基于温度与应变参数的沥青混合料动态模量依赖模型研究
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摘要
为客观表征沥青混合料的非线性黏弹性及其温度、荷载依赖性,采用法国梯形梁试验仪开展了不同应变水平、不同温度、不同加载频率下的沥青混合料二点弯拉动态模量试验。通过引入非线性算子的方法,提出了基于温度与应变参数的沥青混合料动态模量依赖模型构建方法,建立了沥青混合料动态模量主曲面表达式,利用相关系数检验和方差分析方法评价了动态模量依赖模型的可靠性。结果表明:以足尺环道沥青混合料为基础开展的梯形梁二点弯拉试验,0℃时动态模量变异系数均值约为2.5%,45℃时动态模量变异系数均值约为6.2%,10个试验温度下动态模量变异系数均值约为4%,试验方法变异水平低、误差小,具有十分良好的平行性和可靠性;所建立的基于温度与应变参数的动态模量依赖模型表达式,决定系数R~2能够达到0.99以上,F检验的P值为0,模型对试验结果的拟合效果良好,动态模量与温度、应变水平之间具有十分显著的相关性;可采用该模型描述沥青混合料弯拉动态模量,并将沥青混合料动态模量的描述模型由主曲线转变为主曲面。在路面结构分析中使用该模型,能够更加客观地反映实际路面中的非线性响应现象,有效避免了结构分析中由于模量取值不合理,所造成的计算结果失真等问题。
In order to objectively characterize the nonlinear viscoelastic behavior of asphalt mixture and its dependence on temperature and load, the two-point dynamic flexural tensile modulus test of asphalt mixture at different strain levels, temperatures and loading frequencies is carried out by using French trapezoidal beam tester. By introducing the method of nonlinear operator, the dynamic modulus dependency modeling method for asphalt mixture based on temperature and strain parameters is put forward, the expression of dynamic modulus principal surface of asphalt mixture is established, and the reliability of the dynamic modulus dependent model is evaluated by correlation coefficient test and variance analysis method. The result shows that(1) for the two-point flexural tensile test of trapezoidal beam based on asphalt mixture of full-scale test track, the mean values of dynamic modulus variation coefficient at 0 ℃ and 45 ℃ are about 2.5% and 6.2% respectively, the mean values of dynamic modulus variation coefficient at 10 test temperatures is about 4%, the variation level of the test method is low, the error is small, which has a very good parallelism and reliability;(2) for the established dynamic modulus dependent model expression based on temperature and strain parameters, the decision coefficient R~2 can reach more than 0.99, the P value of F test is 0, the fitting effect of the model on the test result is good, and there is a significant correlation of dynamic modulus with temperature and strain level;(3) the model can be used to describe the dynamic flexural tensile modulus of asphalt mixture, and the description model of the dynamic modulus can be transformed from principal curve to principal surface. In pavement structure analysis, this model can reflect the nonlinear response phenomenon in actual pavement more objectively, and can avoid the problems such as distortion of the calculation result caused by unreasonable modulus value in structural analysis effectively.
In order to objectively characterize the nonlinear viscoelastic behavior of asphalt mixture and its dependence on temperature and load, the two-point dynamic flexural tensile modulus test of asphalt mixture at different strain levels, temperatures and loading frequencies is carried out by using French trapezoidal beam tester. By introducing the method of nonlinear operator, the dynamic modulus dependency modeling method for asphalt mixture based on temperature and strain parameters is put forward, the expression of dynamic modulus principal surface of asphalt mixture is established, and the reliability of the dynamic modulus dependent model is evaluated by correlation coefficient test and variance analysis method. The result shows that(1) for the two-point flexural tensile test of trapezoidal beam based on asphalt mixture of full-scale test track, the mean values of dynamic modulus variation coefficient at 0 ℃ and 45 ℃ are about 2.5% and 6.2% respectively, the mean values of dynamic modulus variation coefficient at 10 test temperatures is about 4%, the variation level of the test method is low, the error is small, which has a very good parallelism and reliability;(2) for the established dynamic modulus dependent model expression based on temperature and strain parameters, the decision coefficient R~2 can reach more than 0.99, the P value of F test is 0, the fitting effect of the model on the test result is good, and there is a significant correlation of dynamic modulus with temperature and strain level;(3) the model can be used to describe the dynamic flexural tensile modulus of asphalt mixture, and the description model of the dynamic modulus can be transformed from principal curve to principal surface. In pavement structure analysis, this model can reflect the nonlinear response phenomenon in actual pavement more objectively, and can avoid the problems such as distortion of the calculation result caused by unreasonable modulus value in structural analysis effectively.
引文
[1]姚祖康.沥青路面结构设计[M].北京:人民交通出版社,2011.YAO Zu-kang.Structural Design of Asphalt Pavements[M].Beijing:China Communications Press,2011.
[2]凌天清,王士杰,许志鸿.考虑材料非线性性能的沥青路面位移与应力分析[J].中国公路学报,1999,12(1):1-6.LING Tian-qing,WANG Shi-jie,XU Zhi-hong.Study of Nonlinear Analysis of Flexible Pavements[J].China Journal of Highway and Transport,1999,12(1):1-6.
[3]凌天清,王士杰,许志鸿.柔性路面非线性分析中的几个问题[J].重庆交通大学学报:自然科学版,1994,13(5):35-40.LING Tian-qing,WANG Shi-jie,XU Zhi-hong.Some Problem in Nonlinear Analysis Flexible Pavement[J].Journal of Chongqing Jiaotong Institute:Natural Science Edition,1994,13(5):35-40.
[4]WITCZAK M W,ANDREI D,MIRZA W.Development of Revised Predictive Model for the Dynamic(Complex)Modulus of Asphalt Mixtres,Inter-team Technical Report,NCHRP 1-37A[R].Washington,D.C.:University of Maryland,1999.
[5]HIRSCH T J.Modulus of Elasticity of Concrete Affected by Elastic Moduli of Cement Paste Matrix and Aggregate[J].Journal of the American Concrete Institute,1962,59(3):427-452.
[6]CHRISTENSEN D W,Jr,PELLINEN T,BONAQUIST RF.Hirsch Model for Estimating the Modulus of Asphalt Concrete[J].Journal of Association of Asphalt Paving Technologists,2003,72:97-121.
[7]JTG D50-2017,公路沥青路面设计规范[S].JTG D50-2017,Specifications for Design of Highway Asphalt Pavement[S].
[8]KIM Y R,LITTLE D,SONG I.Effect of Mineral Fillers on Fatigue Resistance and Fundamental Material Characteristics:Mechanstic Evaluation[J].Transportation Research Road,2003,1832:1-8.
[9]周兴业,王旭东,苏波.路面实体结构模型力学响应试验方法研究[J].公路交通科技,2017,34(6):23-29.ZHOU Xing-ye,WANG Xu-dong,SU Bo.Study on Mechanical Response Test Method for Real Pavement Structure Model[J].Journal of Highway and Transportation Research and Development,2017,34(6):23-29.
[10]张鹏,国兴玉,王旭光,等.足尺路面加速加载试验设备技术研究[J].山东交通学院学报,2011,19(4):41-45.ZHANG Peng,GUO Xing-yu,WANG Xu-guang,et al.Research on Experiment Equipment Technology of Full-size Road Surface Loading[J].Journal of Shandong Jiaotong University,2011,19(4):41-45.
[11]METCALF J B.Application of Full-scale Accelerated Pavement Testing[M].Washington,D.C.:Nation Academy Press,1996.
[12]HUANG Y H.Pavement Analysis and Design[M].Upper Saddle River,NJ:Prentice Hall,1993.
[13]PRIEST A L,TIMM D H.A Full-scale Pavement Structural Study for Mechanistic-empirical Pavement Design[J].Journal of the Association of Asphalt Paving Technologists,2005,74:519-556.
[14]韦金城,王林,杨永顺,等.永久性沥青路面试验路力学响应分布的数值仿真[J].公路交通科技,2010,27(6):15-19,33.WEI Jin-cheng,WANG Lin,YANG Yong-shun,et al.Numerical Simulation of Mechanical Response of Perpetual Road Test Asphalt Pavement[J].Journal of Highway and Transportation Research and Development,2010,27(6):15-19,33.
[15]董泽蛟,柳浩,谭忆秋,等.沥青路面三向应变响应现场实测研究[J].华南理工大学学报:自然科学版,2009,37(7):46-51.DONG Ze-jiao,LIU Hao,TAN Yi-qiu,et al.Field Measurement of Three-Direction Strain Response of Asphalt Pavement[J].Journal of South China University of Technology:Natural Science Edition,2009,37(7):46-51.
[16]田泽峰,范兴华,刘云全.足尺沥青路面加速加载试验实践导论[M].沈阳:东北大学出版社,2012.TIAN Ze-feng,FAN Xing-hua,LIU Yun-quan.Introduction of Full Scale Accelerated Pavement Test on Asphalt Pavement Practice[M].Shenyang:Northeastern University Press,2012.
[17]郭大智,冯德成.层状弹性体系力学[M].哈尔滨:哈尔滨工业大学出版社,2001.GUO Da-zhi,FENG De-cheng.Layered Elastic System Mechanics[M].Harbin:Harbin Institute of Technology Press,2001.
[18]王旭东.足尺路面试验环道路面结构与材料设计[J].公路交通科技,2017,34(6):30-37.WANG Xu-dong.Design of Pavement Structure and Material for Full-scale Test Track[J].Journal of Highway and Transportation Research and Development,2017,34(6):30-37.
[2]凌天清,王士杰,许志鸿.考虑材料非线性性能的沥青路面位移与应力分析[J].中国公路学报,1999,12(1):1-6.LING Tian-qing,WANG Shi-jie,XU Zhi-hong.Study of Nonlinear Analysis of Flexible Pavements[J].China Journal of Highway and Transport,1999,12(1):1-6.
[3]凌天清,王士杰,许志鸿.柔性路面非线性分析中的几个问题[J].重庆交通大学学报:自然科学版,1994,13(5):35-40.LING Tian-qing,WANG Shi-jie,XU Zhi-hong.Some Problem in Nonlinear Analysis Flexible Pavement[J].Journal of Chongqing Jiaotong Institute:Natural Science Edition,1994,13(5):35-40.
[4]WITCZAK M W,ANDREI D,MIRZA W.Development of Revised Predictive Model for the Dynamic(Complex)Modulus of Asphalt Mixtres,Inter-team Technical Report,NCHRP 1-37A[R].Washington,D.C.:University of Maryland,1999.
[5]HIRSCH T J.Modulus of Elasticity of Concrete Affected by Elastic Moduli of Cement Paste Matrix and Aggregate[J].Journal of the American Concrete Institute,1962,59(3):427-452.
[6]CHRISTENSEN D W,Jr,PELLINEN T,BONAQUIST RF.Hirsch Model for Estimating the Modulus of Asphalt Concrete[J].Journal of Association of Asphalt Paving Technologists,2003,72:97-121.
[7]JTG D50-2017,公路沥青路面设计规范[S].JTG D50-2017,Specifications for Design of Highway Asphalt Pavement[S].
[8]KIM Y R,LITTLE D,SONG I.Effect of Mineral Fillers on Fatigue Resistance and Fundamental Material Characteristics:Mechanstic Evaluation[J].Transportation Research Road,2003,1832:1-8.
[9]周兴业,王旭东,苏波.路面实体结构模型力学响应试验方法研究[J].公路交通科技,2017,34(6):23-29.ZHOU Xing-ye,WANG Xu-dong,SU Bo.Study on Mechanical Response Test Method for Real Pavement Structure Model[J].Journal of Highway and Transportation Research and Development,2017,34(6):23-29.
[10]张鹏,国兴玉,王旭光,等.足尺路面加速加载试验设备技术研究[J].山东交通学院学报,2011,19(4):41-45.ZHANG Peng,GUO Xing-yu,WANG Xu-guang,et al.Research on Experiment Equipment Technology of Full-size Road Surface Loading[J].Journal of Shandong Jiaotong University,2011,19(4):41-45.
[11]METCALF J B.Application of Full-scale Accelerated Pavement Testing[M].Washington,D.C.:Nation Academy Press,1996.
[12]HUANG Y H.Pavement Analysis and Design[M].Upper Saddle River,NJ:Prentice Hall,1993.
[13]PRIEST A L,TIMM D H.A Full-scale Pavement Structural Study for Mechanistic-empirical Pavement Design[J].Journal of the Association of Asphalt Paving Technologists,2005,74:519-556.
[14]韦金城,王林,杨永顺,等.永久性沥青路面试验路力学响应分布的数值仿真[J].公路交通科技,2010,27(6):15-19,33.WEI Jin-cheng,WANG Lin,YANG Yong-shun,et al.Numerical Simulation of Mechanical Response of Perpetual Road Test Asphalt Pavement[J].Journal of Highway and Transportation Research and Development,2010,27(6):15-19,33.
[15]董泽蛟,柳浩,谭忆秋,等.沥青路面三向应变响应现场实测研究[J].华南理工大学学报:自然科学版,2009,37(7):46-51.DONG Ze-jiao,LIU Hao,TAN Yi-qiu,et al.Field Measurement of Three-Direction Strain Response of Asphalt Pavement[J].Journal of South China University of Technology:Natural Science Edition,2009,37(7):46-51.
[16]田泽峰,范兴华,刘云全.足尺沥青路面加速加载试验实践导论[M].沈阳:东北大学出版社,2012.TIAN Ze-feng,FAN Xing-hua,LIU Yun-quan.Introduction of Full Scale Accelerated Pavement Test on Asphalt Pavement Practice[M].Shenyang:Northeastern University Press,2012.
[17]郭大智,冯德成.层状弹性体系力学[M].哈尔滨:哈尔滨工业大学出版社,2001.GUO Da-zhi,FENG De-cheng.Layered Elastic System Mechanics[M].Harbin:Harbin Institute of Technology Press,2001.
[18]王旭东.足尺路面试验环道路面结构与材料设计[J].公路交通科技,2017,34(6):30-37.WANG Xu-dong.Design of Pavement Structure and Material for Full-scale Test Track[J].Journal of Highway and Transportation Research and Development,2017,34(6):30-37.