柔性基层沥青路面设计指标及性能预估模型研究
|
摘要
柔性基层沥青路面以其优良的路用性能成为我国半刚性基层沥青路面的必要补充形式。相对于半刚性基层沥青路面而言，随着其沥青层厚度的增加，路面结构层受力必然要发生一定的变化，在此条件下如何进行柔性基层沥青路面的结构设计就成为其在我国得以推广应用迫切需要解决的问题。
在沥青路面结构服务期内，我国沥青路面设计采用的弯沉指标及国外采用的路基顶面压应变、沥青层底部拉应变指标均不能真实反映实际道路的破坏情况，本文以柔性基层沥青路面的病害为切入点，提出以车辙、Top-Down裂纹、反射裂纹(仅对混合式基层沥青路面)为设计指标，建立了相应的柔性基层沥青路面性能预估模型，在此基础上完成了路面结构车辙深度及疲劳寿命的计算。最后以青岛-银川高速公路采用混合式路面试验段为依托工程，进行了车辙深度和反射裂纹、Top-Down裂纹疲劳寿命的预估计算。
首先通过频率扫描试验确定了三种不同沥青混合料在不同温度下对应的动模量及相位角，根据粘弹性力学中的时温等效原理，应用WLF方程，通过Sig-moidal函数及非线性最小二乘法确定某一温度下沥青混合料的动态模量主曲线及相位角主曲线，并在此基础上通过傅立叶变换确定广义Maxwell模型的粘弹性参数，为后期的车辙计算奠定了基础。此外，由于ANSYS有限元程序自身对材料模型的要求，需把通过试验确定的松弛模量转化成剪切模量及体积模量再用于有限元计算，鉴于此，推导了广义Maxwell模型的三维本构方程，应用留数定理确定了蠕变函数的系数，基于以上研究，确定了沥青混合料的剪切模量及体积模量的表达式。同时，应用FWD实测试验路段的弯沉值，根据BP神经网络的L-M动量项法确定了路基土及半刚性底基层材料的动模量值，并在沥青混合料频率扫描试验的基础上，结合有效深度的定义确定了沥青混合料在一定的设计车速、结构层厚度情况下对应的模量值，为试验段路面性能预估提供必要的参数。
车辙计算时，利用概率统计理论计算了不同荷载偏移距离下路面不同位置的荷载作用的概率，应用有限元程序计算路面结构的车辙。应用所建模型，进行了基于荷载大小、行车速度、荷载作用次数、轮胎中线偏移距离及土基模量等五个因素的车辙正交计算。通过方差分析法确定了各因素对车辙影响的显著程度，以期为今后的路面设计及养护工作提供必要的参考。
Top-Down裂纹疲劳寿命计算时，采用概率统计的方法将荷载按正态分布的原则作用到路面结构模型上，应用改进的Paris公式及四阶龙格-库塔法则计算不同荷载作用位置、不同裂纹位置对应的路面结构的疲劳寿命。在此基础上，根据Miner损伤原则，确定了基于Top-Down裂纹的路面结构疲劳寿命。
对于混合式基层沥青路面进行反射裂纹疲劳寿命计算时，考虑车辆荷载每次经过裂纹时对裂尖造成的影响不同，根据断裂力学原理及修正后的Miner法则计算路面结构反射裂纹的疲劳寿命。
最后以青银高速公路混合式路面试验段为依托工程，进行了车辙深度及Top-Down裂纹、反射裂纹等疲劳寿命的预估计算。
本文从柔性基层沥青路面的病害入手，提出车辙、Top-Down裂纹、反射裂纹为设计指标，建立了柔性基层沥青路面性能预估模型，为柔性基层沥青路面在我国的推广应用起到一定的推进作用。
The flexible base is the necessary supplement to simi-rigid base for its excellentperformance. Its stress in the structure layer, which is caused by the vehicle load, is changedcertainly with the increase of depth of asphalt layer against the simi-rigid base. Under thecondition, it is a problem that calls for immediate solution in order to do the adoption andapplication of asphalt pavement with flexible base.
The indexes of deflection, compressive strain on the top of subgrade and tensile strain onthe bottom of asphalt layer, couldn't reflect the real pavement distress. The indexes of therutting, Top-Down crack and reflecting crack are proposed as the pavement design indexbased on the distress of asphalt pavement with flexible base. The performance forecastingmodels of asphalt pavement with flexible base are built. Upon the above research, the ruttingdepth and fatigue life of pavement are calculated. At last, taking Qindao-Yinchuan freewayfor instance, the rutting depth and fatigue life which originate from the Top-Down cracks andreflecting cracks, are calculated.
The dynamic modulus and phase angle of three kinds of asphalt mixture are determinedbased on the Frequency Sweep Test at different temperatures. In accordance with thetime-temperature equivalence principle, the master curves of dynamic modulus and phaseangle are determined through the applying of WLF equation and Sig-moidal function. Uponthe above research, the viscoelastic parameters of the generalized Maxwell model arecalculated by the Fourier transform. The achievements lay foundations of the ruttingcalculation. Moreover, the relaxation modulus determined by the test must be transformedinto bulk modulus and shear modulus in order to be applied by the finite element calculation.In view of this, the three-dimensional constitutive equation of generalized Maxwell model isdeduced. The coefficients of creep function are determined by the residue theorem. Uponthe above research, the expressions of bulk modulus and shear modulus are confirmed. At thesame time, the modulus of subgrade and simi-rigid material is backcalculated through the BPneural network according to the FWD. At last, the modulus of asphalt mixture are calculatedunder the circumstances of the certain vehicle speed and thickness of structure layer, based on the Frequency Sweep Test and considering the definition of effective depth. The above studiesprovide necessary parameters for the performance forecasting of test road.
When the rutting is numerically computed by using a commercial FEA program, ANSYS,the probability of loading at different pavement position is calculated according to theprobability and statistics theory under the circumstances of the different wander distance. Fivefactors including the magnitude of wheel loading, the wander distance, the speed of wheelloading, the number of load repetitions, and the modulus of subgrade are studied to evaluatetheir contributions of rutting development for asphalt pavements. The significance that eachfactor impacts on the rutting is analyzed in order to offer necessary, support for the pavementdesign and maintenance in the future.
When the fatigue life derived from the Top-Down crack is calculated, the load is appliedto the FEA model according to the rule of normal distribution. The improved Parisexpressions and fourth-order Runge-Kutta principle are adopted to calculate the fatigue life ofcorresponding pavement structure at different loading position and cracking position. On thebasis of this, the whole fatigue life derived from the Top-Down crack is calculated accordingto the Miner damage principle.
The fatigue life derived from the reflecting crack is calculated according to the Minerdamage principle, considering the factor that the development of the top for crack is differentwhen a vehicle load passed the crack.
At last, taking Qindao-Yinchuan freeway for instance, the rutting depth and fatigue lifewhich originate from the Top-Down cracks and reflecting cracks, are calculated.
在沥青路面结构服务期内，我国沥青路面设计采用的弯沉指标及国外采用的路基顶面压应变、沥青层底部拉应变指标均不能真实反映实际道路的破坏情况，本文以柔性基层沥青路面的病害为切入点，提出以车辙、Top-Down裂纹、反射裂纹(仅对混合式基层沥青路面)为设计指标，建立了相应的柔性基层沥青路面性能预估模型，在此基础上完成了路面结构车辙深度及疲劳寿命的计算。最后以青岛-银川高速公路采用混合式路面试验段为依托工程，进行了车辙深度和反射裂纹、Top-Down裂纹疲劳寿命的预估计算。
首先通过频率扫描试验确定了三种不同沥青混合料在不同温度下对应的动模量及相位角，根据粘弹性力学中的时温等效原理，应用WLF方程，通过Sig-moidal函数及非线性最小二乘法确定某一温度下沥青混合料的动态模量主曲线及相位角主曲线，并在此基础上通过傅立叶变换确定广义Maxwell模型的粘弹性参数，为后期的车辙计算奠定了基础。此外，由于ANSYS有限元程序自身对材料模型的要求，需把通过试验确定的松弛模量转化成剪切模量及体积模量再用于有限元计算，鉴于此，推导了广义Maxwell模型的三维本构方程，应用留数定理确定了蠕变函数的系数，基于以上研究，确定了沥青混合料的剪切模量及体积模量的表达式。同时，应用FWD实测试验路段的弯沉值，根据BP神经网络的L-M动量项法确定了路基土及半刚性底基层材料的动模量值，并在沥青混合料频率扫描试验的基础上，结合有效深度的定义确定了沥青混合料在一定的设计车速、结构层厚度情况下对应的模量值，为试验段路面性能预估提供必要的参数。
车辙计算时，利用概率统计理论计算了不同荷载偏移距离下路面不同位置的荷载作用的概率，应用有限元程序计算路面结构的车辙。应用所建模型，进行了基于荷载大小、行车速度、荷载作用次数、轮胎中线偏移距离及土基模量等五个因素的车辙正交计算。通过方差分析法确定了各因素对车辙影响的显著程度，以期为今后的路面设计及养护工作提供必要的参考。
Top-Down裂纹疲劳寿命计算时，采用概率统计的方法将荷载按正态分布的原则作用到路面结构模型上，应用改进的Paris公式及四阶龙格-库塔法则计算不同荷载作用位置、不同裂纹位置对应的路面结构的疲劳寿命。在此基础上，根据Miner损伤原则，确定了基于Top-Down裂纹的路面结构疲劳寿命。
对于混合式基层沥青路面进行反射裂纹疲劳寿命计算时，考虑车辆荷载每次经过裂纹时对裂尖造成的影响不同，根据断裂力学原理及修正后的Miner法则计算路面结构反射裂纹的疲劳寿命。
最后以青银高速公路混合式路面试验段为依托工程，进行了车辙深度及Top-Down裂纹、反射裂纹等疲劳寿命的预估计算。
本文从柔性基层沥青路面的病害入手，提出车辙、Top-Down裂纹、反射裂纹为设计指标，建立了柔性基层沥青路面性能预估模型，为柔性基层沥青路面在我国的推广应用起到一定的推进作用。
The flexible base is the necessary supplement to simi-rigid base for its excellentperformance. Its stress in the structure layer, which is caused by the vehicle load, is changedcertainly with the increase of depth of asphalt layer against the simi-rigid base. Under thecondition, it is a problem that calls for immediate solution in order to do the adoption andapplication of asphalt pavement with flexible base.
The indexes of deflection, compressive strain on the top of subgrade and tensile strain onthe bottom of asphalt layer, couldn't reflect the real pavement distress. The indexes of therutting, Top-Down crack and reflecting crack are proposed as the pavement design indexbased on the distress of asphalt pavement with flexible base. The performance forecastingmodels of asphalt pavement with flexible base are built. Upon the above research, the ruttingdepth and fatigue life of pavement are calculated. At last, taking Qindao-Yinchuan freewayfor instance, the rutting depth and fatigue life which originate from the Top-Down cracks andreflecting cracks, are calculated.
The dynamic modulus and phase angle of three kinds of asphalt mixture are determinedbased on the Frequency Sweep Test at different temperatures. In accordance with thetime-temperature equivalence principle, the master curves of dynamic modulus and phaseangle are determined through the applying of WLF equation and Sig-moidal function. Uponthe above research, the viscoelastic parameters of the generalized Maxwell model arecalculated by the Fourier transform. The achievements lay foundations of the ruttingcalculation. Moreover, the relaxation modulus determined by the test must be transformedinto bulk modulus and shear modulus in order to be applied by the finite element calculation.In view of this, the three-dimensional constitutive equation of generalized Maxwell model isdeduced. The coefficients of creep function are determined by the residue theorem. Uponthe above research, the expressions of bulk modulus and shear modulus are confirmed. At thesame time, the modulus of subgrade and simi-rigid material is backcalculated through the BPneural network according to the FWD. At last, the modulus of asphalt mixture are calculatedunder the circumstances of the certain vehicle speed and thickness of structure layer, based on the Frequency Sweep Test and considering the definition of effective depth. The above studiesprovide necessary parameters for the performance forecasting of test road.
When the rutting is numerically computed by using a commercial FEA program, ANSYS,the probability of loading at different pavement position is calculated according to theprobability and statistics theory under the circumstances of the different wander distance. Fivefactors including the magnitude of wheel loading, the wander distance, the speed of wheelloading, the number of load repetitions, and the modulus of subgrade are studied to evaluatetheir contributions of rutting development for asphalt pavements. The significance that eachfactor impacts on the rutting is analyzed in order to offer necessary, support for the pavementdesign and maintenance in the future.
When the fatigue life derived from the Top-Down crack is calculated, the load is appliedto the FEA model according to the rule of normal distribution. The improved Parisexpressions and fourth-order Runge-Kutta principle are adopted to calculate the fatigue life ofcorresponding pavement structure at different loading position and cracking position. On thebasis of this, the whole fatigue life derived from the Top-Down crack is calculated accordingto the Miner damage principle.
The fatigue life derived from the reflecting crack is calculated according to the Minerdamage principle, considering the factor that the development of the top for crack is differentwhen a vehicle load passed the crack.
At last, taking Qindao-Yinchuan freeway for instance, the rutting depth and fatigue lifewhich originate from the Top-Down cracks and reflecting cracks, are calculated.
引文
[1]．沈金安，如何解决路面结构设计中存在的问题[R]，第二届全国公路科技创新高层论坛，2004年．
[2]．沈金安，李福普等，高速公路沥青路面早期损坏分析与防治对策[M]，北京人民交通出版社，2004年．
[3]．沈金安，国外沥青路面设计方法总汇[M]，北京：人民交通出版社，2004年．
[4]．黄晓明，车同芝，张晓冰．沥青稳定基层路面结构设计综述[J]，河南交通科技，1999，V19(3)
[5]．姚祖康，对我国沥青路面现行设计指标的评述[J]，公路，2003，第2期
[6]．中华人民共和国交通部发布，公路沥青路面设计规范(JTG D50-2006)[S]，北京：人民交通出版社，2006年
[7]．朱照宏，许志鸿，柔性路面设计理论与方法[M]，上海：同济大学出版社，1985
[8]．黄卫，钱振东．高等沥青路面设计理论与方法[M]，北京：科学出版社，2001
[9]. AASHTO. AASHTO Guide for Design of Pavement Structures. Washington, 1993.
[10]．孙立军，路面结构行为理论[M]，上海：同济大学出版社，2004年．
[11]．交通部公路科学研究所译，壳牌路面设计手册[R]，1981．
[12]. TRB. Design of New and Reconstructed Flexible Pavements[R]. National Cooperative Highway REsearch Program, 2004
[13]. Carl L.Monismith. Evolution of Long-Lasting Asphalt Pavement Design Methodology: A Perspective [R]. International Symposium on Design and Construction of Long Lasting Asphalt Pavements,2003
[14]. M E Nunn. Design of Long-life Flexible Pavements for Heavy TraffiC. TRL Report 250.
[15]. Perpetual Bituminous Pavement, Transportation Research Circular Number 503,2001年.
[16]. A.A.A.Molenaar.Predication of Fatigue in Asphalt Pavements: Do We Follow the Right Approach [J]. TRB Annual Meeting. 2007
[17]．张志清，傅海滨等，防止沥青路面车辙产生的结构设计参数分析[J]，北京工业大学学报，2007
[18]．韩庆华．张永德等，柔性基层沥青路面车辙深度影响因素分析[J]，交通标准化，2009年，第一期
[19]．李高明，卢明华，高燕．车辙形成机理浅析[J]，交通标准化，2007年，第12期
[20]. Thomas D. White, HohnE.Haddock. Contributions of Pavement Structural layers to Rutting of Hot Mix Asphalt Pavement[R], Transportation Research Board,2003
[21]．徐世法．沥青路面的车辙深度与行车安全性[J]，北京建筑工程学院学报，1994，10(1)：47-51．
[22]．孙之芜，沥青路面早期破坏原因分析及预防措施[D]，合肥：合肥工业大学，2007
[23]. Sridhar Raju. Analysis of Top-Down Cracking Behavior of Asphalt Pavements. TRB Annual Meeting, 2008.
[24]. Sridhar RAJU, S.Satya Kumar, K. Sudhkar Reddy, et al, Analysis of Top-Down Cracking Behavior of Asphalt Pavements[R], TRB Annual Meeting, 2008
[25]．沙庆林著，高等级公路半刚性基层沥青路面[M]，北京：人民交通出版社，1999年
[26]．孙雅珍，赵颖华，含反射裂缝沥青路面粘弹损伤分析[J]，沈阳建筑工程学院学报(自然科学版)， 2002，V18(2)
[27]．杨挺青著，粘弹性力学[M]，上海：同济大学出版社，1989
[28].M.W. Witczak, Javed Bari. Development of A Master Curve (E~*) Database for Lime Modified Asphaltic Mixtures[R]. Arizona State University Research Project,2004
[29]．积分变换[M]，南京工学院数学教研组，北京：高等教育出版社，2003年
[30]．周光泉，刘孝敏，粘弹性理论[M]，合肥：中国科学技术大学出版社，1996
[31]．郭大智，任瑞波著，层状粘弹性体系力学[M]，哈尔滨：哈尔滨工业大学出版社，2001
[32]．(美)莫维尼(Moaveni，S)著，王菘译，有限元分析-ANSYS理论与应用[M]，第三版，北京：电子工业出版社，2008
[33].M.W. Witczak, K. Kaloush, T. Pellinen, Test Method for Dynamic Modulus of Asphalt Concrete Mixtures for Permanent Deformation[R]. NCHRP 465, 2002
[34].T. O. Medani, M. Huurman.Constructing the Stiffness Master Curves for Asphaltic Mixes[J],Delft University of Technology Faculty of Civil Engineering and GeoSciences
[35].Lytton, R.L., Uzan, J., Fernando, E.M., Roque, R., Hiltunen, D. and Stoffels,S.M., "Development and Validation of Performance Prediction Models and Specifications for Asphalt Binders and Paving Mixes," SHRP Report A-357,SHRP/NRC, Washington DC, USA, 1993.
[36]．陈爱文等，应用贝雷法设计和检验级配[J]，中外公路，2004
[37]．郝培文等，应用贝雷法进行级配组成设计的关键技术[J]，长安大学学报，2004，24(6)1-6
[38]. William R Vavrik William J Ping Samuel H Carpenter, Bailey Method for Gradation Selection in HMA Mixture Design, Transportation Research Circular Number E-C044, 2002
[39]．滕旭秋，李晓钟，沥青碎石基层混合料设计及碾压工艺研究[J]，兰州交通大学学报(自然科学版)，2007，V26(4)
[40].Pellinen, T.K., and Witczak M.W., "Stress Dependent Master Curve Construction for Dynamic (Complex) Modulus" Annual Meeting Association of Asphalt Paving Technologists, 2002.
[41].Andrei, D., Witczak, M., W, and Mirza, M. W. (1999).Development of Revised Predictive Model for the Dynamic(Complex) Modulus of Asphalt Mixtures. Development of the2002 Guide for the Design of New and Rehabilitated Pavement Structures, NCHRP 1-37A. Interim Team Technical Report. Department of Civil Engineering, University of Maryland at College Park, MD.
[42].AASHTO2002, Part2, Chart2, 2.2.8-2.2.11
[43]．赵延庆等，沥青混合料动态模量及其主曲线的确定与分析[J]，公路，2006，第八期，P163-166．
[44].Sunhgho Mun, Nonliner finite element analysis of pavements and its application to performance evaluation[D]. North Carolina State University.2003
[45].S.W.Park. R.A.Schapery. Methods of interconversion between linear viscoelastic material functions. Part Ⅰ-a nulnerical lnethod based on Prony series[J]. International Journal of Solids and Structures.1999,1653-1675
[46].R.A.Schapery, S.W.Park. Methods of interconversion between linear viscoelastic material functions. Part Ⅱ-an approximate analytical method[J].International Journal of Solids and Structures. 1999,1677-1699
[47]．黄崇伟，苏尔好，周正峰．利用FWD数据反算模量方法研究[J]，城市道桥与防洪，2007
[48]．查旭东，基于同伦方法的路面模量反算的研究[D]，西安：长安大学，2001
[49].Yusuf Mehta, Reynaldo Roque. Evaluation of FWD Data for Determination of Layer Moduli of Pavements[J],Journal of Materials in Civil Engineering, 2003
[50].Washington State Department of Transportation. EVERSERIES~(?) USER'S GUIDE-Pavement Analysis Computer Software and Case Studies, 2005.
[51].John R. Tabb, William G. A. Ray.et al. SHRP'S Layer Moduli Backcalculation Procedure[R], Strategic Highway Research Program.SHRP-P-655.1993
[52]．王后裕，朱可善等．沥青混合料蠕变柔量的一种实用模型及其应用[J]，固体力学学报，2002，23(2)：232-236．
[53]．钱家欢，殷宗泽，土工原理与计算[M]，第二版，北京：水利水电出版社，2003
[54]．邓亚红，车辆动荷载作用下路基下伏黄土暗穴稳定性分析[D]，西安：长安大学，2004
[55]．博弈创作室编著，ANSYS7.0基础教程与实例详解[M]，北京：中国水利水电出版社，2004．
[56]．李静，戴经梁，沥青混合料有效温度的计算和应用[J]，重庆交通学院学报，2004，V23
[57]．(美)黄仰贤著，余定选，齐诚译，路面分析与设计[M]，北京：人民交通出版社，1998
[58].Jianfeng Hua, Finite element modeling and analysis of accelerated pavement testing devices and rutting phenomenon[D],Purdue University,2000
[59]．张登良，李俊，高等级道路沥青路面车辙研究[J]，中国公路学报，第8卷第1期，1995
[60]．叶国铮．柔性路面疲劳与优化设计[M]，北京：人民交通出版社，1989
[61]．盛骤，谢式千等，概率论与数理统计[M]，北京：高等教育出版社，1997年．
[62]．李志辉，罗平，SPSS for Windows统计分析教程[M]，第2版，北京：电子工业出版社，2005
[63]．汪荣鑫．数理统计[M]．西安：西安交通大学出版社，2000
[64]．唐启义，冯光明，实用统计分析及其DPS数据处理系统[M]，北京：科学出版社，2002
[65]．沈成康著，断裂力学[M]，上海：同济大学出版社，1996
[66]. Anthonyr. Ingraffea, Stress-intensity Factor Computation in Three Dimensions with Quarter-point Elements[J], International Journal for Numerical Methods in Engineering,1980,V(15),1427-1445.
[67]．朱伯芳著，有限单元法原理与应用(第二版)[M]，北京：中国水利水电出版社，2004
[68]．小飒工作室编，最新经典ANSYS及Workbench教程[M]，北京：电子工业出版社，2004
[69]．吴志学，表面裂纹疲劳扩展的数值模拟，应用力学学报[J]，2006，V23(4)，563-567
[70]．吴志学，表面裂纹疲劳扩展的数值模拟(Ⅱ)，应用力学学报[J]，2007，V24(1)，42-46
[71]．龚曙光，谢桂兰，ANSYS操作命令与参数化编程[M]，北京：机械工业出版社，2004
[72]．宋启明，李国成，三维J积分在ANSYS中的计算，石油化工设备，V135(12)，2006
[73]．崔胜民，汽车轮胎行驶性能与测试[M]，北京：机械工业出版社，1998
[74].Jacobs, M.M.J. Crack growth in asphaltic mixes[D], Civil Engineering and Geosciences, 1995,
[75].L.A. Myers, B.E. Ruth, C. Drakos, Measurement of Contact Stress for Different Truck Tire Type to Evaluate Their Influence on Near-Surface Cracking and Rutting[J], 78th Annual Meeting of the Transportation Research Board, Washington, D.C, 1999
[76].Leslie Ann Myers. Development and Propagation of Surface-initiated Longitudinal Wheel Path Cracks in Flexible Highway[D]. The Ohio State University, 2000
[77]．郑健龙，周志刚等，沥青路面抗裂设计理论与方法[M]，北京：人民交通出版社，2002
[78]．罗睿，利用权函数理论分析沥青路面疲劳寿命[D]，南京：东南大学博士学位论文，2002年
[79]．倪向贵，李新亮，王秀喜，疲劳裂纹扩展规律Paris公式的一般修正及应用[J]，压力容器，2006，V23(12)
[80]．岳福青，杨春风，断裂力学理论在道路疲劳寿命预测中的应用[J]，昆明理工大学学报，2003，V28(6)
[81]．公路工程沥青及沥青混合料试验规程(JTJ 052-2000)[S]，北京：人民交通出版社
[82]．七维高科有限公式，综合优化软件包1stOpt使用手册
[83]．曾梦澜，马正军等，广义Paris公式预测沥青路面的疲劳寿命[J]，湖南大学学报，2005．
[84]．John H．Mathews著，周璐译，数值方法(Matlab版)[M]，第四版，北京：电子工业出版社，2007
[85]．沙庆林著，高速公路沥青路面早期破坏现象及预防[M]，北京：人民交通出版社，2001年
[86].Vanelstraete, L.Francken. Prevention of Reflection Cracking in Pavements[R].Rilem Report 18,1997
[87].A.A.A.Molenaar, Fatigue and reflection cracking due to traffic loads.AAPT1984,vol.53,440-474
[88].Aloysius Tjan, Crock Propagation Modeling in Flexible Pavement Structures[D], Arizona State University, 1996
[89].Mostafa M. Elseifi,Imad L. Al-Qadi,A Simplified Overlay Design Model against Reflective Cracking Utilizing Service Life Prediction[J],TRB2003
[90]．阚前华，谭长建，张娟等，ANSYS高级工程应用实例分析与二次开发[M]，北京：电子工业出版社，2006
[91].Fujie Zhou, Sheng Hu,Tom Scullion. Development and Verification of the Overlay Tester Based Fatigue Cracking Predicition Approach[R]. Texas Transportation Institute.2006
[92].Updated Traffic Frequency Calculation for Asphalt Layers[R]. Appendix CC-3-Guide for Mechanistic-Empirical Design, NCHRP, 2003
[2]．沈金安，李福普等，高速公路沥青路面早期损坏分析与防治对策[M]，北京人民交通出版社，2004年．
[3]．沈金安，国外沥青路面设计方法总汇[M]，北京：人民交通出版社，2004年．
[4]．黄晓明，车同芝，张晓冰．沥青稳定基层路面结构设计综述[J]，河南交通科技，1999，V19(3)
[5]．姚祖康，对我国沥青路面现行设计指标的评述[J]，公路，2003，第2期
[6]．中华人民共和国交通部发布，公路沥青路面设计规范(JTG D50-2006)[S]，北京：人民交通出版社，2006年
[7]．朱照宏，许志鸿，柔性路面设计理论与方法[M]，上海：同济大学出版社，1985
[8]．黄卫，钱振东．高等沥青路面设计理论与方法[M]，北京：科学出版社，2001
[9]. AASHTO. AASHTO Guide for Design of Pavement Structures. Washington, 1993.
[10]．孙立军，路面结构行为理论[M]，上海：同济大学出版社，2004年．
[11]．交通部公路科学研究所译，壳牌路面设计手册[R]，1981．
[12]. TRB. Design of New and Reconstructed Flexible Pavements[R]. National Cooperative Highway REsearch Program, 2004
[13]. Carl L.Monismith. Evolution of Long-Lasting Asphalt Pavement Design Methodology: A Perspective [R]. International Symposium on Design and Construction of Long Lasting Asphalt Pavements,2003
[14]. M E Nunn. Design of Long-life Flexible Pavements for Heavy TraffiC. TRL Report 250.
[15]. Perpetual Bituminous Pavement, Transportation Research Circular Number 503,2001年.
[16]. A.A.A.Molenaar.Predication of Fatigue in Asphalt Pavements: Do We Follow the Right Approach [J]. TRB Annual Meeting. 2007
[17]．张志清，傅海滨等，防止沥青路面车辙产生的结构设计参数分析[J]，北京工业大学学报，2007
[18]．韩庆华．张永德等，柔性基层沥青路面车辙深度影响因素分析[J]，交通标准化，2009年，第一期
[19]．李高明，卢明华，高燕．车辙形成机理浅析[J]，交通标准化，2007年，第12期
[20]. Thomas D. White, HohnE.Haddock. Contributions of Pavement Structural layers to Rutting of Hot Mix Asphalt Pavement[R], Transportation Research Board,2003
[21]．徐世法．沥青路面的车辙深度与行车安全性[J]，北京建筑工程学院学报，1994，10(1)：47-51．
[22]．孙之芜，沥青路面早期破坏原因分析及预防措施[D]，合肥：合肥工业大学，2007
[23]. Sridhar Raju. Analysis of Top-Down Cracking Behavior of Asphalt Pavements. TRB Annual Meeting, 2008.
[24]. Sridhar RAJU, S.Satya Kumar, K. Sudhkar Reddy, et al, Analysis of Top-Down Cracking Behavior of Asphalt Pavements[R], TRB Annual Meeting, 2008
[25]．沙庆林著，高等级公路半刚性基层沥青路面[M]，北京：人民交通出版社，1999年
[26]．孙雅珍，赵颖华，含反射裂缝沥青路面粘弹损伤分析[J]，沈阳建筑工程学院学报(自然科学版)， 2002，V18(2)
[27]．杨挺青著，粘弹性力学[M]，上海：同济大学出版社，1989
[28].M.W. Witczak, Javed Bari. Development of A Master Curve (E~*) Database for Lime Modified Asphaltic Mixtures[R]. Arizona State University Research Project,2004
[29]．积分变换[M]，南京工学院数学教研组，北京：高等教育出版社，2003年
[30]．周光泉，刘孝敏，粘弹性理论[M]，合肥：中国科学技术大学出版社，1996
[31]．郭大智，任瑞波著，层状粘弹性体系力学[M]，哈尔滨：哈尔滨工业大学出版社，2001
[32]．(美)莫维尼(Moaveni，S)著，王菘译，有限元分析-ANSYS理论与应用[M]，第三版，北京：电子工业出版社，2008
[33].M.W. Witczak, K. Kaloush, T. Pellinen, Test Method for Dynamic Modulus of Asphalt Concrete Mixtures for Permanent Deformation[R]. NCHRP 465, 2002
[34].T. O. Medani, M. Huurman.Constructing the Stiffness Master Curves for Asphaltic Mixes[J],Delft University of Technology Faculty of Civil Engineering and GeoSciences
[35].Lytton, R.L., Uzan, J., Fernando, E.M., Roque, R., Hiltunen, D. and Stoffels,S.M., "Development and Validation of Performance Prediction Models and Specifications for Asphalt Binders and Paving Mixes," SHRP Report A-357,SHRP/NRC, Washington DC, USA, 1993.
[36]．陈爱文等，应用贝雷法设计和检验级配[J]，中外公路，2004
[37]．郝培文等，应用贝雷法进行级配组成设计的关键技术[J]，长安大学学报，2004，24(6)1-6
[38]. William R Vavrik William J Ping Samuel H Carpenter, Bailey Method for Gradation Selection in HMA Mixture Design, Transportation Research Circular Number E-C044, 2002
[39]．滕旭秋，李晓钟，沥青碎石基层混合料设计及碾压工艺研究[J]，兰州交通大学学报(自然科学版)，2007，V26(4)
[40].Pellinen, T.K., and Witczak M.W., "Stress Dependent Master Curve Construction for Dynamic (Complex) Modulus" Annual Meeting Association of Asphalt Paving Technologists, 2002.
[41].Andrei, D., Witczak, M., W, and Mirza, M. W. (1999).Development of Revised Predictive Model for the Dynamic(Complex) Modulus of Asphalt Mixtures. Development of the2002 Guide for the Design of New and Rehabilitated Pavement Structures, NCHRP 1-37A. Interim Team Technical Report. Department of Civil Engineering, University of Maryland at College Park, MD.
[42].AASHTO2002, Part2, Chart2, 2.2.8-2.2.11
[43]．赵延庆等，沥青混合料动态模量及其主曲线的确定与分析[J]，公路，2006，第八期，P163-166．
[44].Sunhgho Mun, Nonliner finite element analysis of pavements and its application to performance evaluation[D]. North Carolina State University.2003
[45].S.W.Park. R.A.Schapery. Methods of interconversion between linear viscoelastic material functions. Part Ⅰ-a nulnerical lnethod based on Prony series[J]. International Journal of Solids and Structures.1999,1653-1675
[46].R.A.Schapery, S.W.Park. Methods of interconversion between linear viscoelastic material functions. Part Ⅱ-an approximate analytical method[J].International Journal of Solids and Structures. 1999,1677-1699
[47]．黄崇伟，苏尔好，周正峰．利用FWD数据反算模量方法研究[J]，城市道桥与防洪，2007
[48]．查旭东，基于同伦方法的路面模量反算的研究[D]，西安：长安大学，2001
[49].Yusuf Mehta, Reynaldo Roque. Evaluation of FWD Data for Determination of Layer Moduli of Pavements[J],Journal of Materials in Civil Engineering, 2003
[50].Washington State Department of Transportation. EVERSERIES~(?) USER'S GUIDE-Pavement Analysis Computer Software and Case Studies, 2005.
[51].John R. Tabb, William G. A. Ray.et al. SHRP'S Layer Moduli Backcalculation Procedure[R], Strategic Highway Research Program.SHRP-P-655.1993
[52]．王后裕，朱可善等．沥青混合料蠕变柔量的一种实用模型及其应用[J]，固体力学学报，2002，23(2)：232-236．
[53]．钱家欢，殷宗泽，土工原理与计算[M]，第二版，北京：水利水电出版社，2003
[54]．邓亚红，车辆动荷载作用下路基下伏黄土暗穴稳定性分析[D]，西安：长安大学，2004
[55]．博弈创作室编著，ANSYS7.0基础教程与实例详解[M]，北京：中国水利水电出版社，2004．
[56]．李静，戴经梁，沥青混合料有效温度的计算和应用[J]，重庆交通学院学报，2004，V23
[57]．(美)黄仰贤著，余定选，齐诚译，路面分析与设计[M]，北京：人民交通出版社，1998
[58].Jianfeng Hua, Finite element modeling and analysis of accelerated pavement testing devices and rutting phenomenon[D],Purdue University,2000
[59]．张登良，李俊，高等级道路沥青路面车辙研究[J]，中国公路学报，第8卷第1期，1995
[60]．叶国铮．柔性路面疲劳与优化设计[M]，北京：人民交通出版社，1989
[61]．盛骤，谢式千等，概率论与数理统计[M]，北京：高等教育出版社，1997年．
[62]．李志辉，罗平，SPSS for Windows统计分析教程[M]，第2版，北京：电子工业出版社，2005
[63]．汪荣鑫．数理统计[M]．西安：西安交通大学出版社，2000
[64]．唐启义，冯光明，实用统计分析及其DPS数据处理系统[M]，北京：科学出版社，2002
[65]．沈成康著，断裂力学[M]，上海：同济大学出版社，1996
[66]. Anthonyr. Ingraffea, Stress-intensity Factor Computation in Three Dimensions with Quarter-point Elements[J], International Journal for Numerical Methods in Engineering,1980,V(15),1427-1445.
[67]．朱伯芳著，有限单元法原理与应用(第二版)[M]，北京：中国水利水电出版社，2004
[68]．小飒工作室编，最新经典ANSYS及Workbench教程[M]，北京：电子工业出版社，2004
[69]．吴志学，表面裂纹疲劳扩展的数值模拟，应用力学学报[J]，2006，V23(4)，563-567
[70]．吴志学，表面裂纹疲劳扩展的数值模拟(Ⅱ)，应用力学学报[J]，2007，V24(1)，42-46
[71]．龚曙光，谢桂兰，ANSYS操作命令与参数化编程[M]，北京：机械工业出版社，2004
[72]．宋启明，李国成，三维J积分在ANSYS中的计算，石油化工设备，V135(12)，2006
[73]．崔胜民，汽车轮胎行驶性能与测试[M]，北京：机械工业出版社，1998
[74].Jacobs, M.M.J. Crack growth in asphaltic mixes[D], Civil Engineering and Geosciences, 1995,
[75].L.A. Myers, B.E. Ruth, C. Drakos, Measurement of Contact Stress for Different Truck Tire Type to Evaluate Their Influence on Near-Surface Cracking and Rutting[J], 78th Annual Meeting of the Transportation Research Board, Washington, D.C, 1999
[76].Leslie Ann Myers. Development and Propagation of Surface-initiated Longitudinal Wheel Path Cracks in Flexible Highway[D]. The Ohio State University, 2000
[77]．郑健龙，周志刚等，沥青路面抗裂设计理论与方法[M]，北京：人民交通出版社，2002
[78]．罗睿，利用权函数理论分析沥青路面疲劳寿命[D]，南京：东南大学博士学位论文，2002年
[79]．倪向贵，李新亮，王秀喜，疲劳裂纹扩展规律Paris公式的一般修正及应用[J]，压力容器，2006，V23(12)
[80]．岳福青，杨春风，断裂力学理论在道路疲劳寿命预测中的应用[J]，昆明理工大学学报，2003，V28(6)
[81]．公路工程沥青及沥青混合料试验规程(JTJ 052-2000)[S]，北京：人民交通出版社
[82]．七维高科有限公式，综合优化软件包1stOpt使用手册
[83]．曾梦澜，马正军等，广义Paris公式预测沥青路面的疲劳寿命[J]，湖南大学学报，2005．
[84]．John H．Mathews著，周璐译，数值方法(Matlab版)[M]，第四版，北京：电子工业出版社，2007
[85]．沙庆林著，高速公路沥青路面早期破坏现象及预防[M]，北京：人民交通出版社，2001年
[86].Vanelstraete, L.Francken. Prevention of Reflection Cracking in Pavements[R].Rilem Report 18,1997
[87].A.A.A.Molenaar, Fatigue and reflection cracking due to traffic loads.AAPT1984,vol.53,440-474
[88].Aloysius Tjan, Crock Propagation Modeling in Flexible Pavement Structures[D], Arizona State University, 1996
[89].Mostafa M. Elseifi,Imad L. Al-Qadi,A Simplified Overlay Design Model against Reflective Cracking Utilizing Service Life Prediction[J],TRB2003
[90]．阚前华，谭长建，张娟等，ANSYS高级工程应用实例分析与二次开发[M]，北京：电子工业出版社，2006
[91].Fujie Zhou, Sheng Hu,Tom Scullion. Development and Verification of the Overlay Tester Based Fatigue Cracking Predicition Approach[R]. Texas Transportation Institute.2006
[92].Updated Traffic Frequency Calculation for Asphalt Layers[R]. Appendix CC-3-Guide for Mechanistic-Empirical Design, NCHRP, 2003
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |