含裂纹路面结构的理论分析
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摘要
近年来,随着我国公路交通事业的不断发展,主体公路网的建设已经基本完成。旧路的养护和维修成为道路工程技术人员及科研工作者关注的重点。在交通荷载及温度应力的反复作用下,在旧路面结构中出现裂纹是一种比较常见的路面早期损坏形式。随着裂缝的不断扩展,严重影响了路面上车辆行驶的安全性和舒适性。开展含裂纹路面结构以及有加铺层的含裂纹路面结构的研究可以更加全面的评价路面的使用状况。同时也对路面进行维修以及加铺的路面的合理的选择具有非常重要的理论意义和实用价值。针对这一问题本文开展以下几个方面进行研究：
(1)建立含裂纹旧水泥路面的理论分析模型,分别考虑了裂纹出现在路表面及面层底部两种情况,将水泥路面视为Winkler地基上的弹性板,利用傅立叶积分变换将偏微分方程组转化为常微分方程组,使微分方程组的求解更加简单。引入位错密度函数并应用留数定理计算复杂积分,推导出任一点位移与应力的解析表达式。对建立的奇异积分方程,应用Lobatto—Chebyshev法求解奇异积分方程并根据应力强度因子的定义求得应力强度因子的数值解。分析含裂纹水泥路面在车辆荷载作用下路面内部应力分布状态及影响裂纹尖端应力分布的因素。对路面的及时维修做出合理的判断。
(2)建立含裂纹沥青路面的理论分析模型,将沥青路面视为各向同性的多层弹性体,利用傅立叶积分变换,引入位错密度函数,建立奇异积分方程,推导出任一点应力与位移的解析表达式,应用Lobatto—Chebyshev法求解奇异积分方程求得应力强度因子的数值解。分析含裂纹沥青路面在荷载作用下裂纹尖端附近的应力分布状态。
(3)对有加铺层结构含裂纹水泥路面进行应力、位移及应力强度因子解析表达式的推导,并求解应力强度因子的数值解。分别选择不同的加铺层厚度、加铺层弹性模量及不同的荷载位置分析加铺层对于阻止裂纹扩展的作用。分析加铺层厚度、弹性模量等因素对加铺层作用的影响。
(4)对有加铺层结构含裂纹旧沥青路面进行应力、位移及应力强度因子解析表达式的推导,并求解应力强度因子的数值解。分析加铺层对旧沥青路面中裂纹扩展的阻碍作用。分别选择在不同荷载位置及不同加铺层弹性模量情况下旧沥青路面中裂纹尖端应力强度因子值的大小。
In recent years, with the development of highway transportation, the construction of main road network has been finished in our country. Therefore, more and more engineers and experts pay their attention to the research of pavement maintenance and rehabilitation. Cracking is one of the main forms of early damage of pavement structure caused by cyclic traffic and temperature loads. With the propagation of cracks in the pavement, it will seriously affect the travelling safety and comfort. In order to evaluate the comprehensive situation of the pavement and take the appropriate measures to repair the road, the research for the pavement with cracks and pavement with an overlay is necessary. This dissertation has mainly covered the studies on four issues as follows:
(1) In order to simplify the problem, a cement concrete pavement is reduced to an elastic plate on Winkler foundation with cracks on the surface or at the bottom. To solve the problem simply, the Fourier transform is used to convert the partial differential equations into the ordinary differential equations. Dislocation density function is introduced and the residue theorem is used to calculate the complex integrals. Lobatto—Chebyshev integration formula, as a numerical method, is used to solve the singular integral equations. The numerical solutions of stress intensity factors at the crack tip are given. Cement concrete pavement with a crack is considered with the method described in this part and the influence factors are analyzed that affect the stress distributions near the crack tip. According to the results of calculation, appropriate decisions on whether the old road should be repaired or not can be made.
(2) A model for asphalt concrete pavement is established. It is reduced to the elastic multilayered structure with a crack in one layer perpendicular to the surface. To solve the problem simply, the Fourier transform is used to convert the partial differential equations into the ordinary differential equations. Dislocation density function is introduced. According to the boundary conditions, the residue theorem is used to calculate the complex integrals and the stresses and strains of any point in the pavement can be expressed by the dislocation density function. Lobatto—Chebyshev integration formula, as a numerical method, is used to solve the singular integral equations. The numerical solutions of stress intensity factors at the crack tip are given. The stress and strain distributions near the crack tip are analyzed by the method mentioned in this part.
(3) To analyze the mechanical behaviors of the cement concrete pavement with an asphalt overlay, the expressions of stresses and displacements are derived and the numerical results of the stress intensity factors of the crack tip are calculated. Comparing the numerical results of stress intensity factors with different thicknesses and elastic moduli of the overlay and different horizontal distances of the traffic load from the crack, the main factors that impact the overlay and optimize the technology of asphalt overlay are obtained.
(4) In order to analyze the mechanical behaviors of the asphalt concrete pavement with an asphalt overlay, the expressions of stresses and displacements are derived and the numerical results of the stress intensity factors of the crack tip are calculated. The actions of asphalt overlay which resist the growth of cracks are analyzed and the stress intensity factors of crack tips with different elastic moduli of the asphalt overlay and different horizontal distances of the traffic load from the crack are obtained and compared.
(1)建立含裂纹旧水泥路面的理论分析模型,分别考虑了裂纹出现在路表面及面层底部两种情况,将水泥路面视为Winkler地基上的弹性板,利用傅立叶积分变换将偏微分方程组转化为常微分方程组,使微分方程组的求解更加简单。引入位错密度函数并应用留数定理计算复杂积分,推导出任一点位移与应力的解析表达式。对建立的奇异积分方程,应用Lobatto—Chebyshev法求解奇异积分方程并根据应力强度因子的定义求得应力强度因子的数值解。分析含裂纹水泥路面在车辆荷载作用下路面内部应力分布状态及影响裂纹尖端应力分布的因素。对路面的及时维修做出合理的判断。
(2)建立含裂纹沥青路面的理论分析模型,将沥青路面视为各向同性的多层弹性体,利用傅立叶积分变换,引入位错密度函数,建立奇异积分方程,推导出任一点应力与位移的解析表达式,应用Lobatto—Chebyshev法求解奇异积分方程求得应力强度因子的数值解。分析含裂纹沥青路面在荷载作用下裂纹尖端附近的应力分布状态。
(3)对有加铺层结构含裂纹水泥路面进行应力、位移及应力强度因子解析表达式的推导,并求解应力强度因子的数值解。分别选择不同的加铺层厚度、加铺层弹性模量及不同的荷载位置分析加铺层对于阻止裂纹扩展的作用。分析加铺层厚度、弹性模量等因素对加铺层作用的影响。
(4)对有加铺层结构含裂纹旧沥青路面进行应力、位移及应力强度因子解析表达式的推导,并求解应力强度因子的数值解。分析加铺层对旧沥青路面中裂纹扩展的阻碍作用。分别选择在不同荷载位置及不同加铺层弹性模量情况下旧沥青路面中裂纹尖端应力强度因子值的大小。
In recent years, with the development of highway transportation, the construction of main road network has been finished in our country. Therefore, more and more engineers and experts pay their attention to the research of pavement maintenance and rehabilitation. Cracking is one of the main forms of early damage of pavement structure caused by cyclic traffic and temperature loads. With the propagation of cracks in the pavement, it will seriously affect the travelling safety and comfort. In order to evaluate the comprehensive situation of the pavement and take the appropriate measures to repair the road, the research for the pavement with cracks and pavement with an overlay is necessary. This dissertation has mainly covered the studies on four issues as follows:
(1) In order to simplify the problem, a cement concrete pavement is reduced to an elastic plate on Winkler foundation with cracks on the surface or at the bottom. To solve the problem simply, the Fourier transform is used to convert the partial differential equations into the ordinary differential equations. Dislocation density function is introduced and the residue theorem is used to calculate the complex integrals. Lobatto—Chebyshev integration formula, as a numerical method, is used to solve the singular integral equations. The numerical solutions of stress intensity factors at the crack tip are given. Cement concrete pavement with a crack is considered with the method described in this part and the influence factors are analyzed that affect the stress distributions near the crack tip. According to the results of calculation, appropriate decisions on whether the old road should be repaired or not can be made.
(2) A model for asphalt concrete pavement is established. It is reduced to the elastic multilayered structure with a crack in one layer perpendicular to the surface. To solve the problem simply, the Fourier transform is used to convert the partial differential equations into the ordinary differential equations. Dislocation density function is introduced. According to the boundary conditions, the residue theorem is used to calculate the complex integrals and the stresses and strains of any point in the pavement can be expressed by the dislocation density function. Lobatto—Chebyshev integration formula, as a numerical method, is used to solve the singular integral equations. The numerical solutions of stress intensity factors at the crack tip are given. The stress and strain distributions near the crack tip are analyzed by the method mentioned in this part.
(3) To analyze the mechanical behaviors of the cement concrete pavement with an asphalt overlay, the expressions of stresses and displacements are derived and the numerical results of the stress intensity factors of the crack tip are calculated. Comparing the numerical results of stress intensity factors with different thicknesses and elastic moduli of the overlay and different horizontal distances of the traffic load from the crack, the main factors that impact the overlay and optimize the technology of asphalt overlay are obtained.
(4) In order to analyze the mechanical behaviors of the asphalt concrete pavement with an asphalt overlay, the expressions of stresses and displacements are derived and the numerical results of the stress intensity factors of the crack tip are calculated. The actions of asphalt overlay which resist the growth of cracks are analyzed and the stress intensity factors of crack tips with different elastic moduli of the asphalt overlay and different horizontal distances of the traffic load from the crack are obtained and compared.
引文
[1]姚祖康.水泥混凝土路面设计[M].合肥：安徽科学技术出版社,1999.
[2]吴国雄,梅迎军,李力.半柔性复合路面设计与施工[M].北京：人民交通出版社,2009.
[3]王秉刚,郑木莲.水泥混凝土路面设计与施工[M].北京：人民交通出版社,2004.
[4]邓学钧,黄晓明.路面设计原理与方法[M].北京：人民交通出版社,2007.
[5]朱照宏,许志鸿.柔性路面设计理论和方法[M].上海：同济大学出版社,1987.
[6]胡长顺,王秉刚.复合式路面设计原理与施工技术[M].北京：人民交通出版社,1999.
[7]林秀贤.柔性路面结构设计方法[M].北京：人民交通出版社,1988.
[8]梁锡三,唐有君.柔性路面设计[M].北京：人民交通出版社,1982.
[9]邓学钧,陈荣生.刚性路面设计[M].北京：人民交通出版社,1990.
[10]黄晓明.水泥路面设计[M].北京：人民交通出版社,2003.
[11]李华,缪昌文,金志强.水泥混凝土路面修补技术[M].北京：人民交通出版社,1999.
[12]黄仰贤.路面分析与设计[M].北京：人民交通出版社,1998.
[13]TSCHEGG E K, EH ART R J A, INGRUBER M M. Fracture Behavior of Geosynthetic Interlayers in Road pavements [J]. Journal of Transportation Engineering,1998,124(5):457-464.
[14]LIU K,WANG F. Computer Modeling Mechanical Analysis for Asphalt Overlay under Coupling Action of Temperature and Loads [J].Advanced in Control Engineering and Information Science,2011,15:5338-5342.
[15]CHEN D H, WON M. Field Investigations of Cracking on Concrete Pavements[J].Journal of Performance of Constructed Facilities.2007,21(6):450-458.
[16]WANG Y H, Mahboub K C, Hancher D E. Dynamic Panel Data Model for Predicting Performance of Asphalt Concrete Overlay [J]. Journal of Transportation Engineering,2008,134(2):86-92.
[17]PRIETO J N, GALLEGO J, PE'REZ I. Application of the Wheel Reflective Cracking Test for Assessing Geosynthetics in Anti-reflection Pavement Cracking Systems [J].Geosynthetics International,2007,14(5):287-297.
[18]RAMSAMOOJ D V, LIN G S, RAMADAN J. Stresses at Joints and Cracks in Highway and airport Pavements[J]. Engineering Fracture Mechanics,1998,60(5-6):507-508.
[19]李淑明.旧PCC路面上AC加铺层设计方法的研究[D].上海：同济大学,2002.
[20]曾四平,郭少华,陈绍名等RCC-AC路面温度荷载型断裂的有限元分析[J].中南大学学报自然科学版,2005,36(1)：149-154.
[21]蒙云,姜波.应用F.C.防治旧砼路面反射裂缝的探索[J].重庆交通学院学报,2007,26(3)：62-66.
[22]彭自强,李辉,徐一心,李纲.城市旧水泥混凝土路面加铺沥青面层裂缝病害研究[J].华中科技大学学报(城市科学版),2010,27(2)：40-44.
[23]周富杰,孙立军.反射裂缝的足尺疲劳试验研究及其力学分析[J].土木工程学报,2001,34(3)：78-85.
[24]王秉纲.有沥青上面层的水泥混凝土路面的应力分析[J].公路,2002,8：23-27.
[25]王芳,王选仓,刘凯.旧水泥板加铺沥青层设计方法研究[J].合肥工业大学学报(自然科学版),2010,33(4)：548-554.
[26]祝海燕,王选仓.沥青加铺混凝土路面的实用计算方法[J].河北工业大学学报,2007,36(6)：106-111.
[27]KIM S M, NELSON P K. Experimental and Numerical Analyses of PCC Overlays on PCC Slabs-on-grade Subjected to Climatic Loading [J]. International Journal of Solids and Structures,2004,41:785-800.
[28]WHITE L W, ZAMAN M. Coupling Elastic Models Through Interfacial Conditions with Application to Concrete Pavement Overlays[J].Applied Mathematics and Computation,2001,123:187-204.
[29]KHODAII A, FALLAH S, FEREIDOON M N. Effects of Geosynthetics on Reduction of Reflection Cracking in Asphalt Overlays[J]. Geotextiles and Geomembranes,2009,27:1-8.
[30]侯利国,洪秀敏,马建青等.碎石化技术在旧水泥路面改造加铺沥青路面中的应用[J].中外公路,2005,25(5)：41-44.
[31]李廷刚,刘甲荣,陈不东.冲压破裂稳固技术在水泥路面白改黑工程中的应用研究[J].公路交通科技,2010,27(7)：36-41.
[32]BOZKURT D. Three-dimensional Finite Element Analysis to Evaluate Reflective Cracking Potential in Asphalt Concrete Overlays [D]. Urbana-Champaig:University of Illinois at Urbana-Champaign, 2002.
[33]CHO Y H, LIU C, DOSSCY T, et al. Asphalt Overlay Design Methods for Rigid Pavements Considering Rutting,Reflection Cracking, and Fatigue Cracking. Research Report 987-9[R]. The University of Texas at Austin,1998,(9):11-18.
[34]ESHAN V D, WILLIAM G B. Thermal reflective cracking of asphalt concrete overlays[J]. International Journal of Pavement Engineering,2010,11(6):477-488.
[35]YIN H M, BUTTLAR W G, PAULINO G H. Simplified Solution for Periodic Thermal Discontinuities in Asphalt Overlays Bonded to Rigid Pavements[J]. Journal of Transportation Engineering,2007,133 (1):39-46.
[36]胡长顺,曹东伟.有防裂夹层结构的旧水泥混凝土路面沥青加铺层力学分析[J].中国公路学报,1995,12：1-8.
[37]王宏畅,侯维俊,黄晓明.沥青加铺层反射裂缝有限元分习[J].华中科技大学学报(城市科学版),2007,24(3)：91-95.
[38]金文成,王先强,黄小弟.水泥路面沥青加罩不同计算参数的有限元分析[J].华中·科技大学学报(自然科学版),2003,12(31)：107-110.
[39]杨德灿,赵文婷,李黎杰等.旧水泥路面沥青加铺层反射裂缝有限元分析[J].华中科技大学学报报,2009.37(1)：61-64.
[40]黄金,吴进良,李鑫等.旧水泥路面沥青加铺层反射裂缝应力分析[J].重庆交通大学学报(自然科学版),2010,29(2)：203-207.
[41]ELSEIFI M A, AL-QADI I L. Effectiveness of Steel Reinforcing Nettings in Combating Fatigue Cracking in New Flexible Pavement Systems [J]. Journal of Transportation Engineering, 2005,131(1):37-45.
[42]赵延庆,王抒红,周长红等.沥青路面Top-Down裂缝的断裂力学分析[J].同济大学学报(自然科学版),2010,38(2)：218-223.
[43]赵延庆,王国忠,王志超等.基于动态模量的沥青路面开裂分析[J].湖南大学学报(自然科学版),2010,37(7)：7-12.
[44]赵磊,樊统江,何兆益等.荷载作用下半刚性基层沥青路面开裂原因分析[J].重庆交通大学学报(自然科学版),2009,28(1)：49-55.
[45]程英伟,汤捷.高等级公路半刚性基层沥青路面开裂的机理分析及防治[J].公路交通技术,2004,12(6)：39-43.
[46]罗辉,李武芳,朱宏平等.沥青路面表面裂纹扩展机理研究[J].应用基础与工程科学学报,2010,18(3)：452-462.
[47]李峰,孙立军.沥青路面Top-Down开裂成因的有限元分析[J].公路交通科技,2006,23(6)：1-5.
[48]ELSEIFI M A, AL-QADI I L. Modeling of Strain Energy Absorbers for Rehabilitated Cracked Flexible Pavements [J]. Journal of Transportation Engineering,2005,131(9):653-661.
[49]WANG Y H, MAHBOUB K C, HANCHER D E. Survival Analysis of Fatigue Cracking for Flexible Pavements Based on Long-Term Pavement Performance Data [J]. Journal of Transportation Engineering,2005,131 (8):608-616.
[50]BORDELON A, ROESLER J. Design with Fiber Reinforcement for Thin Concrete Overlays Bonded to Asphalt [J]. Journal of Transportation Engineering,2012,138 (4):430-435.
[51]GAO L, AGUIAR-MOYA J P, ZHANG Z M. Bayesian Analys is of Heterogene ity in Modeling of Pavement Fatigue Cracking[J]. Journal of Computing in Civil Engineering,2012,26(1):37-43.
[52]KIM J, ROQUE R, BYRON T. Viscoelastic Analysis of Flexible Pavements and Its Effects on Top-Down Cracking [J]. Journal of Materials in Civil Engineering,2009,21(7):324-332.
[53]MOHAMMAD F A, COLLOP A C, BROWN S F. Effects of Surface Cracking on Responses in Flexible Pavements [J]. Proceedings of the Institution of Civil Engineers- Transport,2005,158(2): 127-134.
[54]MIAO Y, HE T G, YANG Q, et al. Multi-domain Hybrid Boundary Node Method for Evaluating Top-down Crack in Asphalt Pavements [J]. Engineering Analysis with Boundary Elements,2010, 34:755-760.
[55]CHANG X, YAN A Z, LIAO M C, et al. Analysis of Periodic Cracks in Surface Layer of Pavement Structures [J]. Engineering Failure Analysis,2011,18:411-420.
[56]AMERI M, MANSOURIAN A, HEIDARY KHAVAS M, et al. Cracked Asphalt Pavement under Traffic Loading-A 3D Finite Element Analysis [J]. Engineering Fracture Mechanics,2011,78:1817-1826.
[57]SUO Z, WONG W G, LUO X H, et al. Evaluation of Fatigue Crack Behavior in Asphalt Concrete Pavements with Different Polymer Modifiers [J]. Construction and Building Materials,2012,27: 117-125.
[58]吴赣昌,张淦生.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)：37-44.
[59]仰建岗,王秉纲,陈拴发.基于修正Neuber方程的沥青路面裂缝形成疲劳寿命预估方法[J].交通运输工程学报,2007,7(2)：50-56.
[60]王新东.沥青路面裂缝的原因及处治措施[J].公路交通科技,2009,26(5)：217-220.
[61]郑建龙,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,2003.
[62]詹永祥,姚海林,卢正.表面含裂缝沥青面低温收缩断裂分析[J].交通科学与工程,2010,26(3)：20-24.
[63]罗辉,朱宏平,陈传尧.预切口沥青混合料小梁疲劳试验研究[J].华中科技大学学报(城市科学版),2008,25(1)：47-51.
[64]LYTTON R L, U.SHANMUGHAM B D. Garrett. Design of asphalt pavements for thermal fatigue cracking[C] Report FHWA/TX-83-284-4, Texas Transportation Institute, Texas A&M University, 1983:91-105.
[65]UZAN J, SIDES A, PERL M. Viscoelasoplatic Model for Predicting Performance of Asphaltic Mixtures[J]. Transportation Research Record,1985:78-88.
[66]ABDULSHAFI A A, MAJIDZADEH K. J-Integral and cyclic plasticity approach to fatigue and fraeture. of asphaltic mixtures[J].Transportation Researeh Reeord,1985:112-123.
[67]ZHANG T G, RAAD L. Numerical Methodology in Fatigue Analysis:Basie Formulation[J]. Journal of Transportation Engineering,1999,125(6):552-559.
[68]ZHANG T G, RAAD L. Numerieal Methodology in Fatigue Analysis:Applications. Journal of Transportation Engineering,2001,127(1):59-66.
[69]KIM H. Discrete fracture modeling of asphalt concrete[J]. William G. Buttlar. International Journal of Solids and Structures,2009,46:2593-2604.
[70]TSCHEGG E K, JAMEK M, LUGMAYR R. Fatigue crack growth in asphalt and asphalt-interfaces[J]. Engineering Fracture Mechanics,2011,78:1044-1054.
[71]SHA Q L. The Cracking of Bituminous Surfacing on Semi-Rigid Road base in China[J]. Australian Road Research.1988,18(2):97-106.
[72]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,1998,4(2)：67-80.
[73]罗睿,黄晓明.沥青路面表面裂缝应力强度因子计算方法研究[J].公路交通技,2002,19(1)：12-15.
[74]巴桑顿珠,黄晓明.西藏沥青路面裂缝温度疲劳扩展寿命分析[J].东南大学学报(自然科学版),2006,36(6)：1013-1017.
[75]陈团结,钱振东,黄卫.交通荷载作用下旧沥青路面裂缝对加铺层的影响[J].公路交通科技,2006,23(4)：23-26.
[76]车法,陈拴发,李增宏等.荷载作用下沥青路面表面开裂的扩展[J].公路交通科技,2010,27(5)：26-30.
[77]田莉,胡霞光.美国沥青路面裂缝处治技术应用与研究进展[J].中外公路,2009,29(6)：93-97.
[78]HAND A J, GALAL K A, WARD D R, et al. Cost-Effectiveness of Joint and Crack Sealing:Synthesis of Practice[J]. Journal of Transportation Engineering,2000,126(6):521-529.
[79]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,2008.
[80]常魁和,高群.公路沥青路面养护新技术[M].北京：人民交通出版社,2001.
[81]吴敏刚,蔡乾东,商博明等.高等级公路沥青路面养护维修技术读本[M].北京：人民交通出版社,2011.
[82]杨书祥,马士宾.沥青路面结构可靠性分析与维修[M].北京：中国建筑工业出版社,2010.
[83]王玉顺,朱敏清.高速公路沥青路面预防性养护技术与应用[M].北京：中国建筑工业出版社,2008.
[84]程培峰,徐永丽.现代公路养护管理技术[M].哈尔滨：东北林业大学出版社,2008.
[85]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,1998,11(1)：21-28.
[86]MOLENAAR A A A, NODS M. Design Method for Plain and Geogrid Reinforced Overlays on Crack Pavement[C].Proceeding of the Third International RILEM Coference.1996,Published by E&FN Spon, an imprint of Chapman&Hall 2-6 Boundary Row London SE18HN, UK.
[87]MONISMITH C L,FINN R D. Flexible Pavement Design:State-of-the-Art—1975[J].Transportation Engineering Journal,1977,103 (1):1-53.
[88]马松林,侯相深,韩海红.沥青路面加铺层结构可靠性分析[J].哈尔滨工业大学学报,2008,40(12)：1995-1998.
[89]江毅,华建湘,曾永旺等.含应力吸收层的旧沥青路面加铺沥青层力学分析[J].公路工程,2010,35(3)：4-9.
[90]李禹德,王朝辉.旧沥青路面开裂状况对加铺层结构影响分析[J].公路交通科技(应用技术版),2011,5：27-29.
[91]孙志雄.焊接断裂力学[M].西安：西北工业大学出版社,1994.
[92]杨卫.宏微观断裂力学[M].北京：国防科技出版社,1995.
[93]LIVNE A, BOUCHBINDER E, SVETLIZKY I, et al. The Near-Tip Fields of Fast Cracks [J]. Science, 2010,327(12):1359-1364.
[94]QIAN J, FATEMI A. Mixed Mode Fatigue Crack Growth:a Literature Survey [J]. Engineering Fracture Mechanics,1996.55(5):969-990.
[95]LAZARUS V. Perturbation approaches of a planar crack in linear elastic fracture mechanics:A review [J]. Journal of the Mechanics and Physics of Solids.2011,59:121-144.
[96]范天佑.断裂动力学的进展[J].力学进展,1986,16(1)：1-13.
[97]JANSSEN M, ZUIDEMA J, WANHILL R J H. Fracture Mechanics [M].2nd Edition. New York: Spon Press,2004.
[98]PEREZ N. Fracture Mechanics [M]. New York:Kluwer Academic Publishers,2004.
[99]UNGER D J. Analytical Fracture Mechanics [M]. London:Academic Press,1995.
[100]沈新普,鲍文博,沈国晓.混凝土断裂与损伤[M].北京：冶金工业出版社,2004.
[101]叶志明.各向异性材料与混凝土材料断裂力学引论[M].北京：中国铁道出版社,2000.
[102]黄克智,肖纪美.材料的损伤断裂机理和宏微观力学理论[M].北京：清华大学出版社,1999.
[103]蔡四维,蔡敏.混凝土的损伤断裂[M].北京：人民交通出版社,2000.
[104]GRIFFITH A A. The phenomena of rupture and flow in solids[J]. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 1920,221:163-198.
[105]GRIFFITH A A. The theory of rupture[C]. Delft:Proceedings of the International Congress Applied Mechanics,1924.55-63.
[106]IRWIN G R. Fracture dynamics [J]. Fracturing of Metals,1948,147-166.
[107]OROWAN E. Fracture and strength of solids[J]. Reports on Progress in Physics.1949,12(1): 185-232.
[108]胡传炘.断裂力学及其工程应用[M].北京：北京工业大学出版社,1989.
[109]李洪升,周承芳.工程断裂力学[M].大连：大连理工大学出版社,1990.
[110]SOLANKI K, DANIEWICZ S R., NEWMAN JR J C. Finite element analysis of plasticity-induced fatigue crack closure:an overview [J]. Engineering Fracture Mechanics,2004,71:149-171.
[111]MR6Z K P, MR6Z Z. On crack path evolution rules [J]. Engineering Fracture Mechanics,2010,77: 1781-1807.
[112]TORIBIO J, ALVAREZ N, GONZALEZ B, et al. A critical review of stress intensity factor solutions for surface cracks in round bars subjected to tension loading[J]. Engineering Failure Analysis,2009,16:794-809.
[113]TILBROOK M, HOFFMAN M. Approximation of curved cracks under mixed-mode loading [J]. Engineering Fracture Mechanics,2007,74:1026-1040.
[114]HOU C Y. Three-dimensional finite element analysis of fatigue crack closure behavior in surface flaws [J]. International Journal of Fatigue,2004,26:1225-1239.
[115]RABCZUK T, BORDAS S, ZI G. On three-dimensional modelling of crack growth using partition of unity methods [J]. Computers and Structures,2010,88:1391-1411.
[116]CIVELEK M B, ERDOGAN F. Crack problems for a rectangular plate and an infinite strip[J]. Int. Journ. of Fracture,1982,19:139-159.
[117]OH C S, SONG J H. Crack Growth and Closure Behaviour of Surface Cracks under Pure Bending Loading [J]. International Journal of Fatigue,2001,23:251-258.
[118]TERMAATH S C, PHOENIX S L, HUI C Y. A Technique for Studying Interacting Cracks of Complex Geometry in 2D [J]. Engineering Fracture Mechanics,2006,73:1086-1114.
[119]DYSKIN A V, GERMANOVICH L N. USTINOV K B. Asymptotic Analysis of Crack Interaction with Free Boundary [J]. International Journal of Solids and Structures,2000,37:857-886.
[120]JONES R, MOLENT L, WALKER K. Fatigue Crack Growth in a Diverse Range of Materials [J]. International Journal of Fatigue,2012,40:43-50.
[121]CIVELEK M B, ERDOGAN F. Elastic-plastic problem for a plate with a part-through crack under extension and bending[J]. International Journal of Fracture,1982,20:33-46.
[122]GEORGIADIS H G. An integral equation approach to self-similar plane-elastodynamic crack problems [J]. Journal of Elasticity,1991.25:17-30.
[123]MEGUID S A, TAN M, ZHU Z H. Analysis of cracks perpendicular to biomaterial interfaces using a novel finite element[J]. International Journal of Fracture,1995,73:1-23.
[124]GINER E, SABSABI M, FUENMAYOR F J. Calculation of KH in Crack Face Contacts Using X-FEM.Application to fretting fatigue [J]. Engineering Fracture Mechanics,2011,78:428-445.
[125]LEI J, WANG Y S, GROSS D. Two Dimensional Numerical Simulation of Crack Kinking from an Interface under Dynamic Loading by Time Domain Boundary Element Method [J]. International Journal of Solids and Structures,2007,44:996-1012.
[126]SINGH I V, MISHRA B K, BHATTACHARYA S, et al. The Numerical Simulation of Fatigue Crack Growth Using Extended Finite Element Method [J]. International Journal of Fatigue,2012,36: 109-119.
[127]HWANG C G, WAWRZYNEK P A, INGRAFFEA A R. On the Virtual Crack Extension Method for Calculating the Derivatives of Energy Release Rates for a 3D Planar Crack of Arbitrary Shape under Mode-I Loading [J].Engineering Fracture Mechanics,2001,68:925-947.
[128]AYHAN A O. Mixed Mode Stress Intensity Factors for Deflected and Inclined Surface Cracks in Finite-thickness Plates [J]. Engineering Fracture Mechanics.2004,71:1059-1079.
[129]NOROOZI A H, GLINKA G, LAMBERT S. Prediction of Fatigue Crack Growth under Constant Amplitude Loading and a Single Overload Based on Elasto-plastic Crack Tip Stresses and Strains [J]. Engineering Fracture Mechanics,2008,75:188-206.
[130]YANG J H, LEE K Y. Penny-shaped crack in a piezoelectric cylinder under electro-mechanical loads [J]. Archive of Applied Mechanics,2003,73:323-336.
[131]ZHANG X, JEFFREY R G. Numerical studies on crack problems in three-layered elastic media using an image method[J]. International Journal of Fracture,2006,139:477-493.
[132]ARAKERE N K, KNUDSEN E C, WELLS D,et al. Swanson. Determination of mixed-mode stress intensity factors, fracture toughness, and crack turning angle for anisotropic foam material [J]. International Journal of Solids and Structures,2008,45:4936-4951.
[133]范天佑.断裂力学基础[M].南京：江苏科学技术出版社,1978.
[134]范天佑.断裂动力学引论[M].北京：北京理工大学出版社,1990.
[135]赵建生.断裂力学及断裂物理[M].武汉：华中科技大学出版社,2003.
[136]李永东.理论与应用断裂力学[M].北京：兵器工业出版社,2005.
[137]FAN T Y, LI C S. Analytic Expression of Meso-Criterion on Dynamic Fracture[J]. Journal of Beijing Institute of Technology,1995,4(2):140-145.
[138]吴祥法,范天佑,安冬梅.用路径守恒积分计算平面准晶裂纹扩展的能量释放率[J].计算力学学报,2000,17(1)：34-42.
[139]周震寰.断裂问题中的哈密顿体系方法及其应用[D].大连：大连理工大学,2011.
[140]赵艳华,徐世娘.Ⅰ-Ⅱ复合型裂纹脆性断裂的最小J2准则[J].工程力学,2008,19(4)：94-98.
[141]范天佑.准晶数学弹性力学和缺陷力学[J].力学进展,2000,30(2)：161-174.
[142]吴志学.估算裂纹应力强度因子的新方法[J].力学学报,2006,38(3)：414-420.
[143]孟波,佘崇民.V型缺口根部裂纹应力强度因子的有限元分析[J].南京航空航天大学学报,2009,41(1)：126-129.
[144]王立清.工程中含接触问题的孔边裂纹应力强度因子数值研究[D].哈尔滨：哈尔滨工业大学,2009.
[145]陈景杰,黄一,刘刚.平板穿透裂纹尖端应力强度因子计算方法研究[J].哈尔滨工程大学学报,2011,32(1)：129-135.
[146]郭瑞平,范天佑.含半椭圆表面裂纹圆柱壳体的三维热弹性动态断裂[J].工程力学,2006,23(5)：29-36.
[147]郭怀民,刘官厅,皮建东.带裂纹的椭圆孔口问题的应力分析[J].固体力学学报,2007,28(3)：308-312.
[148]郁大照,陈跃良.含裂纹螺接件应力强度因子三维有限元分析[J].机械工程学报.2011,47(20)：121-126.
[149]陈建,吴林志,杜善义.采用无单元法计算含边沿裂纹功能梯度材料板的应力强度因子[J].工程力学,2000,17(5)：139-144.
[150]陈增涛,王铎.复合型裂纹的混合开裂准则[J].哈尔滨工业大学学报,1994,26(4)：127-131.
[151]黄佩珍,师俊平,李中华.求解界面裂纹应力强度因子的高次权函数法[J].固体力学学报,2000,21(2)：166-170.
[152]肖洪天,岳中琦.用边界元方法分析复合材料中的裂纹问题[J].计算力学学报,2003,20(6)：721-724.
[153]李琳,周振功,吴林志.压电压磁复合材料中裂纹对反平面简谐弹性波的散射问题[J].应用力学学报,2003,23(1)：101-106.
[154]李永东,贾斌,张男等.功能梯度材料有限宽板的反平面断裂问题研究[J].应用数学和力学,2006,27(6)：683-689.
[155]贾斌,李永东,王振清.蠕变硬化材料中Ⅱ型扩展裂纹尖端场特性研究[J].固体力学学报,2009,30(2)：209-215.
[156]程昌钧,王颖坚,马文华,李家仁.弹性力学[M].北京：高等教育出版社,1999.
[157]徐芝纶.弹性力学简明教程[M].第三版,北京：高等教育出版社,1980.
[158]徐芝纶.弹性力学中的差分方法[M].北京：高等教育出版社,1989.
[159]张振华.弹性力学与有限单元法[M].武汉：华中科技大学出版社,1988.
[160]库贵华,张少雄.断裂力学教程[M].西安：西北工业大学出版社,1994.
[161]赖祖涵.断裂力学原理[M].北京：冶金工业出版社,1990.
[162]张行.断裂力学中应力强度因子的解法[M].北京：国防工业出版社,1992.
[163]李庆芬,·胡胜梅,朱世范.断裂力学及其工程应用[M].哈尔滨：哈尔滨工程大学出版社,1998.
[164]李永东.理论与应用断裂力学[M].北京：兵器工业出版社,2005.
[165]张元林.积分变换[M].北京：高等教育出版社,2003.
[166]包革军,盖云英,冉启文.积分变换[M].哈尔滨：哈尔滨工业大学出版社,1998.
[167]冯复科.复变函数与积分变换[M].北京：科学出版社,2008.
[168]牛少影.复变函数[M].北京：北京邮电大学出版社,2004.
[169]李庆忠.复变函数[M].北京：科学出版社,2000.
[170]路见可.复变函数[M].武汉：武汉大学出版社¨993.
[171]张石生.积分方程[M].重庆：重庆出版社,1988.
[172]路见可,钟寿国.积分方程论[M].北京：高等教育出版社,1990.
[173]侯宗义,李明忠,张万国.奇异积分方程及其应用[M].上海：上海科学技术出版社,1990.
[174]陈梦成.断裂力学中奇异积分方程的数值求解方法[J].华东交通大学学报,2010,27(3)：1-13.
[175]牛忠荣,王秀喜,周焕林等.弹性力学问题中一个新的边界积分方程—自然边界积分方程[J].固体力学学报,2001,22(2)：111-119.
[176]LAURITA C. Condition Numbers for Singular Integral Equations in Weighted L2Spaces [J]. Journal of Computational and Applied Mathematics,2000,116:23-40.
[177]ACARWAL R P, O'REGAN D. Singular Volterra Integral Equations [J]. Applied Mathematics Letters,2000,13:115-120.
[178]AKRL M S, HUSSEIN S H. Numerical treatment of solving singular integral equations by using Sine approximations [J]. Applied Mathematics and Computationa,2011,218:3565-3573.
[179]TAGHVAFARD H, ERJAEE G H. On Solving a System of Singular Volterra Integral Equations of Convolution Type [J].Communications in Nonlinear Science and Numerical Simulation,2011,16: 3486-3492.
[180]JUNGHANNS P, LUTHER U. Cauchy Singular Integral Equations in Spaces of Continuous Functions and Methods for Their Numerical Solution [J]. Journal of Computational and Applied Mathematics,1997,77:201-237.
[181]ZHAO H Q. Fracture and Fatigue Analysis of Functionally Graded and Homogeneous Materials Using Singular Integral Equation Approach[D]. Baltimore:Johns Hopkins University,1998.
[2]吴国雄,梅迎军,李力.半柔性复合路面设计与施工[M].北京：人民交通出版社,2009.
[3]王秉刚,郑木莲.水泥混凝土路面设计与施工[M].北京：人民交通出版社,2004.
[4]邓学钧,黄晓明.路面设计原理与方法[M].北京：人民交通出版社,2007.
[5]朱照宏,许志鸿.柔性路面设计理论和方法[M].上海：同济大学出版社,1987.
[6]胡长顺,王秉刚.复合式路面设计原理与施工技术[M].北京：人民交通出版社,1999.
[7]林秀贤.柔性路面结构设计方法[M].北京：人民交通出版社,1988.
[8]梁锡三,唐有君.柔性路面设计[M].北京：人民交通出版社,1982.
[9]邓学钧,陈荣生.刚性路面设计[M].北京：人民交通出版社,1990.
[10]黄晓明.水泥路面设计[M].北京：人民交通出版社,2003.
[11]李华,缪昌文,金志强.水泥混凝土路面修补技术[M].北京：人民交通出版社,1999.
[12]黄仰贤.路面分析与设计[M].北京：人民交通出版社,1998.
[13]TSCHEGG E K, EH ART R J A, INGRUBER M M. Fracture Behavior of Geosynthetic Interlayers in Road pavements [J]. Journal of Transportation Engineering,1998,124(5):457-464.
[14]LIU K,WANG F. Computer Modeling Mechanical Analysis for Asphalt Overlay under Coupling Action of Temperature and Loads [J].Advanced in Control Engineering and Information Science,2011,15:5338-5342.
[15]CHEN D H, WON M. Field Investigations of Cracking on Concrete Pavements[J].Journal of Performance of Constructed Facilities.2007,21(6):450-458.
[16]WANG Y H, Mahboub K C, Hancher D E. Dynamic Panel Data Model for Predicting Performance of Asphalt Concrete Overlay [J]. Journal of Transportation Engineering,2008,134(2):86-92.
[17]PRIETO J N, GALLEGO J, PE'REZ I. Application of the Wheel Reflective Cracking Test for Assessing Geosynthetics in Anti-reflection Pavement Cracking Systems [J].Geosynthetics International,2007,14(5):287-297.
[18]RAMSAMOOJ D V, LIN G S, RAMADAN J. Stresses at Joints and Cracks in Highway and airport Pavements[J]. Engineering Fracture Mechanics,1998,60(5-6):507-508.
[19]李淑明.旧PCC路面上AC加铺层设计方法的研究[D].上海：同济大学,2002.
[20]曾四平,郭少华,陈绍名等RCC-AC路面温度荷载型断裂的有限元分析[J].中南大学学报自然科学版,2005,36(1)：149-154.
[21]蒙云,姜波.应用F.C.防治旧砼路面反射裂缝的探索[J].重庆交通学院学报,2007,26(3)：62-66.
[22]彭自强,李辉,徐一心,李纲.城市旧水泥混凝土路面加铺沥青面层裂缝病害研究[J].华中科技大学学报(城市科学版),2010,27(2)：40-44.
[23]周富杰,孙立军.反射裂缝的足尺疲劳试验研究及其力学分析[J].土木工程学报,2001,34(3)：78-85.
[24]王秉纲.有沥青上面层的水泥混凝土路面的应力分析[J].公路,2002,8：23-27.
[25]王芳,王选仓,刘凯.旧水泥板加铺沥青层设计方法研究[J].合肥工业大学学报(自然科学版),2010,33(4)：548-554.
[26]祝海燕,王选仓.沥青加铺混凝土路面的实用计算方法[J].河北工业大学学报,2007,36(6)：106-111.
[27]KIM S M, NELSON P K. Experimental and Numerical Analyses of PCC Overlays on PCC Slabs-on-grade Subjected to Climatic Loading [J]. International Journal of Solids and Structures,2004,41:785-800.
[28]WHITE L W, ZAMAN M. Coupling Elastic Models Through Interfacial Conditions with Application to Concrete Pavement Overlays[J].Applied Mathematics and Computation,2001,123:187-204.
[29]KHODAII A, FALLAH S, FEREIDOON M N. Effects of Geosynthetics on Reduction of Reflection Cracking in Asphalt Overlays[J]. Geotextiles and Geomembranes,2009,27:1-8.
[30]侯利国,洪秀敏,马建青等.碎石化技术在旧水泥路面改造加铺沥青路面中的应用[J].中外公路,2005,25(5)：41-44.
[31]李廷刚,刘甲荣,陈不东.冲压破裂稳固技术在水泥路面白改黑工程中的应用研究[J].公路交通科技,2010,27(7)：36-41.
[32]BOZKURT D. Three-dimensional Finite Element Analysis to Evaluate Reflective Cracking Potential in Asphalt Concrete Overlays [D]. Urbana-Champaig:University of Illinois at Urbana-Champaign, 2002.
[33]CHO Y H, LIU C, DOSSCY T, et al. Asphalt Overlay Design Methods for Rigid Pavements Considering Rutting,Reflection Cracking, and Fatigue Cracking. Research Report 987-9[R]. The University of Texas at Austin,1998,(9):11-18.
[34]ESHAN V D, WILLIAM G B. Thermal reflective cracking of asphalt concrete overlays[J]. International Journal of Pavement Engineering,2010,11(6):477-488.
[35]YIN H M, BUTTLAR W G, PAULINO G H. Simplified Solution for Periodic Thermal Discontinuities in Asphalt Overlays Bonded to Rigid Pavements[J]. Journal of Transportation Engineering,2007,133 (1):39-46.
[36]胡长顺,曹东伟.有防裂夹层结构的旧水泥混凝土路面沥青加铺层力学分析[J].中国公路学报,1995,12：1-8.
[37]王宏畅,侯维俊,黄晓明.沥青加铺层反射裂缝有限元分习[J].华中科技大学学报(城市科学版),2007,24(3)：91-95.
[38]金文成,王先强,黄小弟.水泥路面沥青加罩不同计算参数的有限元分析[J].华中·科技大学学报(自然科学版),2003,12(31)：107-110.
[39]杨德灿,赵文婷,李黎杰等.旧水泥路面沥青加铺层反射裂缝有限元分析[J].华中科技大学学报报,2009.37(1)：61-64.
[40]黄金,吴进良,李鑫等.旧水泥路面沥青加铺层反射裂缝应力分析[J].重庆交通大学学报(自然科学版),2010,29(2)：203-207.
[41]ELSEIFI M A, AL-QADI I L. Effectiveness of Steel Reinforcing Nettings in Combating Fatigue Cracking in New Flexible Pavement Systems [J]. Journal of Transportation Engineering, 2005,131(1):37-45.
[42]赵延庆,王抒红,周长红等.沥青路面Top-Down裂缝的断裂力学分析[J].同济大学学报(自然科学版),2010,38(2)：218-223.
[43]赵延庆,王国忠,王志超等.基于动态模量的沥青路面开裂分析[J].湖南大学学报(自然科学版),2010,37(7)：7-12.
[44]赵磊,樊统江,何兆益等.荷载作用下半刚性基层沥青路面开裂原因分析[J].重庆交通大学学报(自然科学版),2009,28(1)：49-55.
[45]程英伟,汤捷.高等级公路半刚性基层沥青路面开裂的机理分析及防治[J].公路交通技术,2004,12(6)：39-43.
[46]罗辉,李武芳,朱宏平等.沥青路面表面裂纹扩展机理研究[J].应用基础与工程科学学报,2010,18(3)：452-462.
[47]李峰,孙立军.沥青路面Top-Down开裂成因的有限元分析[J].公路交通科技,2006,23(6)：1-5.
[48]ELSEIFI M A, AL-QADI I L. Modeling of Strain Energy Absorbers for Rehabilitated Cracked Flexible Pavements [J]. Journal of Transportation Engineering,2005,131(9):653-661.
[49]WANG Y H, MAHBOUB K C, HANCHER D E. Survival Analysis of Fatigue Cracking for Flexible Pavements Based on Long-Term Pavement Performance Data [J]. Journal of Transportation Engineering,2005,131 (8):608-616.
[50]BORDELON A, ROESLER J. Design with Fiber Reinforcement for Thin Concrete Overlays Bonded to Asphalt [J]. Journal of Transportation Engineering,2012,138 (4):430-435.
[51]GAO L, AGUIAR-MOYA J P, ZHANG Z M. Bayesian Analys is of Heterogene ity in Modeling of Pavement Fatigue Cracking[J]. Journal of Computing in Civil Engineering,2012,26(1):37-43.
[52]KIM J, ROQUE R, BYRON T. Viscoelastic Analysis of Flexible Pavements and Its Effects on Top-Down Cracking [J]. Journal of Materials in Civil Engineering,2009,21(7):324-332.
[53]MOHAMMAD F A, COLLOP A C, BROWN S F. Effects of Surface Cracking on Responses in Flexible Pavements [J]. Proceedings of the Institution of Civil Engineers- Transport,2005,158(2): 127-134.
[54]MIAO Y, HE T G, YANG Q, et al. Multi-domain Hybrid Boundary Node Method for Evaluating Top-down Crack in Asphalt Pavements [J]. Engineering Analysis with Boundary Elements,2010, 34:755-760.
[55]CHANG X, YAN A Z, LIAO M C, et al. Analysis of Periodic Cracks in Surface Layer of Pavement Structures [J]. Engineering Failure Analysis,2011,18:411-420.
[56]AMERI M, MANSOURIAN A, HEIDARY KHAVAS M, et al. Cracked Asphalt Pavement under Traffic Loading-A 3D Finite Element Analysis [J]. Engineering Fracture Mechanics,2011,78:1817-1826.
[57]SUO Z, WONG W G, LUO X H, et al. Evaluation of Fatigue Crack Behavior in Asphalt Concrete Pavements with Different Polymer Modifiers [J]. Construction and Building Materials,2012,27: 117-125.
[58]吴赣昌,张淦生.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)：37-44.
[59]仰建岗,王秉纲,陈拴发.基于修正Neuber方程的沥青路面裂缝形成疲劳寿命预估方法[J].交通运输工程学报,2007,7(2)：50-56.
[60]王新东.沥青路面裂缝的原因及处治措施[J].公路交通科技,2009,26(5)：217-220.
[61]郑建龙,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,2003.
[62]詹永祥,姚海林,卢正.表面含裂缝沥青面低温收缩断裂分析[J].交通科学与工程,2010,26(3)：20-24.
[63]罗辉,朱宏平,陈传尧.预切口沥青混合料小梁疲劳试验研究[J].华中科技大学学报(城市科学版),2008,25(1)：47-51.
[64]LYTTON R L, U.SHANMUGHAM B D. Garrett. Design of asphalt pavements for thermal fatigue cracking[C] Report FHWA/TX-83-284-4, Texas Transportation Institute, Texas A&M University, 1983:91-105.
[65]UZAN J, SIDES A, PERL M. Viscoelasoplatic Model for Predicting Performance of Asphaltic Mixtures[J]. Transportation Research Record,1985:78-88.
[66]ABDULSHAFI A A, MAJIDZADEH K. J-Integral and cyclic plasticity approach to fatigue and fraeture. of asphaltic mixtures[J].Transportation Researeh Reeord,1985:112-123.
[67]ZHANG T G, RAAD L. Numerical Methodology in Fatigue Analysis:Basie Formulation[J]. Journal of Transportation Engineering,1999,125(6):552-559.
[68]ZHANG T G, RAAD L. Numerieal Methodology in Fatigue Analysis:Applications. Journal of Transportation Engineering,2001,127(1):59-66.
[69]KIM H. Discrete fracture modeling of asphalt concrete[J]. William G. Buttlar. International Journal of Solids and Structures,2009,46:2593-2604.
[70]TSCHEGG E K, JAMEK M, LUGMAYR R. Fatigue crack growth in asphalt and asphalt-interfaces[J]. Engineering Fracture Mechanics,2011,78:1044-1054.
[71]SHA Q L. The Cracking of Bituminous Surfacing on Semi-Rigid Road base in China[J]. Australian Road Research.1988,18(2):97-106.
[72]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,1998,4(2)：67-80.
[73]罗睿,黄晓明.沥青路面表面裂缝应力强度因子计算方法研究[J].公路交通技,2002,19(1)：12-15.
[74]巴桑顿珠,黄晓明.西藏沥青路面裂缝温度疲劳扩展寿命分析[J].东南大学学报(自然科学版),2006,36(6)：1013-1017.
[75]陈团结,钱振东,黄卫.交通荷载作用下旧沥青路面裂缝对加铺层的影响[J].公路交通科技,2006,23(4)：23-26.
[76]车法,陈拴发,李增宏等.荷载作用下沥青路面表面开裂的扩展[J].公路交通科技,2010,27(5)：26-30.
[77]田莉,胡霞光.美国沥青路面裂缝处治技术应用与研究进展[J].中外公路,2009,29(6)：93-97.
[78]HAND A J, GALAL K A, WARD D R, et al. Cost-Effectiveness of Joint and Crack Sealing:Synthesis of Practice[J]. Journal of Transportation Engineering,2000,126(6):521-529.
[79]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,2008.
[80]常魁和,高群.公路沥青路面养护新技术[M].北京：人民交通出版社,2001.
[81]吴敏刚,蔡乾东,商博明等.高等级公路沥青路面养护维修技术读本[M].北京：人民交通出版社,2011.
[82]杨书祥,马士宾.沥青路面结构可靠性分析与维修[M].北京：中国建筑工业出版社,2010.
[83]王玉顺,朱敏清.高速公路沥青路面预防性养护技术与应用[M].北京：中国建筑工业出版社,2008.
[84]程培峰,徐永丽.现代公路养护管理技术[M].哈尔滨：东北林业大学出版社,2008.
[85]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,1998,11(1)：21-28.
[86]MOLENAAR A A A, NODS M. Design Method for Plain and Geogrid Reinforced Overlays on Crack Pavement[C].Proceeding of the Third International RILEM Coference.1996,Published by E&FN Spon, an imprint of Chapman&Hall 2-6 Boundary Row London SE18HN, UK.
[87]MONISMITH C L,FINN R D. Flexible Pavement Design:State-of-the-Art—1975[J].Transportation Engineering Journal,1977,103 (1):1-53.
[88]马松林,侯相深,韩海红.沥青路面加铺层结构可靠性分析[J].哈尔滨工业大学学报,2008,40(12)：1995-1998.
[89]江毅,华建湘,曾永旺等.含应力吸收层的旧沥青路面加铺沥青层力学分析[J].公路工程,2010,35(3)：4-9.
[90]李禹德,王朝辉.旧沥青路面开裂状况对加铺层结构影响分析[J].公路交通科技(应用技术版),2011,5：27-29.
[91]孙志雄.焊接断裂力学[M].西安：西北工业大学出版社,1994.
[92]杨卫.宏微观断裂力学[M].北京：国防科技出版社,1995.
[93]LIVNE A, BOUCHBINDER E, SVETLIZKY I, et al. The Near-Tip Fields of Fast Cracks [J]. Science, 2010,327(12):1359-1364.
[94]QIAN J, FATEMI A. Mixed Mode Fatigue Crack Growth:a Literature Survey [J]. Engineering Fracture Mechanics,1996.55(5):969-990.
[95]LAZARUS V. Perturbation approaches of a planar crack in linear elastic fracture mechanics:A review [J]. Journal of the Mechanics and Physics of Solids.2011,59:121-144.
[96]范天佑.断裂动力学的进展[J].力学进展,1986,16(1)：1-13.
[97]JANSSEN M, ZUIDEMA J, WANHILL R J H. Fracture Mechanics [M].2nd Edition. New York: Spon Press,2004.
[98]PEREZ N. Fracture Mechanics [M]. New York:Kluwer Academic Publishers,2004.
[99]UNGER D J. Analytical Fracture Mechanics [M]. London:Academic Press,1995.
[100]沈新普,鲍文博,沈国晓.混凝土断裂与损伤[M].北京：冶金工业出版社,2004.
[101]叶志明.各向异性材料与混凝土材料断裂力学引论[M].北京：中国铁道出版社,2000.
[102]黄克智,肖纪美.材料的损伤断裂机理和宏微观力学理论[M].北京：清华大学出版社,1999.
[103]蔡四维,蔡敏.混凝土的损伤断裂[M].北京：人民交通出版社,2000.
[104]GRIFFITH A A. The phenomena of rupture and flow in solids[J]. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 1920,221:163-198.
[105]GRIFFITH A A. The theory of rupture[C]. Delft:Proceedings of the International Congress Applied Mechanics,1924.55-63.
[106]IRWIN G R. Fracture dynamics [J]. Fracturing of Metals,1948,147-166.
[107]OROWAN E. Fracture and strength of solids[J]. Reports on Progress in Physics.1949,12(1): 185-232.
[108]胡传炘.断裂力学及其工程应用[M].北京：北京工业大学出版社,1989.
[109]李洪升,周承芳.工程断裂力学[M].大连：大连理工大学出版社,1990.
[110]SOLANKI K, DANIEWICZ S R., NEWMAN JR J C. Finite element analysis of plasticity-induced fatigue crack closure:an overview [J]. Engineering Fracture Mechanics,2004,71:149-171.
[111]MR6Z K P, MR6Z Z. On crack path evolution rules [J]. Engineering Fracture Mechanics,2010,77: 1781-1807.
[112]TORIBIO J, ALVAREZ N, GONZALEZ B, et al. A critical review of stress intensity factor solutions for surface cracks in round bars subjected to tension loading[J]. Engineering Failure Analysis,2009,16:794-809.
[113]TILBROOK M, HOFFMAN M. Approximation of curved cracks under mixed-mode loading [J]. Engineering Fracture Mechanics,2007,74:1026-1040.
[114]HOU C Y. Three-dimensional finite element analysis of fatigue crack closure behavior in surface flaws [J]. International Journal of Fatigue,2004,26:1225-1239.
[115]RABCZUK T, BORDAS S, ZI G. On three-dimensional modelling of crack growth using partition of unity methods [J]. Computers and Structures,2010,88:1391-1411.
[116]CIVELEK M B, ERDOGAN F. Crack problems for a rectangular plate and an infinite strip[J]. Int. Journ. of Fracture,1982,19:139-159.
[117]OH C S, SONG J H. Crack Growth and Closure Behaviour of Surface Cracks under Pure Bending Loading [J]. International Journal of Fatigue,2001,23:251-258.
[118]TERMAATH S C, PHOENIX S L, HUI C Y. A Technique for Studying Interacting Cracks of Complex Geometry in 2D [J]. Engineering Fracture Mechanics,2006,73:1086-1114.
[119]DYSKIN A V, GERMANOVICH L N. USTINOV K B. Asymptotic Analysis of Crack Interaction with Free Boundary [J]. International Journal of Solids and Structures,2000,37:857-886.
[120]JONES R, MOLENT L, WALKER K. Fatigue Crack Growth in a Diverse Range of Materials [J]. International Journal of Fatigue,2012,40:43-50.
[121]CIVELEK M B, ERDOGAN F. Elastic-plastic problem for a plate with a part-through crack under extension and bending[J]. International Journal of Fracture,1982,20:33-46.
[122]GEORGIADIS H G. An integral equation approach to self-similar plane-elastodynamic crack problems [J]. Journal of Elasticity,1991.25:17-30.
[123]MEGUID S A, TAN M, ZHU Z H. Analysis of cracks perpendicular to biomaterial interfaces using a novel finite element[J]. International Journal of Fracture,1995,73:1-23.
[124]GINER E, SABSABI M, FUENMAYOR F J. Calculation of KH in Crack Face Contacts Using X-FEM.Application to fretting fatigue [J]. Engineering Fracture Mechanics,2011,78:428-445.
[125]LEI J, WANG Y S, GROSS D. Two Dimensional Numerical Simulation of Crack Kinking from an Interface under Dynamic Loading by Time Domain Boundary Element Method [J]. International Journal of Solids and Structures,2007,44:996-1012.
[126]SINGH I V, MISHRA B K, BHATTACHARYA S, et al. The Numerical Simulation of Fatigue Crack Growth Using Extended Finite Element Method [J]. International Journal of Fatigue,2012,36: 109-119.
[127]HWANG C G, WAWRZYNEK P A, INGRAFFEA A R. On the Virtual Crack Extension Method for Calculating the Derivatives of Energy Release Rates for a 3D Planar Crack of Arbitrary Shape under Mode-I Loading [J].Engineering Fracture Mechanics,2001,68:925-947.
[128]AYHAN A O. Mixed Mode Stress Intensity Factors for Deflected and Inclined Surface Cracks in Finite-thickness Plates [J]. Engineering Fracture Mechanics.2004,71:1059-1079.
[129]NOROOZI A H, GLINKA G, LAMBERT S. Prediction of Fatigue Crack Growth under Constant Amplitude Loading and a Single Overload Based on Elasto-plastic Crack Tip Stresses and Strains [J]. Engineering Fracture Mechanics,2008,75:188-206.
[130]YANG J H, LEE K Y. Penny-shaped crack in a piezoelectric cylinder under electro-mechanical loads [J]. Archive of Applied Mechanics,2003,73:323-336.
[131]ZHANG X, JEFFREY R G. Numerical studies on crack problems in three-layered elastic media using an image method[J]. International Journal of Fracture,2006,139:477-493.
[132]ARAKERE N K, KNUDSEN E C, WELLS D,et al. Swanson. Determination of mixed-mode stress intensity factors, fracture toughness, and crack turning angle for anisotropic foam material [J]. International Journal of Solids and Structures,2008,45:4936-4951.
[133]范天佑.断裂力学基础[M].南京：江苏科学技术出版社,1978.
[134]范天佑.断裂动力学引论[M].北京：北京理工大学出版社,1990.
[135]赵建生.断裂力学及断裂物理[M].武汉：华中科技大学出版社,2003.
[136]李永东.理论与应用断裂力学[M].北京：兵器工业出版社,2005.
[137]FAN T Y, LI C S. Analytic Expression of Meso-Criterion on Dynamic Fracture[J]. Journal of Beijing Institute of Technology,1995,4(2):140-145.
[138]吴祥法,范天佑,安冬梅.用路径守恒积分计算平面准晶裂纹扩展的能量释放率[J].计算力学学报,2000,17(1)：34-42.
[139]周震寰.断裂问题中的哈密顿体系方法及其应用[D].大连：大连理工大学,2011.
[140]赵艳华,徐世娘.Ⅰ-Ⅱ复合型裂纹脆性断裂的最小J2准则[J].工程力学,2008,19(4)：94-98.
[141]范天佑.准晶数学弹性力学和缺陷力学[J].力学进展,2000,30(2)：161-174.
[142]吴志学.估算裂纹应力强度因子的新方法[J].力学学报,2006,38(3)：414-420.
[143]孟波,佘崇民.V型缺口根部裂纹应力强度因子的有限元分析[J].南京航空航天大学学报,2009,41(1)：126-129.
[144]王立清.工程中含接触问题的孔边裂纹应力强度因子数值研究[D].哈尔滨：哈尔滨工业大学,2009.
[145]陈景杰,黄一,刘刚.平板穿透裂纹尖端应力强度因子计算方法研究[J].哈尔滨工程大学学报,2011,32(1)：129-135.
[146]郭瑞平,范天佑.含半椭圆表面裂纹圆柱壳体的三维热弹性动态断裂[J].工程力学,2006,23(5)：29-36.
[147]郭怀民,刘官厅,皮建东.带裂纹的椭圆孔口问题的应力分析[J].固体力学学报,2007,28(3)：308-312.
[148]郁大照,陈跃良.含裂纹螺接件应力强度因子三维有限元分析[J].机械工程学报.2011,47(20)：121-126.
[149]陈建,吴林志,杜善义.采用无单元法计算含边沿裂纹功能梯度材料板的应力强度因子[J].工程力学,2000,17(5)：139-144.
[150]陈增涛,王铎.复合型裂纹的混合开裂准则[J].哈尔滨工业大学学报,1994,26(4)：127-131.
[151]黄佩珍,师俊平,李中华.求解界面裂纹应力强度因子的高次权函数法[J].固体力学学报,2000,21(2)：166-170.
[152]肖洪天,岳中琦.用边界元方法分析复合材料中的裂纹问题[J].计算力学学报,2003,20(6)：721-724.
[153]李琳,周振功,吴林志.压电压磁复合材料中裂纹对反平面简谐弹性波的散射问题[J].应用力学学报,2003,23(1)：101-106.
[154]李永东,贾斌,张男等.功能梯度材料有限宽板的反平面断裂问题研究[J].应用数学和力学,2006,27(6)：683-689.
[155]贾斌,李永东,王振清.蠕变硬化材料中Ⅱ型扩展裂纹尖端场特性研究[J].固体力学学报,2009,30(2)：209-215.
[156]程昌钧,王颖坚,马文华,李家仁.弹性力学[M].北京：高等教育出版社,1999.
[157]徐芝纶.弹性力学简明教程[M].第三版,北京：高等教育出版社,1980.
[158]徐芝纶.弹性力学中的差分方法[M].北京：高等教育出版社,1989.
[159]张振华.弹性力学与有限单元法[M].武汉：华中科技大学出版社,1988.
[160]库贵华,张少雄.断裂力学教程[M].西安：西北工业大学出版社,1994.
[161]赖祖涵.断裂力学原理[M].北京：冶金工业出版社,1990.
[162]张行.断裂力学中应力强度因子的解法[M].北京：国防工业出版社,1992.
[163]李庆芬,·胡胜梅,朱世范.断裂力学及其工程应用[M].哈尔滨：哈尔滨工程大学出版社,1998.
[164]李永东.理论与应用断裂力学[M].北京：兵器工业出版社,2005.
[165]张元林.积分变换[M].北京：高等教育出版社,2003.
[166]包革军,盖云英,冉启文.积分变换[M].哈尔滨：哈尔滨工业大学出版社,1998.
[167]冯复科.复变函数与积分变换[M].北京：科学出版社,2008.
[168]牛少影.复变函数[M].北京：北京邮电大学出版社,2004.
[169]李庆忠.复变函数[M].北京：科学出版社,2000.
[170]路见可.复变函数[M].武汉：武汉大学出版社¨993.
[171]张石生.积分方程[M].重庆：重庆出版社,1988.
[172]路见可,钟寿国.积分方程论[M].北京：高等教育出版社,1990.
[173]侯宗义,李明忠,张万国.奇异积分方程及其应用[M].上海：上海科学技术出版社,1990.
[174]陈梦成.断裂力学中奇异积分方程的数值求解方法[J].华东交通大学学报,2010,27(3)：1-13.
[175]牛忠荣,王秀喜,周焕林等.弹性力学问题中一个新的边界积分方程—自然边界积分方程[J].固体力学学报,2001,22(2)：111-119.
[176]LAURITA C. Condition Numbers for Singular Integral Equations in Weighted L2Spaces [J]. Journal of Computational and Applied Mathematics,2000,116:23-40.
[177]ACARWAL R P, O'REGAN D. Singular Volterra Integral Equations [J]. Applied Mathematics Letters,2000,13:115-120.
[178]AKRL M S, HUSSEIN S H. Numerical treatment of solving singular integral equations by using Sine approximations [J]. Applied Mathematics and Computationa,2011,218:3565-3573.
[179]TAGHVAFARD H, ERJAEE G H. On Solving a System of Singular Volterra Integral Equations of Convolution Type [J].Communications in Nonlinear Science and Numerical Simulation,2011,16: 3486-3492.
[180]JUNGHANNS P, LUTHER U. Cauchy Singular Integral Equations in Spaces of Continuous Functions and Methods for Their Numerical Solution [J]. Journal of Computational and Applied Mathematics,1997,77:201-237.
[181]ZHAO H Q. Fracture and Fatigue Analysis of Functionally Graded and Homogeneous Materials Using Singular Integral Equation Approach[D]. Baltimore:Johns Hopkins University,1998.