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

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1、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 MechanicalProperties of Asphalt ConcreteSeracettin Arasan 1 , Engin Yener 2 , Fatih Hattatoglu 3 , Suat Akbulut 4 , Sinan Hinislioglu 51, 3, 4, 5-Atatur

2、k University, Engineering Faculty, Department of Civil Engineering ,25240 Erzurum, Turkey2-Bayburt University, Department of Civil Engineering, Bayburt, Turkeyarasanatauni.edu.tr ABSTRACTThe importance of the shape of aggregate particles on their mechanical behavior is well recognized. In asphalt co

3、ncrete, 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, fra

4、ctal theory uses the concept offractal 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

5、 dimension of aggregate increasesKeywords: Fractal dimension, asphalt concrete, Marshall Stability, flow, aggregate1. IntroductionThe 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

6、 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 pavementperformance and for selecting aggregates

7、 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 irregul

8、arity, 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

9、has the shape formed in nature, has been usually analyzed using Euclidian geometry. The key parameter for fractal analysis is the fractal dimension, which is a real noninteger number, differing from themore familiar Euclidean or topological dimension. The fractal dimension for a line of any shape va

10、ries 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, g

11、eography, 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 fracta

12、l dimension of aggregate on engineering properties of soils 18, 19 and asphalt concrete20, 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 underta

13、ken to verify whether there is a relationship between the fractal dimension (DR) and the mechanical properties of asphalt concrete.2. Materials and MethodsThe bitumen used was AC-20 bitumen. Crushed Basalt was used as the aggregatematerial. A typical heavy traffic gradation for hot mix asphalts (HMA

14、), 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 us

15、ed 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, fra

16、ctal dimension of aggregates was calculated with areaperimeter method 16.3. Correlation between fractal dimension and mechanical propertiesThe correlation between fractal dimension of aggregate and flow, Marshall Stability, and MQ of asphalt concrete are presented in Figure1, 2, and 3, respectively.

17、 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

18、 aggregates to sphere or smooth aggregate surfaces resulted in bigger flow values.Figure1: The correlation between fractal dimension and flowFigure 2: The correlation between fractal dimension and Marshall StabilityFigure 3: The correlation between fractal dimension and MQA linear relationship is fo

19、und 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 incr

20、easing aggregate irregularities increases stability. Similarly, Ishai and Gellber 23 related that HMA stability to geometric irregularities in aggregate particles using the packing volumeconcept developed by Tons and Goetz 24. They found a significant increase in asphalt mix stability with increasin

21、g geometric irregularities of the aggregate particles 23.4. ConclusionsThe 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 aggre

22、gates 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.References1. Kuo CY, Frost JD, Lai JS, Wang LB. ThreeDimensional Image Analysis ofAggregate Particles from Orthog

23、onal 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 , 200519:1551633. Shklarsky

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31、ize 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 di

32、mension 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., Huan

33、g, Z., 2007. Fractal characteristicsof gradedaggregate in asphalt Mixture. Huazhong Keji Daxue Xuebao (Ziran KexueBan)/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

34、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., 2021. The Correlation between Shape of Aggregate and Mechanical Properties of Asphalt Concrete: Digital Image

35、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. Hig

36、hway ResearchRecord 236, Transportation Research Board, National Research Council,Washington DC 1968 79-96. InternationalJournalofCivilAndStructuralEngineering，2021,1(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 51、3、4、5阿

37、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 arasanatauni.edu.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，疲劳反响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

38、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，疲劳反响以及混合物的最优粘合性1。大量的几何不规那么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

39、学概念来描述几何不规那么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状的一行线在一维与二维之间变化，在外表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开展程序来确定颗粒

40、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标准指定为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

41、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表达在下面三个表格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,结果说明骨料颗粒的形状近似球形

42、，或光滑的骨料球体外表导致更大的流动性数值。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外表的不规那么性1416,众所周知,增加骨料颗粒的不规那么性能够增加稳定度。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那么性相关联。他们发现增加沥青混合物的稳定度能够显著提高混合物

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