光纤传感技术监测沥青混合料应变响应有效性研究
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摘要
现阶段我国沥青路面的早期损坏现象十分严重,损坏类型错综复杂,严重地影响了行车的安全性和舒适性,极大地降低了路面的使用品质,缩短了路面的使用寿命,因此解决沥青路面早期损坏在我国现阶段的道路建设和管理养护中是十分必要的。研究表明,进行沥青路面的“健康监测”,准确地获取路面结构受力状态信息,进而探究早期损坏机理,采取合理有效的预防措施是解决沥青路面早期损坏的根本办法。光纤传感技术的出现为准确地获取路面结构受力状态信息提供了可能。光纤光栅传感器以其良好的耐久性和稳定性已成为工程应用的热点,借助它在其它工程领域的成功经验将光纤智能传感技术移植到道路工程中,实现沥青路面的“健康监测”。但现有的光纤光栅传感器模量较大(一般在50~70GPa),与沥青混合料模量(一般在1.0~1.2GPa)不匹配,导致两者协同变形性较差,传感器采集的信息与路面该点的真实信息存在差异,不能直接用于评价该点的受力状态,因此研究光纤传感技术监测沥青混合料应变响应有效性是解决光纤光栅传感器在路面中应用的前提和基础,是十分必要的。
针对实际沥青路面的不同受力状态,本文设计了单一受力模式试验和复杂受力模式试验,对传感器实时输出的数据与理论真实值进行对比分析,得出两者间的相互关系,并进行传感器短期和长期响应监测,同时采用有限元技术进行仿真分析,以评价光纤光栅传感器监测沥青混合料应变响应的有效性,并进行影响因素分析,为传感器实测数据的修正及传感器进一步的改进与开发提供依据。本文的主要研究工作包括以下几点:
首先,针对有限元仿真的需要,为真实反映沥青混合料的粘弹特性,分别设计了单轴动态蠕变试验和动态模量试验进行沥青混合料粘弹参数的测定,并通过拟合计算得到大型有限元软件ABAQUS中提供的粘弹模型参数。
其次,针对沥青路面中受拉和受压的单一受力状态分别设计了植入传感器的四点弯曲梁试验和动态单轴压缩试验。受拉传感器埋设于四点弯曲梁纯拉区,基于实测梁底竖向挠度得到理论计算应变,受压传感器埋设于单轴压缩圆柱试件中心,外接LVDT传感器测定真实应变。对比分析传感器实测应变与理论计算应变和真实应变间的相互关系,进而得出传感器监测沥青混合料应变响应的有效性并建立传感器实测应变的理论修正公式,变化试验温度得到温度对两者关系的影响。
第三,应用建立在相似理论基础上的模化方法和有限元仿真进行路面复杂受力模型设计。确定了模型与路面原型间各参数的对应关系,建立典型路面结构的三维有限元模型,确定轮载影响范围,进行单、双轮均布荷载等效,面层结构与路面全结构等效,最终确定了路面复杂受力模型。
第四,针对确定的复杂受力模型设计了三层复合板轮载试验,将传感器埋设于复合板上面层底部和中面层中部,进行不同温度下的短期循环加载和标准车辙试验,得出不同温度下传感器监测沥青混合料短期及长期应变响应的有效性。
最后,建立上述各室内试验的有限元模型,分析传感器的存在以及传感器模量和型式对传感器附近区域及模型各力学参数的影响,确定合理的传感器模量及型式,以指导传感器的进一步开发。实现了移动荷载的数值模拟,进行复合板模型在一次轮碾瞬态作用及短期轮载循环作用下的动态应变响应时程分析,得出了有限元模拟的准确性,埋设传感器可以准确地反映路面结构内部的主要受力状态,并探讨了车辙形成的主要影响因素。
本文在光纤传感技术监测沥青混合料应变响应有效性、传感器实测应变修正和沥青混合料室内试验的有限元模拟分析方面所做的一系列工作,将为光纤光栅传感器的进一步改进与开发、光纤传感技术在道路工程中的应用、工程研究方法和工具的更新以及非线性有限元在沥青路面结构设计与分析中的应用奠定坚实的基础。
Nowadays, the early damage of asphalt pavement is very serious, these damages severely affect the safety and comfort of driving vehicles, consumedly lower the using character and shorten the service life of pavement, so solving the early damage is important in the construction and management of asphalt pavement. The investigations show that, carrying on "the health monitoring" of asphalt pavement, accurately obtainting the mechanical information of pavement structure, inquirying the mechanism and taking the reasonable and effective preventive measures are the keys to solve the problem. The appearance of the Fiber Optic Sensing Technology made it possible to accurately obtain the information of pavement structure. The Fiber Bragg Grating sensor (FBG) has become the hot point of the engineering application with its long longevity and good stability. By virtue of the success experiences in other project domain, we transplanted the Fiber Optic Sensing Technology to road engineering, real-time gathered and monitored the mechanical information of pavement structure by embeding the FBG inside pavement to realize "the health monitoring" of asphalt pavement. However, the existing FBG’s modulus is big (generally abaut 50~70GPa), badly matched with asphalt mixture (generally abaut 1.0~1.2GPa), this caused the worse coordination between them, then the information collected by the FBG has a bigger difference with pavement real response, cannot directly be used to appraise the mechanical condition. So study on the effectiveness of monitoring asphalt mixture’s strain response based on the Fiber Optic Sensing Technology is the precondition and foundation to solve the applications of the FBG in asphalt pavement.
This paper designed the laboratory test of the single and complex bearing mode, conducted the comparative study between the actual strains measured dy the FBG and the calculated true strains, carried on the short and long term strain response monitoring, then applied the finite element simulation to appraise the effectiveness of monitoring asphalt mixture’s strain response based on the FBG, then conducted the quantitative depiction, provided the basis for modifying the data collected by the FBG. The content of paper mainly contain following aspects:
Firstly, we respectively designed the dynamic uniaxial creep test and the dynamic modulus test to determine the viscoelastic parameters of asphalt mixture for truly reflecting the viscoelastic properties of asphalt mixture, then fitting calculated the model parameters corresponding to the viscoelastic model provided by FEM.
Secondly, based on the tensile and compression situation inside the pavement, the four-point-bend beam test and the dynamic uniaxial compression test were designed respectively. FBGs subjected to tension were embeded in the pure tension region of the beam, we abtained the caculated strains based on the vertical deflection at the beam bottom. FBGs subjected to compression were embeded in the center of the cylindrical specimen, and the true strains were determined by external LVDT sensors. We conducted the comparative study between the actual strains measured by FBG and the calculated true strains, concluded the effectiveness and established the modified formula of the measured strains.
Thirdly, the complex bearing model of the pavement was designed by applying the modelling method based on the similarity theory and finite element simulation. The relationship between the prototype and model was determined and the finite element model was established to determine the influence scope of the wheel loads, then we conducted the equivalent between the single and double wheel loads and the quivalent between the bituminous surface structure and the whole pavement structure to abtain the most reasonable complex bearing model.
Fourthly, the three-lays composite loading test was designed based on the complex bearing model, FBGs were embeded inside the bottom of the upper layer and the center of the middle layer, the short cycle load and standard rutting test under the variable temperature were applied respectively, we draw the conclusion that the short and long terms stain response monitoring under the variable temperature by FBG were effective.
Finally, the finite element model was established of the laboratory tests mentioned above by ABAQUS to analyze the influence on the mechanical indexes close to the location of the FBG and the whole model due to the existing of the FBG, the FBG modulus and styles, we determined the most reasonable FBG modulus and styles. Especially, we realized the simulation of the moving load, conducted the time history analysis of the dynamic strain response, then we draw the conclusion that the FEM simulation is accurate and the FBGs are able to reflect the mainly mechanical condition of the pavement. Furthermore, we investigated the mechanism of the rutting.
In this paper, some research about the effectiveness of monitoring asphalt mixture’s strain response based on the fiber optic sensing tecnology, the modified formula of the measured strains by FBG and the accurately finite element simulation and analysis, will lay a solid foundation for the further research and development of FBG, promote the development of FBG technology in road engineering, accelerate the scientific research methods and tools updating in engineering fields, and supply sufficient data and technical supports for rutting theoretical investigation and analysis of asphalt pavement.
针对实际沥青路面的不同受力状态,本文设计了单一受力模式试验和复杂受力模式试验,对传感器实时输出的数据与理论真实值进行对比分析,得出两者间的相互关系,并进行传感器短期和长期响应监测,同时采用有限元技术进行仿真分析,以评价光纤光栅传感器监测沥青混合料应变响应的有效性,并进行影响因素分析,为传感器实测数据的修正及传感器进一步的改进与开发提供依据。本文的主要研究工作包括以下几点:
首先,针对有限元仿真的需要,为真实反映沥青混合料的粘弹特性,分别设计了单轴动态蠕变试验和动态模量试验进行沥青混合料粘弹参数的测定,并通过拟合计算得到大型有限元软件ABAQUS中提供的粘弹模型参数。
其次,针对沥青路面中受拉和受压的单一受力状态分别设计了植入传感器的四点弯曲梁试验和动态单轴压缩试验。受拉传感器埋设于四点弯曲梁纯拉区,基于实测梁底竖向挠度得到理论计算应变,受压传感器埋设于单轴压缩圆柱试件中心,外接LVDT传感器测定真实应变。对比分析传感器实测应变与理论计算应变和真实应变间的相互关系,进而得出传感器监测沥青混合料应变响应的有效性并建立传感器实测应变的理论修正公式,变化试验温度得到温度对两者关系的影响。
第三,应用建立在相似理论基础上的模化方法和有限元仿真进行路面复杂受力模型设计。确定了模型与路面原型间各参数的对应关系,建立典型路面结构的三维有限元模型,确定轮载影响范围,进行单、双轮均布荷载等效,面层结构与路面全结构等效,最终确定了路面复杂受力模型。
第四,针对确定的复杂受力模型设计了三层复合板轮载试验,将传感器埋设于复合板上面层底部和中面层中部,进行不同温度下的短期循环加载和标准车辙试验,得出不同温度下传感器监测沥青混合料短期及长期应变响应的有效性。
最后,建立上述各室内试验的有限元模型,分析传感器的存在以及传感器模量和型式对传感器附近区域及模型各力学参数的影响,确定合理的传感器模量及型式,以指导传感器的进一步开发。实现了移动荷载的数值模拟,进行复合板模型在一次轮碾瞬态作用及短期轮载循环作用下的动态应变响应时程分析,得出了有限元模拟的准确性,埋设传感器可以准确地反映路面结构内部的主要受力状态,并探讨了车辙形成的主要影响因素。
本文在光纤传感技术监测沥青混合料应变响应有效性、传感器实测应变修正和沥青混合料室内试验的有限元模拟分析方面所做的一系列工作,将为光纤光栅传感器的进一步改进与开发、光纤传感技术在道路工程中的应用、工程研究方法和工具的更新以及非线性有限元在沥青路面结构设计与分析中的应用奠定坚实的基础。
Nowadays, the early damage of asphalt pavement is very serious, these damages severely affect the safety and comfort of driving vehicles, consumedly lower the using character and shorten the service life of pavement, so solving the early damage is important in the construction and management of asphalt pavement. The investigations show that, carrying on "the health monitoring" of asphalt pavement, accurately obtainting the mechanical information of pavement structure, inquirying the mechanism and taking the reasonable and effective preventive measures are the keys to solve the problem. The appearance of the Fiber Optic Sensing Technology made it possible to accurately obtain the information of pavement structure. The Fiber Bragg Grating sensor (FBG) has become the hot point of the engineering application with its long longevity and good stability. By virtue of the success experiences in other project domain, we transplanted the Fiber Optic Sensing Technology to road engineering, real-time gathered and monitored the mechanical information of pavement structure by embeding the FBG inside pavement to realize "the health monitoring" of asphalt pavement. However, the existing FBG’s modulus is big (generally abaut 50~70GPa), badly matched with asphalt mixture (generally abaut 1.0~1.2GPa), this caused the worse coordination between them, then the information collected by the FBG has a bigger difference with pavement real response, cannot directly be used to appraise the mechanical condition. So study on the effectiveness of monitoring asphalt mixture’s strain response based on the Fiber Optic Sensing Technology is the precondition and foundation to solve the applications of the FBG in asphalt pavement.
This paper designed the laboratory test of the single and complex bearing mode, conducted the comparative study between the actual strains measured dy the FBG and the calculated true strains, carried on the short and long term strain response monitoring, then applied the finite element simulation to appraise the effectiveness of monitoring asphalt mixture’s strain response based on the FBG, then conducted the quantitative depiction, provided the basis for modifying the data collected by the FBG. The content of paper mainly contain following aspects:
Firstly, we respectively designed the dynamic uniaxial creep test and the dynamic modulus test to determine the viscoelastic parameters of asphalt mixture for truly reflecting the viscoelastic properties of asphalt mixture, then fitting calculated the model parameters corresponding to the viscoelastic model provided by FEM.
Secondly, based on the tensile and compression situation inside the pavement, the four-point-bend beam test and the dynamic uniaxial compression test were designed respectively. FBGs subjected to tension were embeded in the pure tension region of the beam, we abtained the caculated strains based on the vertical deflection at the beam bottom. FBGs subjected to compression were embeded in the center of the cylindrical specimen, and the true strains were determined by external LVDT sensors. We conducted the comparative study between the actual strains measured by FBG and the calculated true strains, concluded the effectiveness and established the modified formula of the measured strains.
Thirdly, the complex bearing model of the pavement was designed by applying the modelling method based on the similarity theory and finite element simulation. The relationship between the prototype and model was determined and the finite element model was established to determine the influence scope of the wheel loads, then we conducted the equivalent between the single and double wheel loads and the quivalent between the bituminous surface structure and the whole pavement structure to abtain the most reasonable complex bearing model.
Fourthly, the three-lays composite loading test was designed based on the complex bearing model, FBGs were embeded inside the bottom of the upper layer and the center of the middle layer, the short cycle load and standard rutting test under the variable temperature were applied respectively, we draw the conclusion that the short and long terms stain response monitoring under the variable temperature by FBG were effective.
Finally, the finite element model was established of the laboratory tests mentioned above by ABAQUS to analyze the influence on the mechanical indexes close to the location of the FBG and the whole model due to the existing of the FBG, the FBG modulus and styles, we determined the most reasonable FBG modulus and styles. Especially, we realized the simulation of the moving load, conducted the time history analysis of the dynamic strain response, then we draw the conclusion that the FEM simulation is accurate and the FBGs are able to reflect the mainly mechanical condition of the pavement. Furthermore, we investigated the mechanism of the rutting.
In this paper, some research about the effectiveness of monitoring asphalt mixture’s strain response based on the fiber optic sensing tecnology, the modified formula of the measured strains by FBG and the accurately finite element simulation and analysis, will lay a solid foundation for the further research and development of FBG, promote the development of FBG technology in road engineering, accelerate the scientific research methods and tools updating in engineering fields, and supply sufficient data and technical supports for rutting theoretical investigation and analysis of asphalt pavement.
引文
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43陈少幸,张肖宁.沥青混凝土路面光栅应变传感器的试验研究.传感技术学报. 2006,19(2):397~399
44 Qingli HU, Zhi Zhou, Hui Li & Jinping Ou. Health Monitor on Asphalt Pavement of Highway Based on FBG Technique. Proc. of SPIE. 2007,6595(35):1~6
45 CHEN Feng-chen, TAN Yi-qiu, LIU Hao, et al1. Analysis of Strain in Asphalt Pavement Using FRP-OFBG Sensors. ASCE: Proceedings of the 7th International Conference of Chinese Transportation Professionals (ICCTP). 2007:877~885
46陈凤晨,谭忆秋,柳浩,董泽蛟,王宝新.基于光纤光栅技术的沥青路面结构应变场分析.公路交通科技. 2008,25(10):9~13
47谭忆秋,陈凤晨,董泽蛟,柳浩.基于光纤光栅传感技术的沥青路面永久变形计算方法.大连海事大学学报. 2008,34(4):119~122
48张肖宁.实验粘弹原理.哈尔滨:哈尔滨船舶工程学院出版社. 1990:9~30
49 H.L. Von Quintus, J.A. Scherocman, C.S. Hughes, T.W. Kennedy. Asphalt Aggregate Mixture Analysis System. Transportation Research Board NCHRP Report 388. National Research Council. Washington, D.C. 2000:35~53,135~179
50 Kamil Elias Kaliush. Simple Performance Test for Permanent Deformation of Asphalt Mixtures. Arizona State University. Arizona State,USA. 2001:21~39
51 Ghassan R. Chehab, Emily O'Quinn, Y. Richard Kim. Specimen Geometry Study for Direct Tension Test Based on Mechanical Tests and Air Void Variation in SGC-Compacted Asphalt Concrete Specimens. Annual Meeting of the Transportation Research Board, 2000:125~132
52曹丽萍.沥青路面永久变形叠加方法研究.同济大学博士学位论文. 2007:21~37
53王旭东,沙爱民,许志鸿.沥青路面材料动力特性与动态参数.北京:人民交通出版社. 2002:27~43
54 M.W. Witczak, K. Kaloush, T. Pellinen, M. El-Basyouny, H. von. Quintus. Simple Performance Test for Superpave Mix Design. NCHRP Report 465, Transportation Research Board, National Research Council, National Academy Press, Washington DC, 2002:465~471
55王金昌,陈页开. ABAQUS在土木工程中的应用.浙江:浙江大学出版社. 2006,11:35~38
56 Yun Liao, Viscoelastic FE Modelling of Asphalt Pavements and Its Application to U.S.30 Perpetual Pavement. Doctor Dissertation of the Russ College of Engineering and Technology. 2007:53~59
57胡霞光,李德超,田莉.沥青混合料动态模量研究进展.中外公路. 2007,1(27):132~133
58韦金城,王林,马士杰.多孔隙大碎石沥青混合料动态模量试验研究.石油沥青. 2008,22(1):16~17
59 Schapery R. A. and Park S. W..“Methods of Interconversion between Linear Viscoelastic Materials Functions. Part II– an Approximate Analytical Method”, Int. J. Solis Struc. 1999,36(11):1677~1699
60 M. Marasteanu, D. Anderson. Time-Temperature Dependency of Asphalt Binders And Improved Model, Asphalt Paving Technology. Journal of the Association of Asphalt Paving Technologists. 1996,65:408~448
61 R.M.Christensen. Theory of Viscoelasticity. Second Edition, Acdemic Press, Inc. 1982:39~160
62杨挺青.粘弹性理论及其应用.北京:科学出版社. 2004:69~105
63 Pellinen, T. K., M. W. Witczak. Stress Dependent Master Curve Construction forDynamic (Complex) Modulus. Journal of the Association of Asphalt Paving Technologists. 2002,71:321~345
64张肖宁.沥青与沥青混合料的粘弹力学原理及应用.北京:人民交通出版社. 2006:51~61
65赵延庆,吴剑,文健.沥青混合料动态模童及其主曲线的确定与分析.公路. 2008,(8):16~17
66 S.W.Park, Y.R.Kim. Fitting Prony-Series Viscoelastic Models with Power-Law Presmoothing. Jounal of Material in Civil Engineering. 2001,13(1):27~29
67 Park S. W. and Schapery R. A.,“Methods of Interconversion between Linear Viscoelastic Materials Functions. Part I– a Numerical Method Based on Prony Series,”. Int. J. Solis Struc. 1999,36(11):1653~1675
68 Williams M. L., Landel R. F. and Ferry J. D.,“The Temperature Dependency of Relaxation Mechanisms in Amorphous Polymers and other Glass Forming Liquid”, The Journal of The American Chemical Society. 1955,77(14):3701~3707
69 AASHTO. AASHTO 2002 Pavement Design Guide. American Association of State Highway and Transportation Officials. Washington, D. C. 2004,3(3):46~50
70田庚亮.沥青混合料与光纤光栅传感器协同变形性研究.哈尔滨工业大学2007届优秀毕业论文. 2007:20~21
71张小政.工程化光纤光栅系列传感器的研究与开发.哈尔滨工业大学工学硕士学位论文. 2006:13~15
72田石柱,赵雪峰,欧进萍等.结构健康监测用光纤Bragg光栅温度补偿研究.传感器技术. 2002,21(12):8~10
73赵启林,杨洪,陈浩森.光纤光栅应变传感器的温度补偿.东南大学学报(自然科学版). 2007,37(2):310~314
74姚远,易本顺,肖进胜,李朝辉.光纤布拉格光栅传感器的温度补偿研究.应用激光. 2007,27(3):192~198
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76姜德生,梁磊,南秋明.光纤Bragg光栅传感特性的实验研究.传感器技术. 2003,23(7):7~9
77蔚婷,乔学光,贾振安.改善波形并增敏的光纤光栅温度传感技术.光子学报. 2005,34(8):1209~1211
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40周智,欧进萍.土木工程智能健康监测与诊断系统.传感器技术. 2001,20 (11):1~4
41周智,欧进萍. FBG智能传感器及其在土木工程中的应用研究.功能材料. 2004增刊(35):152~156
42曹照平,王社良,马胜利.光纤传感器在土木工程中的应用.南京建筑工程学院学报. 2000,(4):48~49
43陈少幸,张肖宁.沥青混凝土路面光栅应变传感器的试验研究.传感技术学报. 2006,19(2):397~399
44 Qingli HU, Zhi Zhou, Hui Li & Jinping Ou. Health Monitor on Asphalt Pavement of Highway Based on FBG Technique. Proc. of SPIE. 2007,6595(35):1~6
45 CHEN Feng-chen, TAN Yi-qiu, LIU Hao, et al1. Analysis of Strain in Asphalt Pavement Using FRP-OFBG Sensors. ASCE: Proceedings of the 7th International Conference of Chinese Transportation Professionals (ICCTP). 2007:877~885
46陈凤晨,谭忆秋,柳浩,董泽蛟,王宝新.基于光纤光栅技术的沥青路面结构应变场分析.公路交通科技. 2008,25(10):9~13
47谭忆秋,陈凤晨,董泽蛟,柳浩.基于光纤光栅传感技术的沥青路面永久变形计算方法.大连海事大学学报. 2008,34(4):119~122
48张肖宁.实验粘弹原理.哈尔滨:哈尔滨船舶工程学院出版社. 1990:9~30
49 H.L. Von Quintus, J.A. Scherocman, C.S. Hughes, T.W. Kennedy. Asphalt Aggregate Mixture Analysis System. Transportation Research Board NCHRP Report 388. National Research Council. Washington, D.C. 2000:35~53,135~179
50 Kamil Elias Kaliush. Simple Performance Test for Permanent Deformation of Asphalt Mixtures. Arizona State University. Arizona State,USA. 2001:21~39
51 Ghassan R. Chehab, Emily O'Quinn, Y. Richard Kim. Specimen Geometry Study for Direct Tension Test Based on Mechanical Tests and Air Void Variation in SGC-Compacted Asphalt Concrete Specimens. Annual Meeting of the Transportation Research Board, 2000:125~132
52曹丽萍.沥青路面永久变形叠加方法研究.同济大学博士学位论文. 2007:21~37
53王旭东,沙爱民,许志鸿.沥青路面材料动力特性与动态参数.北京:人民交通出版社. 2002:27~43
54 M.W. Witczak, K. Kaloush, T. Pellinen, M. El-Basyouny, H. von. Quintus. Simple Performance Test for Superpave Mix Design. NCHRP Report 465, Transportation Research Board, National Research Council, National Academy Press, Washington DC, 2002:465~471
55王金昌,陈页开. ABAQUS在土木工程中的应用.浙江:浙江大学出版社. 2006,11:35~38
56 Yun Liao, Viscoelastic FE Modelling of Asphalt Pavements and Its Application to U.S.30 Perpetual Pavement. Doctor Dissertation of the Russ College of Engineering and Technology. 2007:53~59
57胡霞光,李德超,田莉.沥青混合料动态模量研究进展.中外公路. 2007,1(27):132~133
58韦金城,王林,马士杰.多孔隙大碎石沥青混合料动态模量试验研究.石油沥青. 2008,22(1):16~17
59 Schapery R. A. and Park S. W..“Methods of Interconversion between Linear Viscoelastic Materials Functions. Part II– an Approximate Analytical Method”, Int. J. Solis Struc. 1999,36(11):1677~1699
60 M. Marasteanu, D. Anderson. Time-Temperature Dependency of Asphalt Binders And Improved Model, Asphalt Paving Technology. Journal of the Association of Asphalt Paving Technologists. 1996,65:408~448
61 R.M.Christensen. Theory of Viscoelasticity. Second Edition, Acdemic Press, Inc. 1982:39~160
62杨挺青.粘弹性理论及其应用.北京:科学出版社. 2004:69~105
63 Pellinen, T. K., M. W. Witczak. Stress Dependent Master Curve Construction forDynamic (Complex) Modulus. Journal of the Association of Asphalt Paving Technologists. 2002,71:321~345
64张肖宁.沥青与沥青混合料的粘弹力学原理及应用.北京:人民交通出版社. 2006:51~61
65赵延庆,吴剑,文健.沥青混合料动态模童及其主曲线的确定与分析.公路. 2008,(8):16~17
66 S.W.Park, Y.R.Kim. Fitting Prony-Series Viscoelastic Models with Power-Law Presmoothing. Jounal of Material in Civil Engineering. 2001,13(1):27~29
67 Park S. W. and Schapery R. A.,“Methods of Interconversion between Linear Viscoelastic Materials Functions. Part I– a Numerical Method Based on Prony Series,”. Int. J. Solis Struc. 1999,36(11):1653~1675
68 Williams M. L., Landel R. F. and Ferry J. D.,“The Temperature Dependency of Relaxation Mechanisms in Amorphous Polymers and other Glass Forming Liquid”, The Journal of The American Chemical Society. 1955,77(14):3701~3707
69 AASHTO. AASHTO 2002 Pavement Design Guide. American Association of State Highway and Transportation Officials. Washington, D. C. 2004,3(3):46~50
70田庚亮.沥青混合料与光纤光栅传感器协同变形性研究.哈尔滨工业大学2007届优秀毕业论文. 2007:20~21
71张小政.工程化光纤光栅系列传感器的研究与开发.哈尔滨工业大学工学硕士学位论文. 2006:13~15
72田石柱,赵雪峰,欧进萍等.结构健康监测用光纤Bragg光栅温度补偿研究.传感器技术. 2002,21(12):8~10
73赵启林,杨洪,陈浩森.光纤光栅应变传感器的温度补偿.东南大学学报(自然科学版). 2007,37(2):310~314
74姚远,易本顺,肖进胜,李朝辉.光纤布拉格光栅传感器的温度补偿研究.应用激光. 2007,27(3):192~198
75寥延彪.光纤光学.北京:清华大学出版社. 2000:34~41
76姜德生,梁磊,南秋明.光纤Bragg光栅传感特性的实验研究.传感器技术. 2003,23(7):7~9
77蔚婷,乔学光,贾振安.改善波形并增敏的光纤光栅温度传感技术.光子学报. 2005,34(8):1209~1211
78柴伟.光纤布拉格光栅温度传感技术研究.武汉理工大学工学硕士学位论文. 2004:44~46
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