外文资料翻译--分形维数与沥青混凝土力学性能之间的关系

中文 1740 字 毕业设计 外文资料翻译 题 目 分形维数与沥青混凝土 力学性能之间的关系 学 院 土木建筑 专 业 土木工程 班 级 土木 0803 学 生 学 号 指导教师 二 一 二 年 三 月 六 日 The Relationship between the Fractal Dimension and Mechanical Properties of Asphalt Concrete Seracettin Arasan 1 , Engin Yener 2 , Fatih Hattatoglu 3 , Suat Akbulut 4 , Sinan Hinislioglu 5 1, 3, 4, 5-Ataturk University, Engineering Faculty, Department of Civil Engineering ,25240 Erzurum, Turkey 2-Bayburt University, Department of Civil Engineering, Bayburt, Turkey .tr ABSTRACT The importance of the shape of aggregate particles on their mechanical behavior is well recognized. In asphalt concrete, the shape of aggregate particles affects the durability, workability, shear resistance, tensile strength, stiffness, fatigue response, and optimum binder content of the mixture. Due to their irregularity, the shape of aggregates is not accurately described by Euclidian geometry. However, fractal theory uses the concept of fractal dimension, DR, as a way to describe the shape of aggregates. This paper describes a study of the influence of fractal dimension on mechanical properties of asphalt concrete.The flow of asphalt concrete decreases and Marshall Stability increases when the fractal dimension of aggregate increases Keywords: Fractal dimension, asphalt concrete, Marshall Stability, flow, aggregate 1. Introduction The importance of the shape of aggregate particles on their mechanical behavior is also well recognized. In asphalt concrete, the shape of aggregate particles affects the durability, workability, shear resistance, tensile strength, stiffness, fatigue response, and optimum binder content of the mixture 1. The successful quantification of aggregate geometric irregularities is essential for understanding their effects on pavement performance and for selecting aggregates to produce pavements of adequate quality 2. Aggregate morphological characteristics are very complex and cannot be characterized adequately by any single test. As a result, conflicting results have been reported on how aggregate shape influences the quality of HMA mixtures 3-9. Due to their irregularity, the shape of aggregates is not accurately described by Euclidian geometry. Fractals are relatively new mathematical concept for describing the geometry of irregularly shaped objects in terms of frictional numbers rather than integer. The concept of fractals introduced by Mandelbrot 10, which has the shape formed in nature, has been usually analyzed using Euclidian geometry. The key parameter for fractal - 1 - analysis is the fractal dimension, which is a real noninteger number, differing from the more familiar Euclidean or topological dimension. The fractal dimension for a line of any shape varies between one and two, and for a surface between two and three. Fractaltheory uses the concept of fractal dimension, DR, as a way to describe the shape of aggregates. In recent years, fractal geometry techniques have found widespread applications in many disciplines, including medicine, biology, geography, meteorology, manufacturing, and material science. Relatively, there have been a few applications of fractal geometry in civil engineering. Some studies have been devoted to developing procedures to determine the particle fractal dimensions 11-17. Others have focused on the effect of fractal dimension of aggregate on engineering properties of soils 18, 19 and asphalt concrete 20, 21. However, there is no comprehensive study that investigated the effect of aggregate fractal dimension to the Marshall stability, flow, and Marshall Quotient (MQ). Consequently, the present study was undertaken to verify whether there is a relationship between the fractal dimension (DR) and the mechanical properties of asphalt concrete. 2. Materials and Methods The bitumen used was AC-20 bitumen. Crushed Basalt was used as the aggregate material. A typical heavy traffic gradation for hot mix asphalts (HMA), designated as Type I in the Turkish State Highway Specifications, and was selected. The Marshall stability and flow tests were carried out following the procedure of the Test Method for Resistance of Plastic Flow of Bituminous Mixtures Using Marshall Apparatus in ASTM D1559. The imaging system used by the authors consists of a Nikon D80 Camera and Micro 60 mm objective manufactured by Nikon. ImageJ was used as the image analysis program. The other properties of used materials test procedures, imaging system and image processing steps were also detailed in Arasan et al. 22. Additionally, fractal dimension of aggregates was calculated with areaperimeter method 16. 3. Correlation between fractal dimension and mechanical properties The correlation between fractal dimension of aggregate and flow, Marshall Stability, and MQ of asphalt concrete are presented in Figure1, 2, and 3, respectively. It could be seen that the flow decreased as the fractal dimension increased (Figure1). On the other hand, since fractal dimension has a minimum value of 1 for a circle and larger values longer or thinner shapes, or aggregate having rough edges, it can be concluded that approximation of the shape of aggregates to sphere or smooth aggregate surfaces resulted in bigger flow values. - 2 - Figure1: The correlation between fractal dimension and flow - 3 - Figure 2: The correlation between fractal dimension and Marshall Stability Figure 3: The correlation between fractal dimension and MQ - 4 - A linear relationship is found between the fractal dimension and Marshall Stability. Similarly, Figure3 shows that Marshall Quotient increases with increasing fractal dimension. It is an expected result since higher fractal dimension values represent higher aggregate surface irregularities 14-16,and it is well known that increasing aggregate irregularities increases stability. Similarly, Ishai and Gellber 23 related that HMA stability to geometric irregularities in aggregate particles using the packing volume concept developed by Tons and Goetz 24. They found a significant increase in asphalt mix stability with increasing geometric irregularities of the aggregate particles 23. 4. Conclusions The present study was undertaken to investigate the effect of fractal dimension on mechanical properties of asphalt concrete. The test results indicated that there is a strong correlation between fractal dimension of coarse aggregates and mechanical properties of asphalt concrete. Hence, it may be said that the fractal dimension of aggregates is used for determination of mechanical properties of asphalt concrete. References 1. Kuo CY, Frost JD, Lai JS, Wang LB. ThreeDimensional Image Analysis ofAggregate Particles from Orthogonal Projections. Transportation ResearchRecord 1526, National Research Council Washington DC 1996 pp. 98-103. 2. Topal T, Sengoz B. Determination of fine aggregate angularity in relation with the resistance to rutting of hotmix asphalt. Construction and Building Materials , 200519:155163 3. Shklarsky E, Livneh M. The Use of Gravels for Bituminous Mixtures. In:Proceedings of The Association of Asphalt Paving Technologists 1964 Vol. 33, pp. 2365. 4. Li MC, Kett I. Influence of Coarse Aggregate Shape on the Strength of AsphaltConcrete Mixtures. Highway Research Record 1967 178: pp. 93106. 5. Stephens JE, Sinha KC. Influence of Aggregate Shape on Bituminous MixCharacter. Journal of The Association of Asphalt Paving Technologists 1978 Vol.47, pp. 434456. 6. Kalcheff IV, Tunnicliff DG. Effects of Crushed Stone Aggregate Size and Shapeon Properties of Asphalt Concrete. In: Proceedings of Association of Asphalt Paving Technologists 1982 Vol. 51: pp. 453483. 7. Huber GA, Heiman GH. Effect of Asphalt Concrete Parameters on RuttingPerformance: a Field Investigation. In: Proceedings of The Association of AsphaltPaving Technologists 1987 Vol. 56:3361. 8. Krutz NC, Sebaaly PE. Effect of Aggregate Gradation on Permanent Deformation of Asphaltic Concrete. In: Proceedings of The Association of Asphalt Paving Technologists 1993 Vol. 62, pp. 450473. - 5 - 9. Oduroh PK, Mahboub KC, Anderson RM. Flat and Elongated Aggregates inSuperpave Regime. Journal of Materials in Civil Engineering 2000 Vol. 12, pp.124130. 10. Mandelbort, B.B., (1977). Fractals form, change and dimension. Freeman, SanFrancisco, p. 273. 11. Kaye, B.H., (1978). Specification of the ruggedness and/or texture of a fine particle profile by its fractal dimension. Powder Technology, 21, 116. 12. Kennedy, S.K., Lin, W.H.,(1992). A comparison of Fourier and fractaltechniques in the analysis of closed forms. J. Sedimentary Petrology 62 (5), 842-848. 13. Hoyez, B., (1994). The roughness of sand grains: an application of Fourieranalysis and of fractal dimension. Ann. Soc. Gol. du Nord, v.3, 2me srie, p.7383. (In French). 14. Vallejo, L.E., (1995). Fractal analysis of granular materials. Geotechnique, 45,159-163. 15. Vallejo, L.E., Zhou, Y., (1995). The relationship between the fractal dimensionand Krumbeins roundness number. Soils and Foundations, 35 (1), 163-167. 16. Hyslip, J.P., Vallejo, L.E., (1997). Fractal analysis of roughness and size distribution of granular materials. Engineering Geology, 48: 231-244. 17. Akbulut, S., (2002). Fractal Dimensioning of sand grains using image analysis system. Pamukkale University Journal of Engineering Science, 8(3): 329-334. 18. Gori, U., Mari, M., (2001). The correlation between the fractal dimension and internal friction angle of different granular materials, Soils and Foundations, Vol.41(3)41723. 19. Xu, Y. F., Sun, D. A., (2005). Correlation of surface fractal dimension with frictional angle at critical state of sands, Geotechnique, 55 (9), 691-695. 20. Peng, Y., Sun, L., Wang, Y., Huang, Z., 2007. Fractal characteristicsof gradedaggregate in asphalt Mixture. Huazhong Keji Daxue Xuebao (Ziran Kexue Ban)/Journal of Huazhong University of Science and Technology (NaturalScience Edition), 35 (12): 80-82. 21. Yang, R., Xu, Zhihong, (2007). Relationship between fractal dimension and road performance of densegradation asphalt mixture. Tumu Gongcheng Xuebao/China Civil Engineering Journal, 40 (3): 98-103. 22. Arasan, S., Yener, E., Hattatoglu, F., Hinislioglu, S., Akbulut, S., 2010. The Correlation between Shape of Aggregate and Mechanical Properties of Asphalt Concrete: Digital Image Processing Approach (under review). 23. Ishai I, Gellber H. Effect of geometric irregularity of aggregates on the properties and behavior of asphalt concrete. In: Proceedings Association of Asphalt Paving Technologists 1982 51: 494-521. 24. Tons E, Goetz WH. Packing volume concepts for aggregates. Highway Research Record 236, Transportation Research Board, National Research Council,Washington DC 1968 79-96. - 6 - InternationalJournalofCivilAndStructuralEngineering，2010,1(2):165-170. 分形维数与沥青混凝土 力学性能之间的关系 Seracettin Arasan 1 , Engin Yener 2 , Fatih Hattatoglu 3 , Suat Akbulut 4 , Sinan Hinislioglu 5 1、 3、 4、 5阿塔图克大学工程学院、土木工程部门 ,25240处军营 ,土耳其 2 Bayburt大学土木工程部门 ,Bayburt, 土耳其 .tr 摘 要 聚合粒子的形状对 它们力学行为的重要性已经被 很好的认可了。 在沥青混凝土中， 骨料颗粒的形状影响耐久性 ,施工 性 能， 剪 切强度，抗拉强度，刚度，疲劳 反应 以及 混合物 的最优粘合性。 由于他 们的违规 操作 ,骨料形状 并没有被 欧式几何 学理论 准确地描述。然而 ,分形理论 使用分形维数 的概念 ,即 速度三角形定位法 ,作为一种描述聚合物形状的方式 。 这方面的论文详细介绍了关于分形维数能够 影响沥青混凝土的力学性能 的 研究 。 研究证明当分形维度 增长 时会引起 沥青混凝土的流动 性 减少和马歇尔稳定度增加。 关键词 分 形维数，沥青混凝土，马歇尔稳定度，流动性， 骨料 1 介绍 聚合粒子的形状对 它们力学 行为的重要性也已经被很好的认可了。 在沥青 凝土中，骨料颗粒的形状影响耐久性 ,施工性能，剪切强度，抗拉强度，刚度，疲劳反应以及混合物的最优粘合性 1。 大量的几何不规则颗粒的成功聚合 对 理解它们 对 路面性能 的影响 和 选择骨料颗粒来 生产具有充足质量的路面都是十分必要的 2。 聚合物的形态特征非常复杂 ,不能由任何一个充分的测试来表征。 最终 ,关于 骨料颗粒的形状如何影响热拌沥青混凝土混合物质量 的 相互矛盾的结果已经被报道了 39。 由于他们的违规操作 ,骨料形状并没有被欧式几何学理论准确地描述。 分形理论是用相对较新的数学概念 来描述几何不规则形状的物体并对其进行摩擦编号而不是整数编号。 分形的概念由曼德勃罗引入 10，它在本质上有形状成形 ,通常用欧式 几何来分析。分形维数是对分形现象进行 分析的关键参数，是不同于 更熟悉的 欧几里德的几何学维数或拓扑维数的一种真正的具有不完整性号码。分形维数作为具有所有形 - 7 - 状的一行线在一维与二维之间变化，在表面上在二维与三维之间变化。 分形理论使用分形维数的概念 ,即速度三角形定位法 ,作为一种描述聚合物形状的方式。 近年来 ,分形几何技术 被 广泛应用在许多学科 ,包括医学、 生物学、地理、气象、制造材料科学。相对而言 ,已经 有一些 分形几何 的 理论 应用于 土建工程 方面 。一些研究已经致力于 通过发展程序来确定颗粒分形维 数 1117。 别的研究 都聚焦在 具有 分形维 数的 骨料 颗粒对 土壤 的工程性质 18、 19和沥青混凝土 的影响上 20, 21。 然而 ,并没有全面综合的研究来调查分形维数对 马歇尔稳定度、流 动性 、马歇尔智商 (MQ)的影响 。因此 ,本研究着手于进行验证在分形维数 (DR)与 沥青混凝土的力学性能 之间是否有关系 。 2 材料和方法 沥青使用的是 AC20的沥青。压碎的玄武岩作为聚合物的骨料颗粒 材料 。选取了 一个经常交通拥挤的 被土耳其国道技术规范 指定为 i型的热拌沥青的路面层次。执行 马歇尔 稳定性和流动性测试程序的测试方法是使用美国 ASTM D1559标准下的测试沥青混合物的电阻塑流动性的马歇尔仪器进行测试。 作者所采用的 成像系统由一个 D80尼康照相机 和 有 60微 米 物镜镜头的 尼康相机 组成 。 ImageJ作为图像分析程序。 所用的材料的其它性能的测试程序 ,成像系统 ， 图像处理步骤及其它的也详细的在 Arasan中记录了 22。此外 ,聚合物骨料颗粒的分形维数也使用 areaperimeter方法计算出来了 3 分形维数与力 学性能之间的关联 骨料颗粒的分形维数分别和流动性 ,马歇尔稳定度 ,及 马歇尔系数 沥青混凝土的关联体现在下面三个表格 Figure1、 2和 3上。在表格 1中我们可以看到随着分形维数的增加流动性会逐渐减少。另一方面 ,由于分形维数的最小值呈现出一个圆圈的形状 ,大的数值呈现出长而细的较薄的形状 ,或者总有粗糙的边缘 ,结果表明骨料颗粒的形状近似球形，或光滑的骨料球体表面导致更大的流动性数值。 - 8 - 表格 1：分形维数与流动性之间的关系 表格 2：分形维数与马歇尔稳定度之间的关系 - 9 - 表格 3：分形维数与马歇尔 系数之间的关系 一个存在于分形维数与马歇尔稳定度之间的线性关系被发现了。同样 ,图 3显示分形维数随着马歇尔系数的增加而增加。它是一个预期的结果，因为更高的分形维数值代表更高骨料颗粒表面的不规则性 1416,众所周知 ,增加骨料颗粒的不规则性能够增加稳定度。同样的 ,Ishai23和 Gellber认为热拌沥青混合物的稳定度与使用由Tons and Goetz 24开发出的概念的聚合物骨料颗粒的几何不规则性相关联。他们发现增加沥青混合物的稳定度能够显著提高混合物颗粒的几何不规则性 23。 4 结论 本课题旨在研究分形维数对沥青混凝土的力学性能的影响。试验结果表明 ,聚合物的粗糙骨料颗粒的分形维数与沥青混凝土的力学性能之间有较强的联系。因此 ,可以这样说 ,聚合物骨料颗粒的分形维数是用于检测沥青混凝土的力学特性的。 - 10 - 参考书目 1。郭 CY,JD、莱卡 JS王建民 。三维图像分析的骨料颗粒从正交的预测。运输研究 创记录的 1526,国家研究委员会 1996年华盛顿特区 98103页。 2。 Topal T、 b Sengoz测定细骨料 angularity在跟他的关系 hotmix抗车辙的沥青。建设和建筑材料 ,200519:155 - 163 3。 Shklarsky E,Livneh m .的使用对沥青碎石。 在 :诉讼协会的沥青摊铺技术人员1964第 23 -33 页。 4。李 MC,我的 Kett影响粗骨料形状对沥青的力量混凝土的混合物。公路研究记录1967178:93 - 106页。 5。史蒂芬杰 ,KC。影响微创沥青混合料形状性格。协会的杂志沥青摊铺技术人员 1978卷。 47),页 434 - 456。 6。 Kalcheff IV,Tunnicliff DG实验。 影响碎石骨料的大小和