基于路面实测值建立沥青路面平整度数学模型
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摘要
沥青路面因具有表面平整、行车舒适等诸多优点,被广泛应用到高速公路建设中。但是,随着交通量的不断增长,车辆的渠化行驶以及超载的加剧,使得沥青路面产生车辙、推移、拥抱等主要损坏形式。这不仅影响行车速度和危及行车安全,而且大大降低了高等级道路的使用性能。路面的使用性能的变差则主要表现在路面平整度变差。而作为路面使用性能评价的重要指标之一,路面平整度的好坏将影响到到诸多方面。在研究的过程中,能否将路面平整度相关问题转化成数学问题,对路面平整性的随机情况进行总结、分析,寻找其规律性,建立相关的数学模型,则是研究路面平整度有关问题的关键所在。本文则主要探寻研究平整度的可行的数学方法,建立较为精确平整度数学模型,从而为后期研究车路耦合模型,研究路面性能打下基础。
本文在一开始概述了平整度的相关知识,借助国际平整度指数给出表征平整度的评价指标间的相关关系,使得各个指标间可以通过数学方式相互转化。然后,本文用正弦函数表征路面波,得出关于路面平整度标准差与路面波形参数的表达式。对于路面平整度和路面波形参数的两个参数,假定其中一个,通过拉格朗日插值,回归分析等数学手段,得出另外两个参数的相关关系的表达式,建立起路面平整度的数学模型。此外,由于课题组曾对重庆市周边高速公路进行过路面平整度指标的实测,通过在论文中所提出处理数据的数学方法,可以将平整度指标数据进行优化处理,然后可以借助之前所得的相关关系,可得到表征路面状态的一组数据。在处理平整度指标数据之前,提出了借助测量学中的中误差概念对其进行预处理,将数据优化。然后,在处理数据的过程中提出了一个置信误差的概念将路面波化分为多段,并验证了论文提出的分段方法对比传统方法的优越性。最后通过合理的分段下平整度标准差的均值,计算出较为准确的波长值和振幅值,得出试验路段的正弦函数表达式,借助Matlab绘制出路面波正弦函数图为以后计算路面波形函数以及后期的理论研究奠定了良好的理论基础和实践基础。
The asphalt pavement is widely applied to the highway construction because of its surface smooth, driving comfort, and many other advantages. However, with the growth of traffic, driving highly channelizing of vehicles and the aggravation of overloading, there are many damage forms produced in asphalt pavement, such as rut, passage, hug and so on. This situation not only affects traffic speed and threatens driving safety,but also greatly reduces the high-grade road using performance. The worse of road using performance mainly displays in the pavement smoothness getting worse. As one of the most important indexes evaluating road using performance, pavement smoothness, good or bad, is involved in many aspects. So, it is the key to research pavement smoothness problems that transforming the related problems of pavement smoothness into math problems, summarizing and analyzing the stochastic situation of pavement smoothness to find its rule and establish its relevant mathematical model in the process of research. This paper is mainly exploring a feasible mathematical method to research pavement smoothness and establishing a comparatively accurate mathematical mode, in orderto lay the foundation of the following research about Vehicle-Road coupling model and road using performance.
At the front parts of this paper, the author summarizes the related knowledge of smoothness, and then shows the relationship among pavement smoothness indexes through the IRI, so that every index can be transformed into each other by mathematical way. Afterwards, this paper characterizes the pavement wave by sine function, drawing the expression between pavement smoothness standard deviation and pavement waveform parameters. And then,for the three indexes that two pavement waveform parameter adds pavement smoothness index,assuming one of them as known,get the relationship between another two parameters by some math method such as Lagrange interpolation or regression analysis etc. and thus establish road smoothness mathematical model. Becides, because our subject-researching-group have get the actual pavement smoothness index data from highways around Chongqing city, it can be optimized by the math method introducing in this paper for processing data, and then we can get the data of pavement waveform parameter by the relationship abtained in the front parts. Before the process of dealing with the actual pavement smoothness index data, a concept called middle-error is raised to pretreat the data to optimize data. Next, in the process, the pavement wave is divided into many sections with the concept of confidence error given in the paper, and it is proved that the methed given in the paper is better than the traditional method. In the following,with the former methed calculating the mean value of each section and getting accurate wavelength value and amplitude value. So it can be done that obtaining the final sine function expression of pavement wave from test section, and drawing the sine function curve by application of Matlab, so that it can lay the theoretical basis and practical basis for calculating pavement wave function and the later theory research.
本文在一开始概述了平整度的相关知识,借助国际平整度指数给出表征平整度的评价指标间的相关关系,使得各个指标间可以通过数学方式相互转化。然后,本文用正弦函数表征路面波,得出关于路面平整度标准差与路面波形参数的表达式。对于路面平整度和路面波形参数的两个参数,假定其中一个,通过拉格朗日插值,回归分析等数学手段,得出另外两个参数的相关关系的表达式,建立起路面平整度的数学模型。此外,由于课题组曾对重庆市周边高速公路进行过路面平整度指标的实测,通过在论文中所提出处理数据的数学方法,可以将平整度指标数据进行优化处理,然后可以借助之前所得的相关关系,可得到表征路面状态的一组数据。在处理平整度指标数据之前,提出了借助测量学中的中误差概念对其进行预处理,将数据优化。然后,在处理数据的过程中提出了一个置信误差的概念将路面波化分为多段,并验证了论文提出的分段方法对比传统方法的优越性。最后通过合理的分段下平整度标准差的均值,计算出较为准确的波长值和振幅值,得出试验路段的正弦函数表达式,借助Matlab绘制出路面波正弦函数图为以后计算路面波形函数以及后期的理论研究奠定了良好的理论基础和实践基础。
The asphalt pavement is widely applied to the highway construction because of its surface smooth, driving comfort, and many other advantages. However, with the growth of traffic, driving highly channelizing of vehicles and the aggravation of overloading, there are many damage forms produced in asphalt pavement, such as rut, passage, hug and so on. This situation not only affects traffic speed and threatens driving safety,but also greatly reduces the high-grade road using performance. The worse of road using performance mainly displays in the pavement smoothness getting worse. As one of the most important indexes evaluating road using performance, pavement smoothness, good or bad, is involved in many aspects. So, it is the key to research pavement smoothness problems that transforming the related problems of pavement smoothness into math problems, summarizing and analyzing the stochastic situation of pavement smoothness to find its rule and establish its relevant mathematical model in the process of research. This paper is mainly exploring a feasible mathematical method to research pavement smoothness and establishing a comparatively accurate mathematical mode, in orderto lay the foundation of the following research about Vehicle-Road coupling model and road using performance.
At the front parts of this paper, the author summarizes the related knowledge of smoothness, and then shows the relationship among pavement smoothness indexes through the IRI, so that every index can be transformed into each other by mathematical way. Afterwards, this paper characterizes the pavement wave by sine function, drawing the expression between pavement smoothness standard deviation and pavement waveform parameters. And then,for the three indexes that two pavement waveform parameter adds pavement smoothness index,assuming one of them as known,get the relationship between another two parameters by some math method such as Lagrange interpolation or regression analysis etc. and thus establish road smoothness mathematical model. Becides, because our subject-researching-group have get the actual pavement smoothness index data from highways around Chongqing city, it can be optimized by the math method introducing in this paper for processing data, and then we can get the data of pavement waveform parameter by the relationship abtained in the front parts. Before the process of dealing with the actual pavement smoothness index data, a concept called middle-error is raised to pretreat the data to optimize data. Next, in the process, the pavement wave is divided into many sections with the concept of confidence error given in the paper, and it is proved that the methed given in the paper is better than the traditional method. In the following,with the former methed calculating the mean value of each section and getting accurate wavelength value and amplitude value. So it can be done that obtaining the final sine function expression of pavement wave from test section, and drawing the sine function curve by application of Matlab, so that it can lay the theoretical basis and practical basis for calculating pavement wave function and the later theory research.
引文
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[2] Lu Sun,Zhang,Jessica Ruth.Modeling Indirect Statistics of Surface Roughness.Journal of Transportation Engineering.2001,127(2):105.
[3] Christoper Martin Raymond.An Investigation of Roughness Trends in Asphalt Pavement Overlays[D].Waterloo Ontario Cananda;2001.
[4] The Effect of Initial Pavement Smoothness On Long Term Roughness Progression:Some Findings from LTPP and US-LTPP Studies[R].1999.
[5] C.J.Dodds and J.D.Robson.The Description of Road Surface Roughness.Journal of Sound and Vibration,1973,31(2):175-183.
[6] Jorje Marcondes.Spectral Analysis of Highway Pavement Roughness.Journal of Transportion Engineering,ASCE,Vol.117,1992(5):540-549.
[7] Mark.B.Snyder.Predicting Acceleration in Vehicles through Road Roughness. Journal of Transportion Engineering,ASCE,Vol.118,1992(1):33-49.
[8] M.O.Al-Hunaidi and J.H.Rainer.Remedial Measure for Traffic Induced Vibration at a Residential Site.Part 1:Field tests.Canadian Acoustics/Acoustique Canandienne,19(1):3-13,1991.
[9] G.R.Watts.The Generation and Propagation of Vibration in Various Soils Produced by the Dynamic Loading of Road Pavement.Journal of Sound and Vibration,156(2):191-206,1992.
[10] G.R.Watts.The Effects of Traffic-Induced Vibration on Heritage Buildings,Further Case Studies.Research Report 207,Transport and Road Research Laboratory,1989.
[11] G.R.Watts and V.V.Krylov.Ground-Brone Vibrations Generated by Vehicles Crossing Road Humps and Speed Control Cushions.Applied Acoustics,59:221-236,2000.
[12] Karim Chatti,Doseung Lee.Development of New Profile-Based Truck Dynamic Load Index.Transportion Research Record 1806.2002:149-159.
[13] Rayya A Hassan,Kerry McManus.Assessment of Interaction between Road Roughness and Heavy Vehicles.Transportation Research Record 1819.2003:236-243.
[14]唐光武,贺学锋,颜永福.路面不平度的数字模型及计算机模拟研究[J].中国公路学报.2000,13(1):114~117.
[15] Liu Wei,T.F.Fwa,Zhao Zhe.Wavelet Analysis and Interpretation of Road Roughness.Journal of Transportation Engineering.2005,131(2):120~130.
[16]邓学钧,孙璐.车辆-地面结构系统动力学[M].北京:人民交通出版社,2000.
[17]檀润华,陈鹰等.路面对汽车激励的时域模型建立及计算机仿真[J].中国公路学报,1998,11(3):96-102.
[18]金睿臣,宋健.路面不平度的模拟与汽车非线性随机振动的研究[J].清华大学学报(自然科学版),1999,39(8):76-79.
[19]陶向华,黄晓明.车辆动荷载的频域模拟计算与分析[J].华中科技大学学报(城市科学版).2003,20(4):47-50.
[20]张湘伟,何正友.二维泊松过程的数值模拟及其在道路模型中的应用[J].重庆大学学报(自然科学版).1994,17(4):12~16.
[21]孙璐,邓学钧.平整度与机场道面谱分析[J].华东公路.1996,(2):35~39.
[22]李晓雷,韩宝坤.用小波变换分析路面不平度及振动响应[J].北京理工大学学报.2003,23(6):717~719.
[23]曲首平,张立军.路面不平度的时频小波分析[J].长春大学学报. 1999,9(1):5~8.
[24]宋永刚..路面平整度均方差指标与行车舒适性的关系研究[J].路面机械与施工技术.2005,(12):18~21.
[25]谭英.路面平整度定量控制的研究[D].西安:长安大学.2005:22~47.
[26]路面平整度评价体系及其工程应用研究报告.东南大学.2005.
[27]李套玲,孙立军,陆辉.对路面平整度概念的粗浅理解[C].上海市公路学会第五届年会学术论文集.上海:上海公路学会,2003:18-22.
[28]周晓青,孙立军,颜利.路面平整度评价发展及趋势[J].公路交通科技.2005,22(10):18-22.
[29] American Society for Testing and Materials.Terminology Relating to Traveled Surface Characteristics Annual Book of ASTM Standards.1999,Vol.03.04,E867-97: 726-730.
[30] Canadian Strategic Highway Research Program.Summary of Pavement Smoothness Specificatins in Canada and Aroud The World[R].1999.
[31]赵济海,王哲人,关朝雳.路面不平度的测量分析与应用[M];北京:北京理工大学出版社,2000:126-127,14-15.
[32]吴庆雄,陈宝春,奚灵智.路面平整度PSD和IRI评价方法比较[J].交通运输工程学报.2008,8(1).
[33]王国林,魏领军,王启唐,焦贤正.路面平整度主观评价方法及其试验验证[J].中外公路.2009,29(1):40-42.
[34]李峰.高等级公路路面平整度检测方法[J].中国科技信息,2005,(6):138—140.
[35]张明,叶巧玲,冯晓.路面平整度检测技术现状与发展[J].重庆交通大学学报(自然科学版).2007,26(4):112-114,127.
[36]张向东,闫维明,葛惠娟,刘猛.由国际平整度指数模拟路面不平度方法研究[J].公路交通科技.2009,26(4):14.
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