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附件1：外文资料翻译译文公路及隧道沥青路面结构的力学性能石春香 郭忠印（1、上海理工大学，上海200233 ，中国; 2、同济大学，上海200092 ，中国）摘要：一种线性全三维有限元法（ FEM ）被应用于公路隧道在双车轮装载矩形面积考虑横向接触应力诱导加速/减速的车辆作用下关键参数的设计。关键设计参数是被计算的作用在沥青层表面的最大横向拉应力，沥青层底部最大横向拉伸应力和沥青层表面的最大垂直剪应力。影响因素如双车轮重量;沥青层厚度;基层刚度模量和厚度;以及之间的联系结构层对这些关键的设计参数，还应单独审查以提出建设公路隧道沥青路面。关键词：隧道沥青路面结构的三维有限元法;横向力;横向拉应力;纵向剪应力 中图分类号：U 452.2 文献标识码： A导言 几乎所有的机械式柔性路面设计程序确定路面疲劳寿命路面都考虑沥青层底部的拉伸应力或应变。他们含蓄地假设，疲劳裂纹起源于底部的沥青层和向上的表面 路面。假设一个统一的正常接触压力分布在一个圆形的接触面之间的轮胎和路面，按层状弹性理论预计，最大横向拉应力（应变）发生底部的约束层直接作用下的负荷，最大横向压缩应力（应变）发生在路面表面的直接作用下的负荷 1 。 然而，在英国 2 ，美国 3-5 ，日本 6 在我国西北地区 7 有些破裂的道路数据表明，破坏源自表面的路面，而不是在该地基，尤其是厚厚的灵活的结构。 最近，研究人员推测表面开裂现象可能与轮胎与路面之间高度非均匀三维测量接触应力分布有关,其直接诱导了路面结构顶部出现大的横向拉应力 。测量自由滚动轿车和卡车轮胎的表现，除了正常的接触压力，就不可能有大的横向和纵向剪应力代理的接触面积。 传统的层状弹性模型的路面结构通常假定负荷作为一个统一的垂直接触压力分布于圆形接触面积。在这些条件下，最大横向拉应力和压力通常是预测底部的沥青层，由于弯曲应力引起的负荷。然而，在隧道沥青路面，应该指出的是，横向拉伸应力表面远离加载面积（由于负曲率的表面） 。 公路隧道的刚度弹性模量在基岩处显的很高;良好路面的恶化不是路面结构的恶化。车辆进入隧道，司机将车减速，因为弱光和狭隘的空间，会加快车辆离开隧道。存在高横向讲（运行方向）之间的轮胎与路面。 本论文的主要是利用线弹性全三维有限元（远东）计划提出在公路隧道沥青路面下在考虑横向接触应力诱导加速/减速的车辆时的主要参数的设计。主要设计参数的计算方法： 最大横向拉应力max表面的沥青层; 的max底部的沥青层; 最大垂直剪应力max表面沥青层。 1 交通加载表格 传统的层状弹性模型的路面结构通常假定负荷作为一个统一的垂直接触压力分布于圆形接触面积。有限元本文另一方面，装卸条件，简化了使用一个统一的横向联系，纵向考虑压力分布在一个长方形的接触面积，接近真实的接触面之间的轮胎和路面。数值轮胎印刷和胎压给出的表1 。轮胎间距之间的间隔为34厘米。轮胎接触应力已与双车轮重量和轮胎使用的是内部压力经验公式的形式 10 ： p = 0.004 2P+ 0.29pi + 0.145 (1)其中，p是轮胎接触应力; P是双车轮重量;pi是轮胎内部的压力。 表1、轮胎和轮胎气压 12 一般情况下，横向接触应力的定义是： 30 的垂直接触应力，因此按本文件中定义的计算。 2 说明全三维有限元法和路面结构 隧道一般包括沥青路面沥青层，基础和基岩。完整的三维有限元法开发了路面结构显示图 1 。宽沿x方向和Y方向是3.0米深度沿z方向是不同的路面结构层厚度。 8节点的因素是通过在模型。该示意图的边界条件下的路面分析问题中显示图 2 。厂方向是固定在底部的模型;的X方向是固定在左，右架; Y型的方向是固定的正面和背面。联系路面层间条件也被视为特别是层的特点是厚度（hi） ，弹性刚度模量（Ei）和泊松比（vi） 。以下两种型号的隧道路面结构中的表2 。图1 、三维有限元模型图2、图解路面问题分析表2 、不同的路面结构 3 分析计算路面效应 3.1 影响双车轮重量对路面的反应 在各种路面的反应双车轮重量时，要考虑。层之间的联系的条件是完全坚持。以下变种隧道路面结构得到了表3 。表3 、 路面结构-A 数字3-5本结果是考虑沥青层在各种双车轮重量w，而不是考虑横向压力。 图 3、 max在路面图4 、max在路面图 5、 max底部的沥青层 可以看出，在随着车轮重量等级的增大沥青层的压力也随之增加。沥青层底部的横向max小于其max和垂直剪应力在表面的沥青层。这些数字表明，横向讲 之间的轮胎和路面加速恶化的路面。 3.2 影响沥青路面层厚度的效应 在确定各种路面的反应沥青层厚度 h1时，要考虑不同的刚度模量的基础。联系的条件层间完全坚持。以下两种型号的隧道路面结构得到了表4 。表4 、 路面结构-B 图6显示的结果，在不同的沥青层沥青层厚度上，确定了半刚性基层与E = 2GPa。 图6、的影响沥青路面层厚度上强调的半刚性基层 可以看出： （ 1 ）当沥青层厚度为8-10厘米，表面的沥青层与底部的沥青层相比，max和max都高。 （ 2 ） max表面的沥青层的减少而增加沥青层厚度的水平，但衰减的速度下降时，沥青层厚度是超过14厘米。 （ 3 ） max表面的沥青层的增加而增加沥青层厚度的水平，这表明越来越多沥青层厚度水平不利于防止损伤的纵向剪应力。（ 4 ）建议的最佳沥青层厚度是十四厘米对半刚性基层。 图7给出结果在不同的沥青层沥青层厚度的灵活基础与E = 500 MPa。图7、影响沥青路面层厚度上强调的灵活基础 可以看出： （ 1 ）最高强调沥青层的减少而增加沥青层厚度的水平。 （ 2 ）规模以上强调，在半刚性基层，因此半刚性基层课程与高刚度模量应建立在设计程序隧道沥青路面结构。 3.3影响基层厚度对路面反应 在各种路面的答复基层厚度的H2与不同的基石刚度模量时，要考虑。 CCAL完全坚持。以下两种型号的隧道路面结构得到了表5 。 表5 、路面结构-C 图8显示结果沥青层在各基层厚度的硬质基岩与E = 5GPa 。可以看出，参数的变化，因影响基层厚度分钟。如果隧道的基石刚度模量高，基础当然不应当规定的基础课程或厚度需求不要定得厚时，确保建设光滑。 图 8、影响基层厚度对路面强调的刚性基岩 图9给出结果在不同的沥青层厚度基础课程的基础上的灵活与E = 500 MPa。可以看出，这一变化在max底部的沥青层的影响而基层厚度具有重要意义，因此基层应建立和建议的最佳基层厚度为15厘米的灵活的基石。 图9、影响基层厚度对路面强调灵活基石 3.4影响联系条件对路面反应 不同CCAL对路面的反应时，要考虑。第1代表完全坚持层之间;第2号之间的完全坚持沥青层和基层之间，而完全滑动的基础课程和基石;第3号完全滑移的沥青层之间与基层之间，而完全坚持的基础课程和基石;第4号之间的完全滑动层。 以下两种型号的隧道路面结构得到了表6 。表 6、 路面结构-C 图10显示结果沥青层在不同CCAL 。可以看出，这一变化在max底部的沥青层的影响而CCAL是重大的。最有利的情况是完全坚持层之间的最不利的情况是完全层间滑动，因此，加强路面层间约束之间特别是沥青层和基层能够有效地控制裂缝底部的沥青层。 图10 、强调CCAL在路面上的影响 4 结论 力学分析已经完成，以目前的关键设计参数，并提出建设程序，公路隧道沥青路面情况如下： （ 1 ）轮胎和路面的水平应力已证明较高的水平和垂直拉伸应力、剪应力是诱导路面表面损坏的原因，同时，路面底部横向拉伸应力也是很高的。因此，关键的设计参数是表面沥青层的max，底部沥青层的max和表面的沥青层的max。 （ 2 ）半刚性基层课程与高刚度模量应设置，根据基岩刚度其厚度应加以调整。 （ 3 ）提高沥青层厚度级别的半刚性基层的基础是不利于防止纵向剪应力的。最佳沥青层厚度建议14cm的半刚性基层。 （ 4 ）加强边界各层次之间特别是路面的沥青层和基层的联系已证明能有效地控制沥青层底部的max。参考资料 1 安德鲁消委会，雷纳尔河关于沥青路面表面发生纵向开裂预测报告 1 。路面材料与路面设计， 2004年， 15 （ 4 ） ： 409-434 。 2 Jacobs M M J, De bont A H, Molenaar A A A等。沥青混凝土路面裂缝中 / /第7次国际沥青路面配置。英国：英国诺丁汉大学学报， 1992 ： 143-148 。 3 Brown M G, Barksdale R D路面设计和材料中 / /第六届国际配置过程的结构设计中的沥青路面。美国：安阿伯， 1987 ： 118-148 。 4 Dauzats M, Rampal A.表面裂纹发生机制中 / /第六届国际配置过程的结构设计中的沥青路面。美国：安阿伯， 1988 ： 26-34 。 5 Cebon D.车辆产生的道路损坏：审查 1 。车辆系统动力学， 1989 ， 18 ： 107-150 。 6 Komoruya K, Yoshida T, Nitta H.沥青混凝土路面表面纵向裂缝中 / /处理80年度交通研究理事会会议。美国：华盛顿特区， 2001年： 01-0433 。 7 Liang Y, Zhong-yin G, Zhi-yong D.调查与分析公路隧道路面的工作环境 1 。交通科技， 2004 ， 1 ： 27-30 。 8 Myersl R R, Ruth B, Drakos C.对不同卡车轮胎接触应力测量以评估其对地表的裂缝和车辙 R 。美国：国家研究理事会， 1999年。 9 Ikeda T, Itoh m,思考估算大卡车轮胎接触压力方程 中 /系统/ proc 60废止会议的日本土木工程师学会。日本： JSCE ， 1985 ： 465-466 。J. Shanghai Jiaotong Univ. (Sci.), 2008, 13(2): 206210DOI: 10.1007/s12204-008-0206-5Mechanical Properties of Asphalt PavementStructure in Highway TunnelSHI Chun-xiang1(石春香),GUO Zhong-yin2(郭忠印)(1. Shanghai Institute of Technology, Shanghai 200233, China; 2. Tongji University, Shanghai 200092, China)Abstract: A linear full 3D finite element method (FEM) was performed in order to present the key designparameters of highway tunnel asphalt pavement under double-wheel load on rectangular loaded area consideringhorizontal contact stress induced by the acceleration/deceleration of vehicles. The key design parameters arethe maximum horizontal tensile stresses at the surface of the asphalt layer, the maximum horizontal tensilestresses at the bottom of the asphalt layer and the maximum vertical shear stresses at the surface of the as-phalt layer were calculated. The influencing factors such as double-wheel weight; asphalt layer thickness; basecourse stiffness modulus and thickness; and the contact conditions among the structure layers on these keydesign parameters were also examined separately to propose construction procedures of highway tunnel asphaltpavement.Key words: tunnel asphalt pavement structure; three-dimensional finite element method; horizontal force;horizontal tensile stress; vertical shear stressCLC number: U 452.2Document code: AIntroductionAlmost all mechanistic flexible pavement design pro-cedures determine the fatigue life of pavements by con-sidering the tensile stress or strain at the bottom ofthe asphalt layers.They implicitly assume that fa-tigue cracks originate at the bottom of the asphalt lay-ers and propagate upwards towards the surface of thepavement. Assuming a uniform normal contact pres-sure distributed over a circular contact area betweenthe tyre and the pavement surface, layered elastic the-ory predicts that the maximum horizontal tensile stress(strain) occurs at the bottom of bound layers directlyunder the load, and the maximum horizontal compres-sive stress (strain) occurs at the surface of the pavementdirectly under the load1.However, observations from cracked roads in theUK2, the US35, Japan6and in Northwest area ofChina7have shown that the cracking originated fromthe surface of the pavement rather than at the base,particularly for thick flexible constructions.More recently, researchers have hypothesized thatthe surface cracking phenomenon may be related tothe highly non-uniform three dimensional contact stressdistribution measured between the tyre and the pave-ment, inducing large horizontal tensile stresses (strains)in the top section of the pavement structure8.Mea-surements from free-rolling car and truck tyres haveReceived date: 2007-05-28Foundation item: WesternTrafficTechnologyFunds(No. 2002-318-000-23)E-mail: shown that, in addition to the normal contact pressure,there can be large transverse and longitudinal shearstresses acting in the contact area.Traditional layered elastic models of a pavementstructure typically assume that the load is applied asa uniform vertical contact pressure distributed over acircular contact area. Under these conditions the max-imum horizontal tensile stress and strains are usuallypredicted at the bottom of the asphalt layers, due tothe bending stresses induced by the loading. However,on the tunnel asphalt pavements, it should be notedthat horizontal tensile stresses at the surface away fromthe loaded area (due to the negative curvature of thesurface).The elastic stiffness modulus of highway tunnelbedrocks is high; the deterioration of well-constructedpavement is not structural. Furthermore, when vehi-cles enter the tunnels, drivers will decelerate vehiclesbecause of weak light and narrow space, and acceler-ate vehicles when leaving the tunnels. There exist highhorizontal stresses (in the direction of travel) betweenthe tyre and the pavement surface.The objective of this paper is to use a linear elas-tic full 3D finite element (FE) program to present thekey design parameters of highway tunnel asphalt pave-ment under double-wheel loads considering horizontalcontact stress induced by the acceleration/decelerationof vehicles. The following key design parameters wereto be calculated: the maximum horizontal tensilestresses maxat the surface of the asphalt layer; themaxat the bottom of the asphalt layer; the maxi-mum vertical shear stresses maxat the surface of theJ. Shanghai Jiaotong Univ. (Sci.), 2008, 13(2): 206210207asphalt layer.The influencing factors such as double-wheel weight;asphalt layer thickness; base course stiffness modulusand thickness; and the contact situation among thestructure layers on these key design parameters werealso examined separately in order to propose signifi-cant construction problems should be considered in thedesign procedure of the tunnel asphalt pavement.1Traffic Loading FormTraditional layered elastic models of a pavementstructure typically assume that the load is applied asa uniform vertical contact pressure distributed over acircular contact area. The FEM in this paper, on theother hand, the loading conditions were simplified usinga uniform vertical considering horizontal contact pres-sures distributed over a rectangular contact area whichis close to the true contact area between the tyre andpavement. The numeric values of tyre print and tyrepressure are given in the Table 1. Spacing interval be-tween tyres is 34 cm. Tyre contact stresses have beenrelated to double-wheel weight and tyre internal pres-sure using an empirical formula of form10:p = 0.0042P?+ 0.29pi+ 0.145,(1)where, p is the tyre contact stress; P?is the double-wheel weight; piis the tyre internal pressure.Table 1Tyre print and tyre pressure12P?/kNpi/MPap/MPawidth/cmlength/cm200.60.402211.3400.70.522217.6500.750.5732219.8600.80.632221.7800.90.742422.51001.00.8552424.4In general, the horizontal contact stress is defined as30% of the vertical contact stress, so defined in thispaper for calculating.2Description of the Full 3D FEM andPavement Structure VariantsTunnel asphalt pavements generally include asphaltlayers, base course and bedrock. The full 3D FEM de-veloped for the pavement structure is shown in Fig. 1.The width along x-direction and y-direction is 3.0 m.The depth along z-direction is varied at the pavementstructure thickness. 8-node element is adopted in themodel.The schematic representation with boundaryconditions of the pavement analysis problem is shownin Fig. 2.z-direction is fixed on the bottom of themodel; x-direction is fixed on the left and right planes;y-direction is fixed on the front and back planes; thesurface is the free plane.Contact conditions amongpavement layers are also considered particular layer ischaracterized by thickness (hi), elastic stiffness modu-lus (Ei) and Poissons ration (vi). Following variants oftunnel pavement structures were given in the table 2.Fig. 1The full three-dimensional finite element modelzyxLoaded areaAsphalt layerBase courseBedrockFig. 2Schematic representation of the pavementanalysis problemTable 2Pavement structure variantsLayerhi/cmEi/GPaviAsphalt layer8,10,12,14,16,201.50.35Base course0,10,15,25,302.0,0.50.2Bedrock2505.0,0.50.23Analysis of Calculated PavementResponses3.1Effect of Double-wheel Weight onPavement ResponsesPavement responses at various double-wheel weightswere to be considered. Contact conditions among lay-ers are completely sticking. Following variants of thetunnel pavement structure were given in the table 3.Table 3Pavement structure variants-ALayerhi/cmEi/GPaviAsphalt layer141.50.35Base course152.00.2Bedrock2505.00.2Figures 35 present results of the asphalt layer at var-ious double-wheel weights w considering and not con-sidering the horizontal stresses.208J. Shanghai Jiaotong Univ. (Sci.), 2008, 13(2): 20620.40.52040506080100w/kNmax/MPaNot considering horizontal stressConsidering horizontal stressFig. 3maxat the pavement surface2040506080100w/kNNot considering horizontal stressConsidering horizontal stressmax/MPaFig. 4maxat the pavement surface2040506080100Not considering horizontal stressConsidering horizontal stressw/kNmax/MPaFig. 5maxat the bottom of the asphalt layerAs can be seen, the stresses of the asphalt layer in-crease with increasing double-wheel weight level. Theeffect of horizontal forces on the maxat the bottomof the asphalt layer is less than that on the maxandvertical shear stresses at the surface of the asphaltlayer.These figures indicate that horizontal stressesbetween the tyre and the pavement surface acceleratethe deterioration of the pavement surface.3.2Effect of Asphalt Layer Thickness onPavement ResponsesPavement responses at various asphalt layer thick-nesses h1set on the different stiffness modulus basecourse were to be considered.Contact conditionsamong layers are completely sticking. Following vari-ants of the tunnel pavement structure were given in thetable 4.Table 4Pavement structure variants-BLayerhi/cmEi/GPaviw/kNAsphalt layer8,10,12,14,16,201.50.35Base course152.0,0.50.250Bedrock2505.00.2Figure 6 shows the results of the asphalt layer at var-ious asphalt layer thickness set on the semi-rigid basecourse with E = 2 GPa.50.4581012141620h1/cmmax, max/MPamax (surface)max (surface)max (bottom)Fig. 6Effect of asphalt layer thickness on pavementstresses on the semi-rigid base courseAs can be seen:(1) When asphalt layer thickness is set 810 cm, themaxand maxat the surface of the asphalt layer dueto the negative curvature at the wheel interspaces sur-face are higher in magnitude compared to those at thebottom of the asphalt layer.(2) The maxat the surface of the asphalt layer de-crease with increasing asphalt layer thickness level, butthe rate of decay decreases when asphalt layer thicknessis more than 14 cm.(3) The maxat the surface of the asphalt layerincrease with increasing asphalt layer thickness level,which indicates that increasing asphalt layer thicknesslevel is not favorable for preventing the damage inducedby the vertical shear stress.(4) The recommended optimal asphalt layer thicknessis 14cm on the semi-rigid base course.Figure 7 presents results of the asphalt layer at var-ious asphalt layer thickness on the flexible base coursewith E = 500 MPa.0.81.01.281012141620max (surface)max (bottom)max (surface)h1/cmmax, max/MPaFig. 7Effect of asphalt layer thickness on pavementstresses on the flexible base courseAs can be seen:(1) The maximum stresses of the asphalt layer de-crease with increasing asphalt layer thickness level.(2) The magnitude of stresses is more than that onthe semi-rigid base course, so semi-rigid base courseswith higher stiffness modulus should be set in the de-sign procedures of tunnels asphalt pavement structure.J. Shanghai Jiaotong Univ. (Sci.), 2008, 13(2): 2062102093.3Effect of Base Course Thickness onPavement ResponsesPavement responses at various base course thick-nesses h2with the different bedrock stiffness moduluswere to be considered. CCAL are completely sticking.Following variants of the tunnel pavement structurewere given in the table 5.Table 5Pavement structure variants-CLayerhi/cmEi/GPaviw/kNAsphalt layer141.50.35Base course0,10,15,25,302.00.250Bedrock2505.0,0.50.2Figure 8 shows results of the asphalt layer at variousbase course thicknesses on the rigid bedrock with E = 5GPa. As can be seen, the change in parameters due tothe effects of base course thickness is minute.If thetunnel bedrock stiffness modulus is high, base courseshould not be set or the base course thickness needsnot to be set too thick when assuring the constructionsmoothness.0.4010152530h2/cmmax (surface)max (bottom)max (surface)max, max/MPaFig. 8Effect of base course thickness on pavement stresseson the rigid bedrockFigure 9 presents results of the asphalt layer at vari-ous base course thicknesses on the flexible bedrock withE = 500 MPa. As can be seen, the change in the maxat the bottom of the asphalt layer due to the effectsof base course thickness is significant, so base courseshould be set and the recommended optimal base coursethickness is 15 cm on the flexible bedrock.00.81.0010152530h2/cmmax (surface)max (bottom)max (surface)max, max/MPaFig. 9Effect of base course thickness on pavement stresseson the flexible bedrock3.4Effect of Contact Conditions on PavementResponsesInfluence of different CCAL on pavement responseswere to be considered.No. 1 stands for completelysticking among layers; No. 2 for completely sticking be-tween the asphalt layer and the base course while com-pletely sliding between the base course and the bedrock;No. 3 for completely sliding between the asphalt layerand the base course while completely sticking betweenthe base course and the bedrock; No. 4 for completelysliding among layers.Following variants of the tunnel pavement structurewere given in the table 6.Table 6Pavement structure variants-DLayerhi/cmEi/GPaviw/kNAsphalt layer141.50.35Base course152.00.250Bedrock2505.00.2Figure 10 shows results of the asphalt layer at dif-ferent CCAL. As can be seen, the change in the maxat the bottom of the asphalt layer due to the effects ofCCAL is significant. The most advantageous situationis completely sticking among layers; the most disadvan-tageous situation is completely sliding among layers, sostrengthening the bound among pavement layers espe-cially between the asphalt layer and the base course caneffectively control cracking at the bottom of the asphaltlayer. 0.70.81234CCALmax (surface)max (bottom)max (surface)max, max/MPaFig. 10Effect of CCAL on the pavement stresses4ConclusionThe mechanic analysis has been performed in orderto present the key design parameters and propose con-struction procedures of highway tunnel asphalt pave-ment as follows:(1) Inclusion of the horizontal stress between the tyreand the pavement surface has been shown to producehigher local values of horizontal tensile stress and ver-tical shear stress inducing the surface damaging on thepavement surface, at the same time, the magnitude ofthe horizontal tensile stress at the bottom of the pave-ment is high. So the key design parameters are the max210J. Shanghai Jiaotong Univ. (Sci.), 2008, 13(2): 206210at the surface of the asphalt layer, the maxat the bot-tom of the asphalt layer and the maxat the surface ofthe asphalt layer.(2) Semi-rigid base courses w