specification between aggregates were not very well.The boundary layer was generated in this model, so the ratio of the aggregate was cuted down apperently contrast to the real concrete model. But the 3-D reconstruction FEM model generated from the real construction of the concrete beam. So the model was more likely with the real model and the problem that the different aggregate graded concrete can hardly be generated was ravel out rippingly.
引文
[1]中国水利水电科学研究院科研报告,“九五”国家重点科技攻关课题,300m级高拱坝抗震技术研究(课题负责人陈厚群等),1999.
[2]全级配大坝混凝土动态性能研究,水利部科技创新项目,(项目负责人陈厚群),2000.
[3]亢景付,张镜剑,冯乃谦,结构模型试验中模型混凝土配合比研究[J].土木工程学报,1998,(4),53～59.
[4]任朝军.基于细观层次混凝土静、动力学性能的数值模拟：硕士学位论文[D].南京：河海大学,2005,5
[5]Z.P.Bazant,M.R. Tabbara, Random particle models for fracture of aggregate or fiber composites [J] Journal Engineering Mechanics, ASCE,1990,116(8):1686～1705
[6]E.J.Garboczi. Three-dimensional mathematical analysis of particle shape using X-ray tomography and sphercal harmonics:Application to aggregates used in concrete [J]. Cement and Concrete Research, 2002,32:1621-1638.
[7]Zhong X.X., Chang C S. Micromechanical modeling for behavior of cementitious granular materials. Journal of Engineering Mechanics, ASCE,1999,125(11):1280～1288
[8]G. Fu, W. Dekelbab.3-D random packing of polydisperse particles and concrete aggregate grading [J]. Powder Technology,2003,133:147～155.
[9]F.H. Wittmann,P.E. Roelfdtra, H. Sadouki, Simulation and analysis of composite structures [J]. Mater Sci ENGNG,1984,68:239～248.
[10]J.K. Beddow, T.Meloy, Testing and Characterization of Powders and Fine Particles [M]. london: Heyden,1980
[11]王宗敏,不均匀材料(混凝土)裂隙扩展及宏观计算强度与变形[D].北京：清华大学,1996
[12]Z.M. Wang, A.K.H. Kwan, H.C. Chan. Mesoscopic study of concrete I Generation of random aggregate structure and finite element mesh [J]. Computers and structures,1999,70:533～544.
[13]刘光廷,王宗敏.用随机骨料模型数值模拟混凝土材料的断裂.清华大学学报,1996,36(1)：84-89
[14]Ashraf Ragab Mohamed, Will Hansen. Micromechanical modeling of concrete response under static loading-Part Ⅰ:Model development and validation. ACI Matetials Journal,1999,96(2):196～203
[15]Ashraf Ragab Mohamed, Will Hansen. Micromechanical modeling of concrete response under static loading-Part:Model predictions for shear and compressive loading. ACI Materials Journal,1999, 96(3):354～358.
[16]Ashraf Ragab Mohamed, Will Hansen. Micromechanical modeling of crack-aggregate interaction in concrete materials. Cement and Concrete Composites,1999,21:349～359.
[17]岳中琦.岩土细观介质空间分布数字表述和相关力学数值分析的方法、应用和进展[J].岩石力学与工程学报,2006,25(5)：875～888.
[18]Brekelmans W. New method to analyse the mechanincal behavior of the skeletal part. Acta orthop scand,1972; 43:301～305
[19]Rybicki, E. On the mathematical analysis of stress in the human femur. J Biomech,1972;5:203～206
[20]Allesmat H.G.B. Optical analysis of stress and strain in photoelastic particle assemblies. Doctor thesis, Delft University of Technology,1987
[21]Allesmat H.G.B. Using image processing in analyzing stresses in photoelastic granular material. Proc. 10th int. Conf. On Experimental Mechanics, Lisbon,1994:113～118
[22]Raschke S.A; Hryciw R.D; Donohoe G.W. Microdeformations in sands by digital image processing and analysis. Transportation Research Record. National Research Council, Washington, DC, USA.1996: 31～37.
[23]White D.J, Take W.A, Boltoon M.D. Measuring soil deformation in geotechnical models using digital images and PIV analysis. I& International Conference on Computer Methods and Advances in Geomechanics. Rotterdam:Balkema,2001,997～1002
[24]White D.J, Take W.A, etc(University of Cambridge, UK). A deformation measurement system for geotechnical testing based on digital imageing, close-range photogrammetry, and PIV image anslysis. 15'a International Conference on Soil Mechanics Engineering, Rotterdam:Balkema,2002:539～542
[25]Macari-Pasqualino E.J,Costes N.C, Parker J.K. Digital image techniques for volume change measurements in triaxial tests. Proceeding of the Conference on Digital Image Processing:Techniques and Applications in Civil Engineering. Kona, Hawaii, USA.1993:211～219
[26]Bonifazi G, Sappa G, De C.G. Applications of images digital analysis in the characterisation of grains morphology influence in mechanical behavior of granular soils. Materials Research Society Symposium-Proceeding.1995,362:167～172
[27]Lee X, Dassi W.C, Manzione C.W. Characterization of granular material composite structure using computerized tomography. Proceedings of Engineering Mechanics. ASCE, New York, NY, USA.1993: 268～271
[28]Khalid A.Alshibli and Stein Stme. Sand shear band thickness measurement by digital imaging techniques. Journal of Computing in Civil Engineering,1999,13(2):103～109
[29]Oda, M. and Xazama. Microstructure of shear bands and its relation to the mechanisms of fatancy and failure of dense granular soils. Geotechnique,1998,48(4):465～481
[30]Frost J D, Kuo C-Y. Automated determination of the distributiong of local void ratio from digital image [J]. Geotechnical Testing Journal,1996,19(2):107～117
[31]Kuo C.Y, Frost J D. Initial fabric and uniformity of a sand specimen-an image analysis approach. ASME-ASCE-SES Joint Summer Meeting. ASCE, New York, NY, USA.199:214～227
[32]Alshibli K.A; El-Saidany H.A. Quantifying void ratio in granular materials using Voronoi tessellation. Journal of Computing in Civil Engineering.2001,15(3):232～238
[33]Alshibli K.A, Macari E J, Sture S. Digital imaging techniques for assessment of homogeneity of granular meterials [J]. Transportation Research Record,1996(1526):121～128
[34]Wightman C, Muzzio F.J, Wilder J. A quantitative image analysis method for characterizing mixtures of granular materiels.Powder Technology. Switzerland.1996,89(2):165～176
[35]Van Den Berg E.H, Meesters A.G.C.A, Kenter J.A.M, Schlager W. Automated separation of touching grains in digital images of thin sections. Computers & Geosciences.2002,28(2):179～180
[36]Kuo C.Y, Frost J D, Chameau J-L A. Image analysis determinationg of stereology based fabric tensors [J].Geotechnique,1998,48(4):515～525
[37]李元海,朱合华,上野胜利,望月秋利.基于图像相关分析的砂土模型试验变形场量测[J].岩土工程学报,2004,26(1)：36-41.
[38]张嘎,张建民,梁东方.土与结构面接触试验中的土颗粒细观运动测量[J].岩土工程学报,2005,27(8)：903-907.
[39]Howarth, D. F., Oda M., Yamazaki, M., etc. Permeabilith changes in granite with crack growth during immersion in hot [J]. Int. J. C. Quantitative assessmengt of rock texture and correlation with drillabilith and strength properties [J]. Rock Mech. Rock engning.1987,20:57～85
[40]Campbell, Donald H. and Galehouse, Jon S. Quantitative clinker microscopy with the light microscope [J].Cement, Concrete and Aggregates,1991,13(2):94～96.
[41]Wu, Xiang Yang, Baud, P. Wong. Micromechanics of compressive failure and saptial evolution of anisotropic damage in Darley Dale sandstone Teng-fong [J]. International Journal of Rock Mechanics and Mining Scinces,2000,37(1):143～160.
[42]R. Prikryl. Some microstructure aspects of strengh variation in rocks[J]. International Journal of Rock Mechanics & Mining Sciences,2001,38:671～682.
[43]Mnenedez, B., David, C. and Nistal, A.M. Confocal scanning laser microscopy applied to the study of pore and crack networks in rocks [J]. Computer and Geosciences,2001,27(9):1101～1109.
[44]赵永红.受压岩石中裂纹发育过程及分维变化特征[J].科学通报,1995,40(7)：621-623.
[45]张梅英,袁建新,李延芥等.单轴压缩过程中岩石变形破坏机理[J].岩石力学与工程学报,1998,17(1)：1-8.
[46]吴立新,王金庄,孟顺利.煤岩损伤扩展规律的即时压缩SEM研究[J].岩石力学与工程学报,1998,17(1)：9-15.
[47]Yue, Z.Q., Bekking, W., Morin, I. Application of digital image processing to quantitative study of asphalt concrete microstructure [J]. Transportation Research Record,1995,1492:53～60.
[48]Yue, Z.Q., Morin, I. Digital image processing for aggregate orientation in asphalt concrete mixtures [J]. Can. J. Civ. Eng.,1996,23:480～489.
[49]Masad E., Muhunthan B., Shashidhar N.et al. Quantifying Laboratory Compaction Effects on the Internal Structure of Asphalt Concerte [A].TRB [C] 1998
[50]Mora, C. F., Kwan, A.K.H., Chan, H.C.. Particle size distribution analysis of coarse aggregate using digital image processing [J]. Cement and Concrete Research,1998,28(6):921～932.
[51]C.F.Mora, A.K.H.Kwan, Sphericity, shape factor and convexity measurement of aggregate for concrete using digital image processing [J].Cement and concrete Research 30(2000) 351～358.
[52]Kwan, A.K.H., Mora, C. F., Chan, H.C.. Particle shape analysis of coarse aggregate using digital image processing [J].Cement and Concrete Research,1999,29:1403～1410.
[53]Wang, L. B., Frost, J. D., Mohammad, L., Pang, T. Y. Three-Dimensional Aggregate Evaluation Using X-ray Tomography Imaging [C]. Transportation Research Record 2002 AnnualMeeting,2002.
[54]Wang, L. B., Forst, J. D.,Shashidhar N. Microstructure study of westrack mixtures from X-ray Tomography Images [A]. Transportation Research Board [C], WashingtonDC,2001.
[55]Masad E, Button J. Implications of experimental measurements and analyses of the internal structure of HMA [A]. Transportation Research Board [C], WashingtonDC,2004.
[56]] ChenJ.-S., Liao M.-C. Evaluation of intemal resistance in hot-mix asphalt (HMA) concrete [J]. Construction and Bulilding Materials.2002 16.
[57]张婧娜.基于数字图像处理技术的沥青混合料微观结构分析方法研究[D]博士学位论文同济大学2000.
[58]张肖宁,李智,虞将苗.沥青混合料的体积组成及其数字图像处理技术[J].华南理工大学学报(自然科学版),2002,30(11)：113-215.
[59]李晓军,张肖宁.CT技术在沥青胶结颗粒材料内部结构分析中的应用[J].公路交通科技.2005(1).
[60]李智.基于数字图像处理技术的沥青混合料体积组成特性分析[D].博士学位论文
[61]ChenJ.-S., Liao M.-C. Evaluation of intemal resistance in hot-mix asphalt (HMA) concrete [J]. Construction and Bulilding Materials.2002,16.
[62]Wang Duan-yi, Li wei-jie, Zhang Xiao-ning..Evaluation of surface Segregation of Asphalt Pavement by using digital image Technique [J]. Journal of South China University of Technology.2005 33(1):16～20.
[63]杨新华,王习武,陈传尧,蒙培生.用图像处理技术实现沥青混合料有限元建模[J].中南公路工程,2005,30(3)：5-7.
[64]虞将苗,李晓军,王端宜,张肖宁.基于计算机层析识别的沥青混合料有限元模型[J].长安大学学报(自然科学版),2006,26(1)：16-19.
[65]陈沙,岳中琦,谭国焕.基于数字图像的非均质岩土工程材料的数值分析方法[J].岩土工程学报.2005,27(8)：956-963.
[66]岳中琦,陈沙,郑宏等,岩土工程材料的数字图像有限元分析[J].岩石力学与工程学报.2004,23(6)：889-897.
[67]陆秀峰,刘西拉,覃维祖.通过混凝土二维截面推测骨料粒径分布[J].岩石力学与工程学报,2005,24(17)：3107-3112.
[68]Bentz, D. P.. Three-dimensional computer simulation of Portland cement hydration and microstructure development [J]. Journal of the American Ceramic Society,1997,80(1):3～21.
[69]Ammouche, A., Breysse, D., Hornain, H., Didry, O., Marchand, J.. A new image analysis technique for the quantitative assessment of microcracks in cement-based materials [J]. Cement and Concrete Research,2000,3:25～35.
[70]Ammouche, A., Riss, J., Breysse, D., Marchand, J.. Image analysis for the automated study ofmicrocracks in concrete [J].Cement & Concrete Composites,2001,23:267～278.
[71]Dequiedt, A.-S., Coster, M., Chermant, L., Chermant, J.L.. Study of phase dispersion in concrete by image analysis [J]. Cement& Concrete Composites,2001,23:215～226.
[72]Dequiedt, A.-S., Coster, M., Chermant, L., Chermant, J.L.. Distances between air-voids in concrete by automatic methods [J]. Cement & Concrete Composites,2001,23:247～254.
[73]Amo, D.G., Perez, B.C.. Diagnosis of the alkali-silica reactivity potential by means of digital image analysis of aggregate thin sections [J]. Cement and Concrete Research,2001,31:1449～1454.
[74]Diamond, S.. Considerations in image analysis as applied to investigations of the ITZ in concrete [J]. Cement & Concrete Composites,2001,23:171～178.
[75]Diamond, S., Huang, J.. The ITZ in concrete-a different view based on image analysis and SEM observations [J]. Cement & Concrete Composites,2001,23:179～188.
[76]Mouret, M., Ringot, E., Bascou,l A.. Image analysis:a tool for the characterization for hydration of cement in concrete-metrological aspects of magnification on measurement [J]. Cement & Concrete Composites,2001,23:201～206.
[77]Marinon,i N., Pavese, A., Fo,i M.. Characterization of mortar morphology in thin sections by digital image processing [J]. Cement and Concrete Research,2005,35:1613-1619.
[78]Mertens, G., Elsen, J.. Use of computer assisted image analysis for the determination of the grain-size distribution of sands used in mortars [J]. Cement and Concrete Research,2006,36:1453～1459.
[79]S,, E.N., Keane, D.T.. X-ray microtomographic studies of pore structure and permeability in portland cement concrete [J].Materials and Structures,2006,39:611～620.
[80]王宝庭,徐道远,宋玉普.数字图像处理技术在混凝土研究中的应用[J].河海大学学报,1999,27(4)：60～63.
[81]陆秀峰,刘西拉,覃维祖.从混凝土二维截面推测骨料粒径分布[J].岩石力学与工程学报,2005,24(17)：3107～3112.
[82]刘清元,谈桥.基于图像处理的混凝土裂缝的检测[J].武汉理工大学学报,2005,27(4)：69～71.
[83]Herman G T and Liu H K. Three-Dimensional Display of Human organs from Computed Tomograms. Computer Graphies Image Processing.1979. Vol.9
[84]Lorensen W E and Cline H E. Marehing Cubes:A High Resolution 3D Surface Construction Algorithm. Computer Graphies 1987.Vol.21.No.4.163～169
[85]Cline H E and Lorensen W E. Two Algorithms for the 3D Reconstruction of Tomograms. Medical Physics,1988, Vol.15, No.3,225～233.
[86]Keppel E. Approximating Complex Surface by Triangulation of Contour Lines. IBM J. Research and Development.1975. Vol.19
[87]Kehtarnavaz N and de Figueiredo R J P.A Framework for Surface Reconstruction from 3D Contours. Computer Vision Graphies Image Processing,1988, Vol.42
[88]David C.Kay等著.柏东等译.图形图像文件格式大全[M].学苑出版社.1994
[89]章毓晋.图像分割[M].科学出版社.2001
[90]韩思奇,王蕾.图像分割的阐值法综述[J].系统工程与电子技术.2002,6：91-94
[91]贺兴华等.MATLAB7.x图像处理[M].人民邮电出版社.2006
[92]周儒荣.逆向工程与快速原型制造[J].计算机辅助设计与制造,2000,15(4)：299-301
[93]陈琼.三维有限元建模方法的研究现状.口腔医学[J].2006年4月,第26卷第2期.
[94]于力牛.基于实体模型的牙领组织三维有限元建模问题探讨[J].机械设计与研究.2002年4月,第18卷第2期.
[95]陈功.基于逆向工程的医学器官有限元建模方法[J].机械工程学报.200642(1),227～231.
[96]Wittmann F H, Roelfstra P E, Sadouki H. Simulation and analysis of composite structures [J]. Mater. Sci. Engng.,1984,68:239～248
[97]王宗敏,邱志章.混凝土细观随机骨料结构与有限元剖分[J].计算力学学报,2005,22(6)：728～732.
[98]高政国,刘光廷.三维凸型混凝土骨料随机投放算法[J].清华大学学报.2003,43(8)：1120～1123.
[99]孙立国.三级配(全级配)混凝土骨料形状数值模拟及其应用：(硕士学位论文).南京：河海大学,2005.
[100]杜成斌,孙立国.任意形状混凝土骨料的数值模拟及应用[J].水利学报,2006,37(6)：662～667.
[101]李运成,马怀发,陈厚群.混凝土随机凸多面体骨料模型生成及细观有限元剖分[J].水利学报,2006,37(5)：588～592.
[102]Bazant,Z, P, Tabbara, M, R, Random particle models for fracture of aggregate of fiber composites[J]. Journal of Engineering Mechanics, ASCE,1990,116(8):1686～1705.
[103]王宝庭,宋玉普,张燕坤.基于刚体—弹簧模型的混凝土微裂纹行为的模拟[J].工程力学,1990,16(2)：140～144.
[104]邢纪波,俞良群,王永嘉.三维梁—颗粒模型与岩石材料细观力学行为的模拟[J].岩石力学与工程学报,1999,16(6)：627～450.
[105]刘光延,王宗敏.用随机骨料模型数值模拟混凝土材料的断裂[J].清华大学学报,1996,14(2)：84～89.
[106]于庆磊,唐春安,唐世斌.基于数字图像的岩石非均匀性表征技术及初步应用[J].岩石力学与工程学报,2007,26(3)：551～558.
[107]Mehta, P. K. Concrete Structure, Properties and Materials [M]. Indiana Elsevier Applied Science, USA.1986.
[108]李晓军,张金夫,刘凯年,张肖宁.基于CT图像处理技术的岩土材料的有限元模型[J].2006,27(8)：1331～1334.
[109]柏巍,彭刚,戚永乐等.基于CT图像的混凝土细观结构的有限元重建[J].混凝土,2008,2：63～69.
[110]李悦溪.人体胃部三维有限元模型的建立[D].2007,浙江大学硕士学位论文.
[111]潘宏.踝关节三维有限元模型的建立和临床应用[D].2004,安徽医科大学硕士学位论文.
[112]张少峰,孙滢滢,周冰等.利用Matlab和Pro/E软件辅助建立桩核冠的三维有限元模型[J].口腔医学研究,2006,22(3)：267～270
[113]Keneth R C.数字图像处理[M].北京：电子工业出版社,1993.
[114]Hu M K. Visual Pattern Recognition by Moment Invariants [J]. IEEE Trans on Information Theory, 1962, (8):179～187.
[117]黄碧霞.体视学与图像分析技术在沥青混合料级配分析中的应用[D].2007,西南交通大学硕士论文.
[115]蔡元龙.模式识别[M].西安：电子科技大学出版社,1999.
[116]胡江萍.混凝土集料的形状描述[D].国外建材科技,2006,27(6)：17～20
[117]Bowman, E.T., Soga, K., Drummond, T.W.. Particle shapecharacterization using Fourier analysis [J]. CUED/D-Soils/TR315,2000
[118]Kim, H., Haas, C.T., Rauch, A. F., Browne, C.. Wavelet-based three-dimensional descriptors of aggregate particles [J]. Transportation Research Record,2002,1787:109～116.
[119]Erdogan, S. T., Quiroga, P. N., Fowler, D.W., Saleh, H.A., Livingston, R. A., Garbocz,i E. J., Ketcham, P. M.,Hagedorn, J.G, Satterfield, S.G.. Three-dimensional shape analysis of coarse aggregates: new techniques for and preliminary results on several different coarse aggregates and reference rocks [J]. Cement and Concrete Research,2006,36:1619-1627.
[120]张兴平,耿国华,周明全.一种基于面积误差的多边形逼近算法[J].微机发展,2004,14(12)：120-122.
[121]Saykol E, Gulesir G, Gudukbay U, et al. Akinematics-based method for polygon approximation [J].Advances in Information System(ADVIS'2002),2002,2457:186-194.
[122]章毓晋.图像处理和分析[M].北京：清华大学出版社,2000：220-222.
[123]樊宏斌.计算机辅助颅骨面貌复原技术的研究与实现[D].西安：西北大学,2002：20-22.
[124]吴中海,张行功,叶澄清,等.一个适合特征计算的多边形逼近算法[J].计算机学报,1997,20(12)：1129-1132.
[125]郑娅娜.混凝土破坏过程的三维细观数值模拟与CT试验验证：硕士学位论文[D].西安：西安理工大学,2005,3
[126]田威.混凝土破坏过程的三维细观数值模拟与CT试验验证：硕士学位论文[D].西安：西安理工大学,2006,3
[127]梁昕宇.数值混凝土模型的改进及其细观力学特性研究[D].西安：西安理工大学,2008,3
[2]全级配大坝混凝土动态性能研究,水利部科技创新项目,(项目负责人陈厚群),2000.
[3]亢景付,张镜剑,冯乃谦,结构模型试验中模型混凝土配合比研究[J].土木工程学报,1998,(4),53～59.
[4]任朝军.基于细观层次混凝土静、动力学性能的数值模拟：硕士学位论文[D].南京：河海大学,2005,5
[5]Z.P.Bazant,M.R. Tabbara, Random particle models for fracture of aggregate or fiber composites [J] Journal Engineering Mechanics, ASCE,1990,116(8):1686～1705
[6]E.J.Garboczi. Three-dimensional mathematical analysis of particle shape using X-ray tomography and sphercal harmonics:Application to aggregates used in concrete [J]. Cement and Concrete Research, 2002,32:1621-1638.
[7]Zhong X.X., Chang C S. Micromechanical modeling for behavior of cementitious granular materials. Journal of Engineering Mechanics, ASCE,1999,125(11):1280～1288
[8]G. Fu, W. Dekelbab.3-D random packing of polydisperse particles and concrete aggregate grading [J]. Powder Technology,2003,133:147～155.
[9]F.H. Wittmann,P.E. Roelfdtra, H. Sadouki, Simulation and analysis of composite structures [J]. Mater Sci ENGNG,1984,68:239～248.
[10]J.K. Beddow, T.Meloy, Testing and Characterization of Powders and Fine Particles [M]. london: Heyden,1980
[11]王宗敏,不均匀材料(混凝土)裂隙扩展及宏观计算强度与变形[D].北京：清华大学,1996
[12]Z.M. Wang, A.K.H. Kwan, H.C. Chan. Mesoscopic study of concrete I Generation of random aggregate structure and finite element mesh [J]. Computers and structures,1999,70:533～544.
[13]刘光廷,王宗敏.用随机骨料模型数值模拟混凝土材料的断裂.清华大学学报,1996,36(1)：84-89
[14]Ashraf Ragab Mohamed, Will Hansen. Micromechanical modeling of concrete response under static loading-Part Ⅰ:Model development and validation. ACI Matetials Journal,1999,96(2):196～203
[15]Ashraf Ragab Mohamed, Will Hansen. Micromechanical modeling of concrete response under static loading-Part:Model predictions for shear and compressive loading. ACI Materials Journal,1999, 96(3):354～358.
[16]Ashraf Ragab Mohamed, Will Hansen. Micromechanical modeling of crack-aggregate interaction in concrete materials. Cement and Concrete Composites,1999,21:349～359.
[17]岳中琦.岩土细观介质空间分布数字表述和相关力学数值分析的方法、应用和进展[J].岩石力学与工程学报,2006,25(5)：875～888.
[18]Brekelmans W. New method to analyse the mechanincal behavior of the skeletal part. Acta orthop scand,1972; 43:301～305
[19]Rybicki, E. On the mathematical analysis of stress in the human femur. J Biomech,1972;5:203～206
[20]Allesmat H.G.B. Optical analysis of stress and strain in photoelastic particle assemblies. Doctor thesis, Delft University of Technology,1987
[21]Allesmat H.G.B. Using image processing in analyzing stresses in photoelastic granular material. Proc. 10th int. Conf. On Experimental Mechanics, Lisbon,1994:113～118
[22]Raschke S.A; Hryciw R.D; Donohoe G.W. Microdeformations in sands by digital image processing and analysis. Transportation Research Record. National Research Council, Washington, DC, USA.1996: 31～37.
[23]White D.J, Take W.A, Boltoon M.D. Measuring soil deformation in geotechnical models using digital images and PIV analysis. I& International Conference on Computer Methods and Advances in Geomechanics. Rotterdam:Balkema,2001,997～1002
[24]White D.J, Take W.A, etc(University of Cambridge, UK). A deformation measurement system for geotechnical testing based on digital imageing, close-range photogrammetry, and PIV image anslysis. 15'a International Conference on Soil Mechanics Engineering, Rotterdam:Balkema,2002:539～542
[25]Macari-Pasqualino E.J,Costes N.C, Parker J.K. Digital image techniques for volume change measurements in triaxial tests. Proceeding of the Conference on Digital Image Processing:Techniques and Applications in Civil Engineering. Kona, Hawaii, USA.1993:211～219
[26]Bonifazi G, Sappa G, De C.G. Applications of images digital analysis in the characterisation of grains morphology influence in mechanical behavior of granular soils. Materials Research Society Symposium-Proceeding.1995,362:167～172
[27]Lee X, Dassi W.C, Manzione C.W. Characterization of granular material composite structure using computerized tomography. Proceedings of Engineering Mechanics. ASCE, New York, NY, USA.1993: 268～271
[28]Khalid A.Alshibli and Stein Stme. Sand shear band thickness measurement by digital imaging techniques. Journal of Computing in Civil Engineering,1999,13(2):103～109
[29]Oda, M. and Xazama. Microstructure of shear bands and its relation to the mechanisms of fatancy and failure of dense granular soils. Geotechnique,1998,48(4):465～481
[30]Frost J D, Kuo C-Y. Automated determination of the distributiong of local void ratio from digital image [J]. Geotechnical Testing Journal,1996,19(2):107～117
[31]Kuo C.Y, Frost J D. Initial fabric and uniformity of a sand specimen-an image analysis approach. ASME-ASCE-SES Joint Summer Meeting. ASCE, New York, NY, USA.199:214～227
[32]Alshibli K.A; El-Saidany H.A. Quantifying void ratio in granular materials using Voronoi tessellation. Journal of Computing in Civil Engineering.2001,15(3):232～238
[33]Alshibli K.A, Macari E J, Sture S. Digital imaging techniques for assessment of homogeneity of granular meterials [J]. Transportation Research Record,1996(1526):121～128
[34]Wightman C, Muzzio F.J, Wilder J. A quantitative image analysis method for characterizing mixtures of granular materiels.Powder Technology. Switzerland.1996,89(2):165～176
[35]Van Den Berg E.H, Meesters A.G.C.A, Kenter J.A.M, Schlager W. Automated separation of touching grains in digital images of thin sections. Computers & Geosciences.2002,28(2):179～180
[36]Kuo C.Y, Frost J D, Chameau J-L A. Image analysis determinationg of stereology based fabric tensors [J].Geotechnique,1998,48(4):515～525
[37]李元海,朱合华,上野胜利,望月秋利.基于图像相关分析的砂土模型试验变形场量测[J].岩土工程学报,2004,26(1)：36-41.
[38]张嘎,张建民,梁东方.土与结构面接触试验中的土颗粒细观运动测量[J].岩土工程学报,2005,27(8)：903-907.
[39]Howarth, D. F., Oda M., Yamazaki, M., etc. Permeabilith changes in granite with crack growth during immersion in hot [J]. Int. J. C. Quantitative assessmengt of rock texture and correlation with drillabilith and strength properties [J]. Rock Mech. Rock engning.1987,20:57～85
[40]Campbell, Donald H. and Galehouse, Jon S. Quantitative clinker microscopy with the light microscope [J].Cement, Concrete and Aggregates,1991,13(2):94～96.
[41]Wu, Xiang Yang, Baud, P. Wong. Micromechanics of compressive failure and saptial evolution of anisotropic damage in Darley Dale sandstone Teng-fong [J]. International Journal of Rock Mechanics and Mining Scinces,2000,37(1):143～160.
[42]R. Prikryl. Some microstructure aspects of strengh variation in rocks[J]. International Journal of Rock Mechanics & Mining Sciences,2001,38:671～682.
[43]Mnenedez, B., David, C. and Nistal, A.M. Confocal scanning laser microscopy applied to the study of pore and crack networks in rocks [J]. Computer and Geosciences,2001,27(9):1101～1109.
[44]赵永红.受压岩石中裂纹发育过程及分维变化特征[J].科学通报,1995,40(7)：621-623.
[45]张梅英,袁建新,李延芥等.单轴压缩过程中岩石变形破坏机理[J].岩石力学与工程学报,1998,17(1)：1-8.
[46]吴立新,王金庄,孟顺利.煤岩损伤扩展规律的即时压缩SEM研究[J].岩石力学与工程学报,1998,17(1)：9-15.
[47]Yue, Z.Q., Bekking, W., Morin, I. Application of digital image processing to quantitative study of asphalt concrete microstructure [J]. Transportation Research Record,1995,1492:53～60.
[48]Yue, Z.Q., Morin, I. Digital image processing for aggregate orientation in asphalt concrete mixtures [J]. Can. J. Civ. Eng.,1996,23:480～489.
[49]Masad E., Muhunthan B., Shashidhar N.et al. Quantifying Laboratory Compaction Effects on the Internal Structure of Asphalt Concerte [A].TRB [C] 1998
[50]Mora, C. F., Kwan, A.K.H., Chan, H.C.. Particle size distribution analysis of coarse aggregate using digital image processing [J]. Cement and Concrete Research,1998,28(6):921～932.
[51]C.F.Mora, A.K.H.Kwan, Sphericity, shape factor and convexity measurement of aggregate for concrete using digital image processing [J].Cement and concrete Research 30(2000) 351～358.
[52]Kwan, A.K.H., Mora, C. F., Chan, H.C.. Particle shape analysis of coarse aggregate using digital image processing [J].Cement and Concrete Research,1999,29:1403～1410.
[53]Wang, L. B., Frost, J. D., Mohammad, L., Pang, T. Y. Three-Dimensional Aggregate Evaluation Using X-ray Tomography Imaging [C]. Transportation Research Record 2002 AnnualMeeting,2002.
[54]Wang, L. B., Forst, J. D.,Shashidhar N. Microstructure study of westrack mixtures from X-ray Tomography Images [A]. Transportation Research Board [C], WashingtonDC,2001.
[55]Masad E, Button J. Implications of experimental measurements and analyses of the internal structure of HMA [A]. Transportation Research Board [C], WashingtonDC,2004.
[56]] ChenJ.-S., Liao M.-C. Evaluation of intemal resistance in hot-mix asphalt (HMA) concrete [J]. Construction and Bulilding Materials.2002 16.
[57]张婧娜.基于数字图像处理技术的沥青混合料微观结构分析方法研究[D]博士学位论文同济大学2000.
[58]张肖宁,李智,虞将苗.沥青混合料的体积组成及其数字图像处理技术[J].华南理工大学学报(自然科学版),2002,30(11)：113-215.
[59]李晓军,张肖宁.CT技术在沥青胶结颗粒材料内部结构分析中的应用[J].公路交通科技.2005(1).
[60]李智.基于数字图像处理技术的沥青混合料体积组成特性分析[D].博士学位论文
[61]ChenJ.-S., Liao M.-C. Evaluation of intemal resistance in hot-mix asphalt (HMA) concrete [J]. Construction and Bulilding Materials.2002,16.
[62]Wang Duan-yi, Li wei-jie, Zhang Xiao-ning..Evaluation of surface Segregation of Asphalt Pavement by using digital image Technique [J]. Journal of South China University of Technology.2005 33(1):16～20.
[63]杨新华,王习武,陈传尧,蒙培生.用图像处理技术实现沥青混合料有限元建模[J].中南公路工程,2005,30(3)：5-7.
[64]虞将苗,李晓军,王端宜,张肖宁.基于计算机层析识别的沥青混合料有限元模型[J].长安大学学报(自然科学版),2006,26(1)：16-19.
[65]陈沙,岳中琦,谭国焕.基于数字图像的非均质岩土工程材料的数值分析方法[J].岩土工程学报.2005,27(8)：956-963.
[66]岳中琦,陈沙,郑宏等,岩土工程材料的数字图像有限元分析[J].岩石力学与工程学报.2004,23(6)：889-897.
[67]陆秀峰,刘西拉,覃维祖.通过混凝土二维截面推测骨料粒径分布[J].岩石力学与工程学报,2005,24(17)：3107-3112.
[68]Bentz, D. P.. Three-dimensional computer simulation of Portland cement hydration and microstructure development [J]. Journal of the American Ceramic Society,1997,80(1):3～21.
[69]Ammouche, A., Breysse, D., Hornain, H., Didry, O., Marchand, J.. A new image analysis technique for the quantitative assessment of microcracks in cement-based materials [J]. Cement and Concrete Research,2000,3:25～35.
[70]Ammouche, A., Riss, J., Breysse, D., Marchand, J.. Image analysis for the automated study ofmicrocracks in concrete [J].Cement & Concrete Composites,2001,23:267～278.
[71]Dequiedt, A.-S., Coster, M., Chermant, L., Chermant, J.L.. Study of phase dispersion in concrete by image analysis [J]. Cement& Concrete Composites,2001,23:215～226.
[72]Dequiedt, A.-S., Coster, M., Chermant, L., Chermant, J.L.. Distances between air-voids in concrete by automatic methods [J]. Cement & Concrete Composites,2001,23:247～254.
[73]Amo, D.G., Perez, B.C.. Diagnosis of the alkali-silica reactivity potential by means of digital image analysis of aggregate thin sections [J]. Cement and Concrete Research,2001,31:1449～1454.
[74]Diamond, S.. Considerations in image analysis as applied to investigations of the ITZ in concrete [J]. Cement & Concrete Composites,2001,23:171～178.
[75]Diamond, S., Huang, J.. The ITZ in concrete-a different view based on image analysis and SEM observations [J]. Cement & Concrete Composites,2001,23:179～188.
[76]Mouret, M., Ringot, E., Bascou,l A.. Image analysis:a tool for the characterization for hydration of cement in concrete-metrological aspects of magnification on measurement [J]. Cement & Concrete Composites,2001,23:201～206.
[77]Marinon,i N., Pavese, A., Fo,i M.. Characterization of mortar morphology in thin sections by digital image processing [J]. Cement and Concrete Research,2005,35:1613-1619.
[78]Mertens, G., Elsen, J.. Use of computer assisted image analysis for the determination of the grain-size distribution of sands used in mortars [J]. Cement and Concrete Research,2006,36:1453～1459.
[79]S,, E.N., Keane, D.T.. X-ray microtomographic studies of pore structure and permeability in portland cement concrete [J].Materials and Structures,2006,39:611～620.
[80]王宝庭,徐道远,宋玉普.数字图像处理技术在混凝土研究中的应用[J].河海大学学报,1999,27(4)：60～63.
[81]陆秀峰,刘西拉,覃维祖.从混凝土二维截面推测骨料粒径分布[J].岩石力学与工程学报,2005,24(17)：3107～3112.
[82]刘清元,谈桥.基于图像处理的混凝土裂缝的检测[J].武汉理工大学学报,2005,27(4)：69～71.
[83]Herman G T and Liu H K. Three-Dimensional Display of Human organs from Computed Tomograms. Computer Graphies Image Processing.1979. Vol.9
[84]Lorensen W E and Cline H E. Marehing Cubes:A High Resolution 3D Surface Construction Algorithm. Computer Graphies 1987.Vol.21.No.4.163～169
[85]Cline H E and Lorensen W E. Two Algorithms for the 3D Reconstruction of Tomograms. Medical Physics,1988, Vol.15, No.3,225～233.
[86]Keppel E. Approximating Complex Surface by Triangulation of Contour Lines. IBM J. Research and Development.1975. Vol.19
[87]Kehtarnavaz N and de Figueiredo R J P.A Framework for Surface Reconstruction from 3D Contours. Computer Vision Graphies Image Processing,1988, Vol.42
[88]David C.Kay等著.柏东等译.图形图像文件格式大全[M].学苑出版社.1994
[89]章毓晋.图像分割[M].科学出版社.2001
[90]韩思奇,王蕾.图像分割的阐值法综述[J].系统工程与电子技术.2002,6：91-94
[91]贺兴华等.MATLAB7.x图像处理[M].人民邮电出版社.2006
[92]周儒荣.逆向工程与快速原型制造[J].计算机辅助设计与制造,2000,15(4)：299-301
[93]陈琼.三维有限元建模方法的研究现状.口腔医学[J].2006年4月,第26卷第2期.
[94]于力牛.基于实体模型的牙领组织三维有限元建模问题探讨[J].机械设计与研究.2002年4月,第18卷第2期.
[95]陈功.基于逆向工程的医学器官有限元建模方法[J].机械工程学报.200642(1),227～231.
[96]Wittmann F H, Roelfstra P E, Sadouki H. Simulation and analysis of composite structures [J]. Mater. Sci. Engng.,1984,68:239～248
[97]王宗敏,邱志章.混凝土细观随机骨料结构与有限元剖分[J].计算力学学报,2005,22(6)：728～732.
[98]高政国,刘光廷.三维凸型混凝土骨料随机投放算法[J].清华大学学报.2003,43(8)：1120～1123.
[99]孙立国.三级配(全级配)混凝土骨料形状数值模拟及其应用：(硕士学位论文).南京：河海大学,2005.
[100]杜成斌,孙立国.任意形状混凝土骨料的数值模拟及应用[J].水利学报,2006,37(6)：662～667.
[101]李运成,马怀发,陈厚群.混凝土随机凸多面体骨料模型生成及细观有限元剖分[J].水利学报,2006,37(5)：588～592.
[102]Bazant,Z, P, Tabbara, M, R, Random particle models for fracture of aggregate of fiber composites[J]. Journal of Engineering Mechanics, ASCE,1990,116(8):1686～1705.
[103]王宝庭,宋玉普,张燕坤.基于刚体—弹簧模型的混凝土微裂纹行为的模拟[J].工程力学,1990,16(2)：140～144.
[104]邢纪波,俞良群,王永嘉.三维梁—颗粒模型与岩石材料细观力学行为的模拟[J].岩石力学与工程学报,1999,16(6)：627～450.
[105]刘光延,王宗敏.用随机骨料模型数值模拟混凝土材料的断裂[J].清华大学学报,1996,14(2)：84～89.
[106]于庆磊,唐春安,唐世斌.基于数字图像的岩石非均匀性表征技术及初步应用[J].岩石力学与工程学报,2007,26(3)：551～558.
[107]Mehta, P. K. Concrete Structure, Properties and Materials [M]. Indiana Elsevier Applied Science, USA.1986.
[108]李晓军,张金夫,刘凯年,张肖宁.基于CT图像处理技术的岩土材料的有限元模型[J].2006,27(8)：1331～1334.
[109]柏巍,彭刚,戚永乐等.基于CT图像的混凝土细观结构的有限元重建[J].混凝土,2008,2：63～69.
[110]李悦溪.人体胃部三维有限元模型的建立[D].2007,浙江大学硕士学位论文.
[111]潘宏.踝关节三维有限元模型的建立和临床应用[D].2004,安徽医科大学硕士学位论文.
[112]张少峰,孙滢滢,周冰等.利用Matlab和Pro/E软件辅助建立桩核冠的三维有限元模型[J].口腔医学研究,2006,22(3)：267～270
[113]Keneth R C.数字图像处理[M].北京：电子工业出版社,1993.
[114]Hu M K. Visual Pattern Recognition by Moment Invariants [J]. IEEE Trans on Information Theory, 1962, (8):179～187.
[117]黄碧霞.体视学与图像分析技术在沥青混合料级配分析中的应用[D].2007,西南交通大学硕士论文.
[115]蔡元龙.模式识别[M].西安：电子科技大学出版社,1999.
[116]胡江萍.混凝土集料的形状描述[D].国外建材科技,2006,27(6)：17～20
[117]Bowman, E.T., Soga, K., Drummond, T.W.. Particle shapecharacterization using Fourier analysis [J]. CUED/D-Soils/TR315,2000
[118]Kim, H., Haas, C.T., Rauch, A. F., Browne, C.. Wavelet-based three-dimensional descriptors of aggregate particles [J]. Transportation Research Record,2002,1787:109～116.
[119]Erdogan, S. T., Quiroga, P. N., Fowler, D.W., Saleh, H.A., Livingston, R. A., Garbocz,i E. J., Ketcham, P. M.,Hagedorn, J.G, Satterfield, S.G.. Three-dimensional shape analysis of coarse aggregates: new techniques for and preliminary results on several different coarse aggregates and reference rocks [J]. Cement and Concrete Research,2006,36:1619-1627.
[120]张兴平,耿国华,周明全.一种基于面积误差的多边形逼近算法[J].微机发展,2004,14(12)：120-122.
[121]Saykol E, Gulesir G, Gudukbay U, et al. Akinematics-based method for polygon approximation [J].Advances in Information System(ADVIS'2002),2002,2457:186-194.
[122]章毓晋.图像处理和分析[M].北京：清华大学出版社,2000：220-222.
[123]樊宏斌.计算机辅助颅骨面貌复原技术的研究与实现[D].西安：西北大学,2002：20-22.
[124]吴中海,张行功,叶澄清,等.一个适合特征计算的多边形逼近算法[J].计算机学报,1997,20(12)：1129-1132.
[125]郑娅娜.混凝土破坏过程的三维细观数值模拟与CT试验验证：硕士学位论文[D].西安：西安理工大学,2005,3
[126]田威.混凝土破坏过程的三维细观数值模拟与CT试验验证：硕士学位论文[D].西安：西安理工大学,2006,3
[127]梁昕宇.数值混凝土模型的改进及其细观力学特性研究[D].西安：西安理工大学,2008,3