外文資料翻譯--分形維數(shù)與瀝青混凝土力學(xué)性能之間的關(guān)系

中文 1740 字 畢業(yè)設(shè)計 外文資料翻譯 題 目 分形維數(shù)與瀝青混凝土 力學(xué)性能之間的關(guān)系 學(xué) 院 土木建筑 專 業(yè) 土木工程 班 級 土木 0803 學(xué) 生 學(xué) 號 指導(dǎo)教師 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. 分形維數(shù)與瀝青混凝土 力學(xué)性能之間的關(guān)系 Seracettin Arasan 1 , Engin Yener 2 , Fatih Hattatoglu 3 , Suat Akbulut 4 , Sinan Hinislioglu 5 1、 3、 4、 5阿塔圖克大學(xué)工程學(xué)院、土木工程部門 ,25240處軍營 ,土耳其 2 Bayburt大學(xué)土木工程部門 ,Bayburt, 土耳其 .tr 摘 要 聚合粒子的形狀對 它們力學(xué)行為的重要性已經(jīng)被 很好的認(rèn)可了。 在瀝青混凝土中， 骨料顆粒的形狀影響耐久性 ,施工 性 能， 剪 切強(qiáng)度，抗拉強(qiáng)度，剛度，疲勞 反應(yīng) 以及 混合物 的最優(yōu)粘合性。 由于他 們的違規(guī) 操作 ,骨料形狀 并沒有被 歐式幾何 學(xué)理論 準(zhǔn)確地描述。然而 ,分形理論 使用分形維數(shù) 的概念 ,即 速度三角形定位法 ,作為一種描述聚合物形狀的方式 。 這方面的論文詳細(xì)介紹了關(guān)于分形維數(shù)能夠 影響瀝青混凝土的力學(xué)性能 的 研究 。 研究證明當(dāng)分形維度 增長 時會引起 瀝青混凝土的流動 性 減少和馬歇爾穩(wěn)定度增加。 關(guān)鍵詞 分 形維數(shù)，瀝青混凝土，馬歇爾穩(wěn)定度，流動性， 骨料 1 介紹 聚合粒子的形狀對 它們力學(xué) 行為的重要性也已經(jīng)被很好的認(rèn)可了。 在瀝青 凝土中，骨料顆粒的形狀影響耐久性 ,施工性能，剪切強(qiáng)度，抗拉強(qiáng)度，剛度，疲勞反應(yīng)以及混合物的最優(yōu)粘合性 1。 大量的幾何不規(guī)則顆粒的成功聚合 對 理解它們 對 路面性能 的影響 和 選擇骨料顆粒來 生產(chǎn)具有充足質(zhì)量的路面都是十分必要的 2。 聚合物的形態(tài)特征非常復(fù)雜 ,不能由任何一個充分的測試來表征。 最終 ,關(guān)于 骨料顆粒的形狀如何影響熱拌瀝青混凝土混合物質(zhì)量 的 相互矛盾的結(jié)果已經(jīng)被報道了 39。 由于他們的違規(guī)操作 ,骨料形狀并沒有被歐式幾何學(xué)理論準(zhǔn)確地描述。 分形理論是用相對較新的數(shù)學(xué)概念 來描述幾何不規(guī)則形狀的物體并對其進(jìn)行摩擦編號而不是整數(shù)編號。 分形的概念由曼德勃羅引入 10，它在本質(zhì)上有形狀成形 ,通常用歐式 幾何來分析。分形維數(shù)是對分形現(xiàn)象進(jìn)行 分析的關(guān)鍵參數(shù)，是不同于 更熟悉的 歐幾里德的幾何學(xué)維數(shù)或拓?fù)渚S數(shù)的一種真正的具有不完整性號碼。分形維數(shù)作為具有所有形 - 7 - 狀的一行線在一維與二維之間變化，在表面上在二維與三維之間變化。 分形理論使用分形維數(shù)的概念 ,即速度三角形定位法 ,作為一種描述聚合物形狀的方式。 近年來 ,分形幾何技術(shù) 被 廣泛應(yīng)用在許多學(xué)科 ,包括醫(yī)學(xué)、 生物學(xué)、地理、氣象、制造材料科學(xué)。相對而言 ,已經(jīng) 有一些 分形幾何 的 理論 應(yīng)用于 土建工程 方面 。一些研究已經(jīng)致力于 通過發(fā)展程序來確定顆粒分形維 數(shù) 1117。 別的研究 都聚焦在 具有 分形維 數(shù)的 骨料 顆粒對 土壤 的工程性質(zhì) 18、 19和瀝青混凝土 的影響上 20, 21。 然而 ,并沒有全面綜合的研究來調(diào)查分形維數(shù)對 馬歇爾穩(wěn)定度、流 動性 、馬歇爾智商 (MQ)的影響 。因此 ,本研究著手于進(jìn)行驗(yàn)證在分形維數(shù) (DR)與 瀝青混凝土的力學(xué)性能 之間是否有關(guān)系 。 2 材料和方法 瀝青使用的是 AC20的瀝青。壓碎的玄武巖作為聚合物的骨料顆粒 材料 。選取了 一個經(jīng)常交通擁擠的 被土耳其國道技術(shù)規(guī)范 指定為 i型的熱拌瀝青的路面層次。執(zhí)行 馬歇爾 穩(wěn)定性和流動性測試程序的測試方法是使用美國 ASTM D1559標(biāo)準(zhǔn)下的測試瀝青混合物的電阻塑流動性的馬歇爾儀器進(jìn)行測試。 作者所采用的 成像系統(tǒng)由一個 D80尼康照相機(jī) 和 有 60微 米 物鏡鏡頭的 尼康相機(jī) 組成 。 ImageJ作為圖像分析程序。 所用的材料的其它性能的測試程序 ,成像系統(tǒng) ， 圖像處理步驟及其它的也詳細(xì)的在 Arasan中記錄了 22。此外 ,聚合物骨料顆粒的分形維數(shù)也使用 areaperimeter方法計算出來了 3 分形維數(shù)與力 學(xué)性能之間的關(guān)聯(lián) 骨料顆粒的分形維數(shù)分別和流動性 ,馬歇爾穩(wěn)定度 ,及 馬歇爾系數(shù) 瀝青混凝土的關(guān)聯(lián)體現(xiàn)在下面三個表格 Figure1、 2和 3上。在表格 1中我們可以看到隨著分形維數(shù)的增加流動性會逐漸減少。另一方面 ,由于分形維數(shù)的最小值呈現(xiàn)出一個圓圈的形狀 ,大的數(shù)值呈現(xiàn)出長而細(xì)的較薄的形狀 ,或者總有粗糙的邊緣 ,結(jié)果表明骨料顆粒的形狀近似球形，或光滑的骨料球體表面導(dǎo)致更大的流動性數(shù)值。 - 8 - 表格 1：分形維數(shù)與流動性之間的關(guān)系 表格 2：分形維數(shù)與馬歇爾穩(wěn)定度之間的關(guān)系 - 9 - 表格 3：分形維數(shù)與馬歇爾 系數(shù)之間的關(guān)系 一個存在于分形維數(shù)與馬歇爾穩(wěn)定度之間的線性關(guān)系被發(fā)現(xiàn)了。同樣 ,圖 3顯示分形維數(shù)隨著馬歇爾系數(shù)的增加而增加。它是一個預(yù)期的結(jié)果，因?yàn)楦叩姆中尉S數(shù)值代表更高骨料顆粒表面的不規(guī)則性 1416,眾所周知 ,增加骨料顆粒的不規(guī)則性能夠增加穩(wěn)定度。同樣的 ,Ishai23和 Gellber認(rèn)為熱拌瀝青混合物的穩(wěn)定度與使用由Tons and Goetz 24開發(fā)出的概念的聚合物骨料顆粒的幾何不規(guī)則性相關(guān)聯(lián)。他們發(fā)現(xiàn)增加瀝青混合物的穩(wěn)定度能夠顯著提高混合物顆粒的幾何不規(guī)則性 23。 4 結(jié)論 本課題旨在研究分形維數(shù)對瀝青混凝土的力學(xué)性能的影響。試驗(yàn)結(jié)果表明 ,聚合物的粗糙骨料顆粒的分形維數(shù)與瀝青混凝土的力學(xué)性能之間有較強(qiáng)的聯(lián)系。因此 ,可以這樣說 ,聚合物骨料顆粒的分形維數(shù)是用于檢測瀝青混凝土的力學(xué)特性的。 - 10 - 參考書目 1。郭 CY,JD、萊卡 JS王建民 。三維圖像分析的骨料顆粒從正交的預(yù)測。運(yùn)輸研究 創(chuàng)記錄的 1526,國家研究委員會 1996年華盛頓特區(qū) 98103頁。 2。 Topal T、 b Sengoz測定細(xì)骨料 angularity在跟他的關(guān)系 hotmix抗車轍的瀝青。建設(shè)和建筑材料 ,200519:155 - 163 3。 Shklarsky E,Livneh m .的使用對瀝青碎石。 在 :訴訟協(xié)會的瀝青攤鋪技術(shù)人員1964第 23 -33 頁。 4。李 MC,我的 Kett影響粗骨料形狀對瀝青的力量混凝土的混合物。公路研究記錄1967178:93 - 106頁。 5。史蒂芬杰 ,KC。影響微創(chuàng)瀝青混合料形狀性格。協(xié)會的雜志瀝青攤鋪技術(shù)人員 1978卷。 47),頁 434 - 456。 6。 Kalcheff IV,Tunnicliff DG實(shí)驗(yàn)。 影響碎石骨料的大小和