半刚性基层沥青混凝土路面反射裂缝形成扩展机理与基层预裂技术研究
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摘要
半刚性基层沥青路面的反射裂缝在我国高等级公路中普遍存在且难于防治。它严重影响了道路的使用寿命和行车安全。交通荷载和温度荷载是导致反射裂缝形成和扩展的主要因素。本文运用线弹性断裂力学理论对反射裂缝的扩展机理进行了全面分析，对基层预裂技术中合理切缝间距的确定方法进行了研究。
首先，对反射裂缝尖端应力场的奇异性进行了描述，建立了平面断裂问题应力强度因子的有限单元解。
其次，对含反射裂缝路面在交通荷载及温度荷载作用下的结构反应进行了深入分析。把交通荷载分为对称荷载和偏载两种情况，计算了裂缝尖端的拉应力、剪应力以及强度因子，并对路面结构进行了参数分析。对路面突然降温时的温度场进行了数值模拟，计算了温度应力作用下反射裂缝尖端的拉应力、应力强度因子，并对其进行了参数分析。而后对反射裂缝在行车荷载与温度荷载耦合作用下的裂缝扩展模式进行了研究。最后运用Paris公式对不同结构组合的路面进行了反射裂缝扩展速率的计算。分析计算结果表明，反射裂缝的扩展方式取决于裂缝尖端的受力情况，一般为复合型裂纹扩展。通过参数分析掌握了不同结构组合对反射裂缝扩展潜力及扩展速率的影响。
第三，在充分考虑到温度应力以及面层与基层、基层与土基之间的摩擦等因素后，建立了基层含预切缝路面的受力模型。通过结构参数分析掌握了预切缝间面层、基层中最大拉应力的分布规律。然后以预切缝上端应力强度因子、面层与基层内的最大拉应力为约束指标建立了合理预切缝间距的确定方法。
Reflective cracking which seriously affect pavement fatigue life and driving safety is widely existed in our country's highway and become into a hard problem to deal with. Traffic load and temperature load are two main factors accounting for its formation and propagation. In this paper, linear fracture mechanics is employed to give a full analysis to the mechanism of reflective crack's propagation and the reasonable spacing of the induced crack technology is studied as well.
Firstly, after depicting the singularity of stress field at the top of crack, the finite element method to calculate stress intensity factor of plain fracture problems is founded.
Secondly, the structural response of pavement suffering reflective cracking is deeply analyzed in terms of traffic load and thermal load. As for traffic load, two situation were analyzed, symmetrical load and asymmetric load, in each of them, crack top's tension stress, shear stress and stress intensity factor were calculated, also the effect of structural parameters were analyzed. Pavement's temperature distribution field when suffering sudden temperature dropping was numerical simulated. Crack top's tension stress and stress intensity factor caused by thermal stress were computed, structural parameters' sensitivity analysis were made as well. Then, reflective crack's propagation model under traffic load coupled with temperature load was analyzed. At last, reflective crack's propagation speed of different pavement structural combination was analyzed too. The analyzing result indicated that reflective crack's propagation model is decided by the stress at top of the crack, which often is a compound propagation model. By parameter analysis, reflective crack's propagation potential and speed are also cleared.
Thirdly, taking into account thermal stress, friction between surface and base and friction between base and soil, a mechanical model representing the pavement including induced crack is founded. The maximal tension stresses in surface and base between induced crack have been obtained by parametric analysis. Then, taking the maximal tension stress in surface and base and the stress intensity factor at the top of the induced crack as restraining indexes, method to determine the reasonable induced spacing has been determined.
首先，对反射裂缝尖端应力场的奇异性进行了描述，建立了平面断裂问题应力强度因子的有限单元解。
其次，对含反射裂缝路面在交通荷载及温度荷载作用下的结构反应进行了深入分析。把交通荷载分为对称荷载和偏载两种情况，计算了裂缝尖端的拉应力、剪应力以及强度因子，并对路面结构进行了参数分析。对路面突然降温时的温度场进行了数值模拟，计算了温度应力作用下反射裂缝尖端的拉应力、应力强度因子，并对其进行了参数分析。而后对反射裂缝在行车荷载与温度荷载耦合作用下的裂缝扩展模式进行了研究。最后运用Paris公式对不同结构组合的路面进行了反射裂缝扩展速率的计算。分析计算结果表明，反射裂缝的扩展方式取决于裂缝尖端的受力情况，一般为复合型裂纹扩展。通过参数分析掌握了不同结构组合对反射裂缝扩展潜力及扩展速率的影响。
第三，在充分考虑到温度应力以及面层与基层、基层与土基之间的摩擦等因素后，建立了基层含预切缝路面的受力模型。通过结构参数分析掌握了预切缝间面层、基层中最大拉应力的分布规律。然后以预切缝上端应力强度因子、面层与基层内的最大拉应力为约束指标建立了合理预切缝间距的确定方法。
Reflective cracking which seriously affect pavement fatigue life and driving safety is widely existed in our country's highway and become into a hard problem to deal with. Traffic load and temperature load are two main factors accounting for its formation and propagation. In this paper, linear fracture mechanics is employed to give a full analysis to the mechanism of reflective crack's propagation and the reasonable spacing of the induced crack technology is studied as well.
Firstly, after depicting the singularity of stress field at the top of crack, the finite element method to calculate stress intensity factor of plain fracture problems is founded.
Secondly, the structural response of pavement suffering reflective cracking is deeply analyzed in terms of traffic load and thermal load. As for traffic load, two situation were analyzed, symmetrical load and asymmetric load, in each of them, crack top's tension stress, shear stress and stress intensity factor were calculated, also the effect of structural parameters were analyzed. Pavement's temperature distribution field when suffering sudden temperature dropping was numerical simulated. Crack top's tension stress and stress intensity factor caused by thermal stress were computed, structural parameters' sensitivity analysis were made as well. Then, reflective crack's propagation model under traffic load coupled with temperature load was analyzed. At last, reflective crack's propagation speed of different pavement structural combination was analyzed too. The analyzing result indicated that reflective crack's propagation model is decided by the stress at top of the crack, which often is a compound propagation model. By parameter analysis, reflective crack's propagation potential and speed are also cleared.
Thirdly, taking into account thermal stress, friction between surface and base and friction between base and soil, a mechanical model representing the pavement including induced crack is founded. The maximal tension stresses in surface and base between induced crack have been obtained by parametric analysis. Then, taking the maximal tension stress in surface and base and the stress intensity factor at the top of the induced crack as restraining indexes, method to determine the reasonable induced spacing has been determined.
引文
[1] 沙庆林．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，2001．03
[2] 郑健龙，周志刚，张起森．沥青路面抗裂设计理论与方法[M]．北京：人民交通出版社，2002，12
[3] 何兆益．碎石基层防止半刚性路面裂缝及其路用性能研究[D]．东南大学博士论文，东南大学，南京，1997
[4] A.A.A. Molenaar. Structure Performance and Design of Flexible Pavement and Asphalt Overlay[D]. Delft university of technology, Delft, 1983
[5] 东北林学院道桥系译．近代道路路面设计．北京：人民交通出版社，1984
[6] 邓学钧，黄晓明．路面设计原理与方法．北京：人民交通出版社，2001，5
[7] Guide for Design of Pavement Structure. AASHTO. 1994
[8] 黄仰贤．路面分析与设计．北京：人民交通出版社，1998
[9] 公路沥青路面设计规范(JTJ 014-97)北京：人民交通出版社，1997
[10] 公路水泥混凝土路面设计规范(JTJ 012-94)北京：人民交通出版社，1994
[11] 姚祖康主编．公路设计手册．路面．北京：人民交通出版社，1997
[12] 姚祖康著．水泥混凝土路面设计．北京：人民交通出版社，1999
[13] E. M. Kauffman. The Application of Fracture Mechanics Concept to Predict Cracking of Flexible Pavement[D]. Ohio State University, U.S.A.,1973
[14] Majidzadeh, K. C. Buranarom. C. & Karakouzian. Application of Fracture Mechanics for Improved Design of Bituminous Concrete. Report No. FHWA-RD-76-91. Vol. 1, June, 1976
[15] N. F. Coetzee, C. L. Monismith. Analytical Study of Minimization of Reflection Cracking In Asphalt Concrete Overlays by Use of a Rubber-asphalt Interlayer. TRR 700, 1981
[16] J.P. Marchand, H. Goacolou. Cracking in Wearing Course. Proceedings of the 5~(th) ISAP, 1982.
[17] P.W. Jayqwickrama, R.E. Smith, R.L. Lytton, M.R. Tirado. Development of Asphalt Concrete Overlay Design Program for Reflective Cracking. Proceedings of RILEM Conf. On Reflective Cracking in Pavements, 1989.
[18] K. Majidzadeh, G. Sacharieh. The Study of Pavement Overlay Design. Final Report, Ohio State University, 1977.
[19] P. Joseph. Low Temperature Reflection Cracking though Asphalt Overlays[D]. University of Waterloo, Canada, 1987.
[20] J. A. Chen, J. A. D. Vito, G.A. Morris. Finite Element Analysis of Arizona's Three Layer Overlay System of Rigid Pavement to Prevent Reflective Cracking. Proceeding AAPT, Vol. 54, 1982.
[21] A.A.A. Molenear. Effects of Mix Modifications, Membrane Interlayer and Reinforcement on Prevention of Reflective Cracking of Asphalt Overlays. Proceedings of RILRM, 1989.
[22] A. Shalaby, etc. Low Temperature Stresses and Fracture Analysis of Asphalt Overlays. TRR 1539, 1996
[23] Lytton. R.L. & Tseng. K.H. Laboratory Evaluation of Overlays Reinforced with Fabrics. Texas Transportation Institute,1983
[24] S. B. Seeds, B. F. McCulloughm, F. Carmichael. Asphalt Concrete Overlay Design Procedure Research Report 1007, Portland Cement Pavement Transportation, Washington D.C. 1985.
[25] 张起森，郑健龙，刘益河．半刚性基层沥青路面的开裂机理[J]．土木工程学报，1992，2
[26] 刘益河，张起森，李志勇．沥青路面温度应力的光弹性研究[J]．中国公路学报，1991，4
[27] 张起森，刘益河．沥青路面开裂机理分析及试验研究[J]．长沙交通学院学报，1988，4(2)
[28] 刘益河，张起森．用光弹法确定半刚性路面基层开裂和裂缝稳定性问题[J]．长沙交通学院学报，1991，7
[29] 郑健龙，张起森．半刚性路面反射裂缝及其应力强度因子的有限元分析[J]．岩土工程学报，1990，3
[30] 吴赣昌．沥青路面温度裂缝尖端的应力强度因子分析[J]．中国公路学报，1995(2)
[31] 郑健龙，张起森．半刚性基层沥青路面表面裂缝的热效应分析[J]．长沙交通学院学报，1992，8(2)
[32] 吴赣昌，凌天清．半刚性基层温缩裂缝的扩展机理分析[J]．中国公路学报．1998(1)：21—28
[33] 吴赣昌．半刚性路面温度应力分析[M]．北京：科学出版社，1995．56-125．
[34] 周志刚，张起森．结构层组合对路面裂缝扩展的影响[J]．中国公路学报，1997，10(2)
[35] Majicdzadeh, K. & Ramsamooj, D.V. Development of Testing Procedure and a Method to Predict Fatigue Failures of Asphalt Concrete Paving Systems[R]. Ohio state university research foundation. Final report. 1971.
[36] P.D. de Verteuil. Fatigue Properties of Asphalt Concrete Field Specimens[D]. Ohio State university M.S. thesis, 1973.
[37] V.A. Karamians. Effect of Temperature on Fatigue Life of AsphalticMixture[D]. Ohio State University, M.S. thesis, 1973
[38] Ye Guozheng. Fatigue shear and fracture behavior of rubber bituminous pavement[M]. Reflective crack in pavement. London, 1996
[39] Schapery, R.A.. a theory of crack growth in viscoelastic media[R]. Report NN-2764-73-1, mechanics and materials research center. Texas A&M university,1973
[40] SchaperT, R.A.. Models for Damage Growth and Fracture in Nonlinear Viscoelastic particulate composites[J]. Proceedings of 9~(th) U.S. congress of applied mechanics. American society of mechanical engineering.
[41] 丁遂栋，孙利民．断裂力学[M]．北京：机械工业出版社，1997。
[42] 沈成康编著．断裂力学[M]．上海：同济大学出版社，1996
[43] 傅祥炯主编．结构疲劳与断裂[M]．西安：西北工业大学出版社，1995
[44] 刘涛，杨凤鹏主编．精通ANSYS[M]．北京：清华大学出版社，2001
[45] Jorge B. sousa, Jorge C. pais, R.N. stubstad. Mode of loading in reflective and flexural fatigue cracking-a numerical evaluation[J]. 4~(th) international RILEM Conference on reflective cracking in pavement research in practice, Ottawa, Canada, 2000.
[46] A.C. collop, D. cebon, a theoretical analysis of fatigue cracking in flexible pavements[J]. Proceedings of the institution of mechanical engineering, part C, vol. 209, no. C5,1995
[47] Amy L. Epps. an approach to examine thermal fatigue in asphalt concrete[J]. Asphalt paving technology, Vol. 68, 1999
[48] 吴赣昌．半刚性路面温度应力分析[M]．北京：科学出版社，1995．56-125．
[49] 吴赣昌．层状路面结构温度应力分析[J]．中国公路学报，1993，6(4)：1-8．
[50] 吴赣昌．沥青路面温缩裂缝的应力强度分析[J]．中国公路学报，1996，9(1)
[51] 赵佳军，黄晓明，邓学钧．具有接缝的水泥混凝土路面有限元分析[J]．重庆交通学院学报 1991，4
[52] 蒋应军．水泥稳定碎石基层收缩裂缝防治研究[D]．西安：长安大学，2001．
[53] 刘悦．旧水泥混凝土路面沥青加铺层的温度应力分析[D]．两安：长安大学，2000．
[54] 蒋新明，郑舟．摩阻理论在克服半刚性路面收缩裂缝中的应用研究[J]．公路，2002，10：1-6．
[55] 郑恒祥．刚性路面接缝间隔的力学模型[J]．郑州大学学报，2002，34(3)：60-64．
[56] David Harold Timm. A Phenomenological Model to Predict Thermal Crack Spacing of Asphalt Pavements[D]. University of Minnesota, 2001.
[57] Weixin Shen and David J. Kirkner. Thermal Cracking of Viscoelastic Asphalt Concrete
Pavement[J]. Journal of Engineering Mechanics, 2001,7:700-709.
[58] J. Rosier, etc.. Mixed Mode Fatigue Crack Propagation in Pavements Structures under Traffic load[J]. Reflective Cracking in Pavements. London, 1996
[59] A. Vanelstraete, L. Francken. Prevention of Reflective Cracking In Pavement[R]. RILEM Report 18, 1997。
[60] M.M. Jacobs. Crack Growth in Asphalt Mix[D]. Delft University of Technology, Delft. 1995
[61] A.H. de Bondt. Anti-Reflective cracking Design of (reinforced) Asphaltic Overlays[D] Ph.D. Thesis, University of Delft, 1999
[62] T. Vinson, V. Janoo, R. Hass. Summary report on low temperature and thermal Fatigue Cracking. SHAP-/IR-90-O01,1989
[63] M. Shahin, B.F. McCullough. Damage Model for Predicting Temperature Cracking in Flexible Pavement. Transportation Research Record 521, 1974.
[64] A.L. Epps. An approach to examine thermal fatigue in asphalt concrete. Proceedings AAPT, vol. 68, 1999.
[65] S. Carpenter, R. Lytton, J. Epps. Environmental Factors Relevant to Pavement Cracking in west Texas. Research Report 18-1, Texas transportation institute. 1974
[66] H. Chang, K Lytton, S. Carpenter. Prediction of Thermal Reflection Cracking in West Texas. Research Report 18-3, Texas Transportation institute, 1976
[67] S. Carpenter, R. Lytton. Thermal Payment Cracking in West Texas. Research Report 18-4, Texas Transportation Institute, 1977
[68] T. Eugawara, A. Morigoshi. Thermal Fracture of Bituminous Mixtures. Proceeding of Paving in Cold Areas Mini-Workshop, 1984, P291～320
[69] Jorge C. pais, Paulo A. A. Pereira. Prediction of existing reflective cracking potential of flexible pavements. 4~(th) international RILEM Conference on reflective Cracking in pavement research in practice, Ottawa, Canada, 2000
[2] 郑健龙，周志刚，张起森．沥青路面抗裂设计理论与方法[M]．北京：人民交通出版社，2002，12
[3] 何兆益．碎石基层防止半刚性路面裂缝及其路用性能研究[D]．东南大学博士论文，东南大学，南京，1997
[4] A.A.A. Molenaar. Structure Performance and Design of Flexible Pavement and Asphalt Overlay[D]. Delft university of technology, Delft, 1983
[5] 东北林学院道桥系译．近代道路路面设计．北京：人民交通出版社，1984
[6] 邓学钧，黄晓明．路面设计原理与方法．北京：人民交通出版社，2001，5
[7] Guide for Design of Pavement Structure. AASHTO. 1994
[8] 黄仰贤．路面分析与设计．北京：人民交通出版社，1998
[9] 公路沥青路面设计规范(JTJ 014-97)北京：人民交通出版社，1997
[10] 公路水泥混凝土路面设计规范(JTJ 012-94)北京：人民交通出版社，1994
[11] 姚祖康主编．公路设计手册．路面．北京：人民交通出版社，1997
[12] 姚祖康著．水泥混凝土路面设计．北京：人民交通出版社，1999
[13] E. M. Kauffman. The Application of Fracture Mechanics Concept to Predict Cracking of Flexible Pavement[D]. Ohio State University, U.S.A.,1973
[14] Majidzadeh, K. C. Buranarom. C. & Karakouzian. Application of Fracture Mechanics for Improved Design of Bituminous Concrete. Report No. FHWA-RD-76-91. Vol. 1, June, 1976
[15] N. F. Coetzee, C. L. Monismith. Analytical Study of Minimization of Reflection Cracking In Asphalt Concrete Overlays by Use of a Rubber-asphalt Interlayer. TRR 700, 1981
[16] J.P. Marchand, H. Goacolou. Cracking in Wearing Course. Proceedings of the 5~(th) ISAP, 1982.
[17] P.W. Jayqwickrama, R.E. Smith, R.L. Lytton, M.R. Tirado. Development of Asphalt Concrete Overlay Design Program for Reflective Cracking. Proceedings of RILEM Conf. On Reflective Cracking in Pavements, 1989.
[18] K. Majidzadeh, G. Sacharieh. The Study of Pavement Overlay Design. Final Report, Ohio State University, 1977.
[19] P. Joseph. Low Temperature Reflection Cracking though Asphalt Overlays[D]. University of Waterloo, Canada, 1987.
[20] J. A. Chen, J. A. D. Vito, G.A. Morris. Finite Element Analysis of Arizona's Three Layer Overlay System of Rigid Pavement to Prevent Reflective Cracking. Proceeding AAPT, Vol. 54, 1982.
[21] A.A.A. Molenear. Effects of Mix Modifications, Membrane Interlayer and Reinforcement on Prevention of Reflective Cracking of Asphalt Overlays. Proceedings of RILRM, 1989.
[22] A. Shalaby, etc. Low Temperature Stresses and Fracture Analysis of Asphalt Overlays. TRR 1539, 1996
[23] Lytton. R.L. & Tseng. K.H. Laboratory Evaluation of Overlays Reinforced with Fabrics. Texas Transportation Institute,1983
[24] S. B. Seeds, B. F. McCulloughm, F. Carmichael. Asphalt Concrete Overlay Design Procedure Research Report 1007, Portland Cement Pavement Transportation, Washington D.C. 1985.
[25] 张起森，郑健龙，刘益河．半刚性基层沥青路面的开裂机理[J]．土木工程学报，1992，2
[26] 刘益河，张起森，李志勇．沥青路面温度应力的光弹性研究[J]．中国公路学报，1991，4
[27] 张起森，刘益河．沥青路面开裂机理分析及试验研究[J]．长沙交通学院学报，1988，4(2)
[28] 刘益河，张起森．用光弹法确定半刚性路面基层开裂和裂缝稳定性问题[J]．长沙交通学院学报，1991，7
[29] 郑健龙，张起森．半刚性路面反射裂缝及其应力强度因子的有限元分析[J]．岩土工程学报，1990，3
[30] 吴赣昌．沥青路面温度裂缝尖端的应力强度因子分析[J]．中国公路学报，1995(2)
[31] 郑健龙，张起森．半刚性基层沥青路面表面裂缝的热效应分析[J]．长沙交通学院学报，1992，8(2)
[32] 吴赣昌，凌天清．半刚性基层温缩裂缝的扩展机理分析[J]．中国公路学报．1998(1)：21—28
[33] 吴赣昌．半刚性路面温度应力分析[M]．北京：科学出版社，1995．56-125．
[34] 周志刚，张起森．结构层组合对路面裂缝扩展的影响[J]．中国公路学报，1997，10(2)
[35] Majicdzadeh, K. & Ramsamooj, D.V. Development of Testing Procedure and a Method to Predict Fatigue Failures of Asphalt Concrete Paving Systems[R]. Ohio state university research foundation. Final report. 1971.
[36] P.D. de Verteuil. Fatigue Properties of Asphalt Concrete Field Specimens[D]. Ohio State university M.S. thesis, 1973.
[37] V.A. Karamians. Effect of Temperature on Fatigue Life of AsphalticMixture[D]. Ohio State University, M.S. thesis, 1973
[38] Ye Guozheng. Fatigue shear and fracture behavior of rubber bituminous pavement[M]. Reflective crack in pavement. London, 1996
[39] Schapery, R.A.. a theory of crack growth in viscoelastic media[R]. Report NN-2764-73-1, mechanics and materials research center. Texas A&M university,1973
[40] SchaperT, R.A.. Models for Damage Growth and Fracture in Nonlinear Viscoelastic particulate composites[J]. Proceedings of 9~(th) U.S. congress of applied mechanics. American society of mechanical engineering.
[41] 丁遂栋，孙利民．断裂力学[M]．北京：机械工业出版社，1997。
[42] 沈成康编著．断裂力学[M]．上海：同济大学出版社，1996
[43] 傅祥炯主编．结构疲劳与断裂[M]．西安：西北工业大学出版社，1995
[44] 刘涛，杨凤鹏主编．精通ANSYS[M]．北京：清华大学出版社，2001
[45] Jorge B. sousa, Jorge C. pais, R.N. stubstad. Mode of loading in reflective and flexural fatigue cracking-a numerical evaluation[J]. 4~(th) international RILEM Conference on reflective cracking in pavement research in practice, Ottawa, Canada, 2000.
[46] A.C. collop, D. cebon, a theoretical analysis of fatigue cracking in flexible pavements[J]. Proceedings of the institution of mechanical engineering, part C, vol. 209, no. C5,1995
[47] Amy L. Epps. an approach to examine thermal fatigue in asphalt concrete[J]. Asphalt paving technology, Vol. 68, 1999
[48] 吴赣昌．半刚性路面温度应力分析[M]．北京：科学出版社，1995．56-125．
[49] 吴赣昌．层状路面结构温度应力分析[J]．中国公路学报，1993，6(4)：1-8．
[50] 吴赣昌．沥青路面温缩裂缝的应力强度分析[J]．中国公路学报，1996，9(1)
[51] 赵佳军，黄晓明，邓学钧．具有接缝的水泥混凝土路面有限元分析[J]．重庆交通学院学报 1991，4
[52] 蒋应军．水泥稳定碎石基层收缩裂缝防治研究[D]．西安：长安大学，2001．
[53] 刘悦．旧水泥混凝土路面沥青加铺层的温度应力分析[D]．两安：长安大学，2000．
[54] 蒋新明，郑舟．摩阻理论在克服半刚性路面收缩裂缝中的应用研究[J]．公路，2002，10：1-6．
[55] 郑恒祥．刚性路面接缝间隔的力学模型[J]．郑州大学学报，2002，34(3)：60-64．
[56] David Harold Timm. A Phenomenological Model to Predict Thermal Crack Spacing of Asphalt Pavements[D]. University of Minnesota, 2001.
[57] Weixin Shen and David J. Kirkner. Thermal Cracking of Viscoelastic Asphalt Concrete
Pavement[J]. Journal of Engineering Mechanics, 2001,7:700-709.
[58] J. Rosier, etc.. Mixed Mode Fatigue Crack Propagation in Pavements Structures under Traffic load[J]. Reflective Cracking in Pavements. London, 1996
[59] A. Vanelstraete, L. Francken. Prevention of Reflective Cracking In Pavement[R]. RILEM Report 18, 1997。
[60] M.M. Jacobs. Crack Growth in Asphalt Mix[D]. Delft University of Technology, Delft. 1995
[61] A.H. de Bondt. Anti-Reflective cracking Design of (reinforced) Asphaltic Overlays[D] Ph.D. Thesis, University of Delft, 1999
[62] T. Vinson, V. Janoo, R. Hass. Summary report on low temperature and thermal Fatigue Cracking. SHAP-/IR-90-O01,1989
[63] M. Shahin, B.F. McCullough. Damage Model for Predicting Temperature Cracking in Flexible Pavement. Transportation Research Record 521, 1974.
[64] A.L. Epps. An approach to examine thermal fatigue in asphalt concrete. Proceedings AAPT, vol. 68, 1999.
[65] S. Carpenter, R. Lytton, J. Epps. Environmental Factors Relevant to Pavement Cracking in west Texas. Research Report 18-1, Texas transportation institute. 1974
[66] H. Chang, K Lytton, S. Carpenter. Prediction of Thermal Reflection Cracking in West Texas. Research Report 18-3, Texas Transportation institute, 1976
[67] S. Carpenter, R. Lytton. Thermal Payment Cracking in West Texas. Research Report 18-4, Texas Transportation Institute, 1977
[68] T. Eugawara, A. Morigoshi. Thermal Fracture of Bituminous Mixtures. Proceeding of Paving in Cold Areas Mini-Workshop, 1984, P291～320
[69] Jorge C. pais, Paulo A. A. Pereira. Prediction of existing reflective cracking potential of flexible pavements. 4~(th) international RILEM Conference on reflective Cracking in pavement research in practice, Ottawa, Canada, 2000