1、 英 文 翻 译所 属 系 土木工程系 专 业 土木工程（道路与桥梁）学 号 Assessment of Temperature Fluctuations in Asphalt Pavements Due to Thermal Environmental ConditionsUsing a Two-Dimensional, Transient Finite-Difference Approach_Abstract: A transient, two-dimensional finite-difference model is developed to assess temperature fl
2、uctuations in asphalt pavements due to thermal environmental conditions. Fluctuations in temperatures significantly affect pavement stability and the selection of asphalt grading used in pavements. The ability to accurately predict asphalt pavement temperature at different depths and horizontal loca
3、tions based on thermal environmental conditions will greatly help pavement engineers in performing back-calculations of pavement modulus values and in selecting the asphalt grade to be used in various pavement lifts through detailed examination of predicted pavement temperature distributions on vari
4、ous pavement mixes. A more sophisticated selection of asphalt through specification of less expensive asphalt binders in lower lifts is thus possible for the provision of more economical solutions to rising pavement construction costs. As part of the model validation, sensitivity analyses are perfor
5、med to study the impact of a number of thermal environmental and pavement geometric parameters on predicted temperature responses.CE Database subject headings: Asphalt pavements; Asphalt mixes; Pavement condition; Pavement deflection; Heat transfer; Finite difference method; Environmental impacts; T
6、emperature effects._IntroductionThermal environmental conditions, to which pavements are exposed, significantly impact pavement stability and long-term performance. Accurate prediction of the temperature profile in pavements greatly aids pavement engineers in the design process. Specifically, it all
7、ows for the assessment of pavement deflection, back-calculation of pavement modulus values, estimation of frost action and frost penetration as well as thaw onset, calculation of the cooling rates for freshly laid asphalt layers, and assessment of diurnal and seasonal heating and cooling effects. De
8、tailed knowledge of the temperature distribution in asphalt layers allows for a more sophisticated specification of asphalt binders for lower lifts through specification of less expensive binders. Selecting a binder grade is essential in insuring that the asphalt will not experience significant leve
9、ls of distress at extreme temperatures. If the asphalt selected were too soft, it would result in lower structural capacity at high temperatures and experience rutting. On the other hand, if the selected asphalt were too hard, it would be brittle at low temperatures, cracking under loading. The diff
10、erence in cost between low and high grades may be as high as 35%. Since asphalt is the most expensive component in an asphalt mix, selecting acceptable lower grades would result in significant reduction in the overall cost of pavements. In addition, better assessment of the impact of pavement temper
11、ature variations on various pavement mixes such as dense and open-graded asphalt mixes is thus possible with a higher degree of accuracy. Higher standards set for performance grading requirements for lower asphalt lifts including the binder and base courses, and the appropriate binder selection for
12、hot mix asphalt recycling calls for a detailed understanding of the temperature distribution in pavements.A number of current methods dealing with prediction of temperature gradients in pavements, including Superpave algorithms, are based on statistical and probabilistic methods developed using weat
13、her and pavement data collected through the Long-Term Pavement Performance Program (LTPP) under the Strategic Highway Research Program (SHRP). However, such statistical and probabilistic methods display shortcomings in that they tend to either under- or overestimate pavement temperatures, raising qu
14、estions about their accuracy and reliability. More detailed methods utilizing energy balance equations to estimate pavement surface temperatures or numerical models that attempt to predict temperature gradients in asphalt pavements are either steady-state or one-dimensional transient approaches that
15、 fail to account for the thermal history of pavement and for thermal interaction of parallel laid asphalt pavement lifts of varying grades and binders; an aspect of design that is becoming more and more important for increasingly wider asphalt segments. The uncertainties associated with currently av
16、ailable models call for computationally fast and efficient tools that can accurately and reliably predict asphalt pavement temperatures at different pavement depths and horizontal locations based on local ambient environmental conditions and material properties.This paper proposes a method to predic
17、t transient temperature distributions at various depths and horizontal locations in asphalt pavements using a transient, two-dimensional finite-difference model of a pavement section. The model considers a set of primary thermal environmental conditions. Temperature predictions of the proposed model
18、 account for the lateral thermal interaction between pavement lifts of different mixes not only in the vertical but also in the horizontal directions. Ultimately, the model is aimed at providing pavement engineers with an efficient computational tool that attempts to increase the prediction accuracy
19、 of temperatures in asphaltic pavements for more reliable pavement design._Background and Literature SurveyIn the 1960s and 1970s, building upon the pioneering work of Barber (1957), Southgate (1968); Straub et al. (1968); Demsey and Thompson (1970); Rumney and Jimenez (1971); Williamson (1971); Chr
20、istison and Anderson (1972); Williamson (1972); and Berg (1974) developed a series of analytical/statistical and numerical approaches to assess the thermal behavior of asphalt pavements as a function of thermal environmental conditions.More recently, Thompson et al. (1987) developed a climatic datab
21、ase for the State of Illinois. Pavement temperatures were computed with a one-dimensional, transient finite-difference heat transfer model (Climatic-Materials-Structural Program) and with climatic data input. A regression analysis was run to establish a relationship between pavement temperatures and
22、 mean monthly air temperatures for selection of the proper asphalt cement modulus values in pavement design. Hsieh et al. (1989) proposed a three-dimensional numerical modeling approach coupled with moisture diffusion into pavements using TMY (typical meteorological year) weather databases pertainin
23、g to various thermal environmental conditions which were utilized for climate input. Solaimanian and Kennedy (1993) suggested a parabolic equation that described critical temperature extremes in pavements. Using a known value of latitude, the maximum expected surface temperature could then be approx
24、imated. The study recommended using the lowest expected air temperature as the lowest expected pavement temperature for design. A third-order polynomial corollary equation was suggested to predict pavement temperatures at various depths. Baltzer et al. (1994) proposed the BELLS method that was based
25、 on a statistical/probabilistic regression analysis using pavement surface temperatures and 5 day average daily temperatures before testing. The method was originally based on the work of Southgate (1968). The BELLS method was further refined and improved by Lukanen et al. (1998a,b). A database appr
26、oach for estimating asphalt concrete middepth temperature was proposed by Inge and Kim (1995). The method represented improvements for temperature corrections in asphalt concrete deflection calculations in that history terms in air temperature were not needed, allowing for quicker computations.In th
27、e late 1990s, Lukanen et al. (1998a,b) suggested a probabilistic method for asphalt binder selection based on pavement temperatures. The study developed an empirical prediction model based on simple regression analysis to relate the 7-day average high air temperature to the 7-day average high paveme
28、nt temperature. Mohseni (1998) proposed revisions to the SHRP performance grading system for asphalt binder selection, specifically for low temperature applications. The study, based on data from the Long Term Pavement PerformanceSeasonal Monitoring Program (LTPP-SMP), presented revised models for d
29、etermining the low- and high-temperature component of Superpave performance-based binders. Bosscher et al. (1998) conducted a study by using different performance-graded asphalt binders to validate Superpave algorithms (Kennedy et al. 1994) and the binder specification limits. The analysis focused o
30、n the development of a statistical model for estimation of low and high pavement temperatures from meteorological data. It is important to note that, although currently available methods with some modifications have been implemented with varying success for use in the practice of pavement engineerin
31、g, the accuracy and reliability of the currently available methods have been questioned since proposed correlations stipulate constant values for a number of asphalt mix properties, surface convective conditions, and solar irradiation. Specifically, Bosscher et al.(1998) showed that statistical/prob
32、abilistic models incorrectly predicted pavement design temperatures at ambient air temperatures higher than 30C, compounding questions about the accuracy of the reliability estimates used in the currently available recommendations.MethodologyEnvironmental Thermal Energy Interactions in PavementsThe
33、temperature distribution in an asphaltic pavement is directly affected by the thermal environmental conditions to which it is exposed. The primary modes of heat transfer are incident solar radiation, thermal and long-wave radiation between the pavement surface and the sky, free and forced convection
34、, and conduction inside the pavement as shown in Fig. 1.The intensity of solar radiation or solar irradiation! is dependent on diurnal cycles, the latitude, and the incident angle between the surface and suns rays. Thermal or long-wave radiation accounts for radiative heat transfer between the pavem
35、ent surface and the sky. This mechanism generally has a cooling effect, especially during nighttime hours.The surface energy balance on a pavement requires that the sum of all heat transfer through the surface of the pavement must be equal to the heat conducted in the pavement. An adiabatic bottom s
36、urface can be assumed for sufficiently thick pavements stipulating no heat transfer between the pavement and subgrade layers. Similarly, side surfaces of the pavement pavement edges! are considered to be adiabatic for sufficiently large horizontal expansions since spatial temperature changes in the
37、vertical direction will be much greater than horizontal changes at pavement edges, and any heat transfer through pavement edge surfaces can be neglected.Fig. 1. Energy balance on asphalt surfaceFinite-Difference MeshRepresentation of the finite-difference mesh used in the model is shown in Fig. 2. A
38、 uniform square nodal spacing of 2.5 cm in the x and z directions has been used. This nodal spacing was selected to satisfy stability criterion of the explicit finite-difference approach. In the z direction, the domain corresponds to the top of the pavement and bottom of the pavement or the base of
39、the underlying fill material. A pavement of 730 cm horizontal expansion and 50 cm vertical depth is considered resulting in 292 cells in x and 20 cells in z directions. Thus the domain of interest is subdivided into 5,840 cells for each of which an energy balance equation is developed.Fig. 2. Finite
40、-difference nodal network_评价热环境影响下路面沥青混合料温度变化波动使用二维，瞬态有限差分方法摘要:瞬态二维有限差分模型，开发评估由于热环境条件而引起的沥青路面温度状况变化。波动温度显着影响路面稳定性和路面使用的混凝土混合料级配的选择。能够准确地预测沥青路面温度在不同深度和水平位置的基础上热环境条件将大大帮助工程师在履行反算铺装路面模量值和选择沥青等级被用来在各种路面吊机通过详细审查预测分布在各种路面混合物的温度。选择一个更复杂的沥青可以通过规范使用不太昂贵的沥青粘合剂可以提供更经济的解决方案提高路面建设成本。作为该模型的验证，进行敏感性分析研究它的影响，多个热环境和
41、路面几何参数对预测温度的反应。关键词：沥青路面；沥青混合料；路面；路面弯沉；传热；有限差分法；环境的影响；温度的影响。_介绍路面接触的热环境条件，大大影响了路面的稳定性与长期性能。准确预测路面温度的分布情况大大有利于路面工程师的设计。具体来说，它可以评估路面弯沉，反算路面模量值，估计霜冻作用和渗透以及解冻，计算新铺沥青层的冷却速度，并评估昼夜和季节性的加热和冷却对路面的影响。详细了解温度分布在沥青层允许一个更复杂的条件下使用沥青粘合剂且通过价格不太昂贵的粘合剂。选择粘结剂等级可确保沥青在极端温度下强度不够引起危险。如果沥青选太软，那会导致较低的结构能力和强度的高温车辙。另一方面，如果所选的沥青
42、太硬，它会在低温和荷载作用下脆性开裂。高等级与低等级沥青的成本的差异可能高达 35%。由于沥青是最昂贵的组件在混合料，选择可接受的低等级沥青会可显著降低路面的整体成本。此外，可更好地评估在各种路面和密集的开级配沥青混合料等影响下路面温度变化，因此可能有较高的准确度。更高的标准性能等级的要求下沥青摊铺机包括粘合剂和基础，和选择适当的粘合剂的且回收热拌沥青要求详细了解在路面温度分布。目前可通过一些方法预测的温度在路面上的梯度变化，包括算法，它是基于概率统计方法和利用天气和路面的数据收集通过长期路面性能程序下开发的战略公路研究计划。然而，这样的概率统计方法明显不足，他们往往不足或过高估计路面温度，降
43、低了问题的准确性和可靠性。更详细的方法，利用能量平衡方程来估计路面表面温度或数值模型试图预测温度梯度在沥青路面稳态或一维瞬态方法，不考虑路面的热历史和热相互作用的平行铺设沥青路面不同等级和粘合剂；一方面，正变得越来越重要的越来越大的沥青段。不确定性与现有的呼叫模型计算快速和有效的工具，根据当地的环境条件和材料性能能准确可靠地预测沥青路面温度在不同路面深度和横向位置。本文提出了一种使用瞬态二维有限差分模型的方法来预测沥青路面瞬态温度在不同深度和水平位置分布。该模型认为热环境是一个主要条件。温度预测的横向热之间的相互作用在不同路面和在垂直和水平方向的变化的模型。该模型的最终目的是给路面工程师提供了
44、一个有效的计算工具，试图在沥青路面设计中提高预测更可靠的温度精度。背景与文献综述在 60 年代和 70 年代，在创业的 Barber（1957） ，Southgate（1968） ；Straub 等人。（1968） ；Demsey 和 Thompson（1970） ；Rumney 和 Jimenez（1971） ；Williamson （1971） ；Christison 和 Anderson（1972） ；Williamson（1972） ；和 Berg（1974）开发了一系列的分析/统计和数值方法评估沥青路面热环境条件下引起的热效应变化。最近， Thompson 等人（ 1987）在伊利诺
45、斯州制定了一个气候数据库。运用一维瞬态，有限差分法（气候-材料-结构程序）计算路面温度传热模型和气候数据。回归分析为选择合适的沥青混凝土模量确立路面温度和月平均气温的关系。Hsieh 等人（1989）提出了一个三维数值建模方法，加上水分扩散到路面使用 TMY（典型气象年）输入天气数据库有关的各种热环境数据。Solaimanian 和 Kennedy （1993）提出了一个抛物型方程描述的临界温度的极端路面。使用一个已知的纬度值，预期的最高表面温度可以近似。该研究建议使用最低预期的空气温度最低的预期路面温度设计。一个三阶多项式方程推预测路面在不同深度的温度值。Baltzer 等（1994 ）提出
46、了 BELLS 方法，是根据统计/概率回归分析使用路面表面温度和 5 天的每日平均温度测试。该方法最初是基于 Southgate（1968） 。由 Lukanen等人（1998a，b）将 BULLS 方法进一步完善和改进。Kim（1995）用数据库的方法估算沥青混凝土中层深度的温度。该方法是改善沥青混凝土挠曲温度修正计算，历史条件空气中的温度是不需要的，可以更快的计算。在 90 年代末，Lukanen 等人（1998a,b）提出一个概率法从沥青路面温度基础上选择材料。在简单的分析 7 天的空气与路面平均最高气温之间关系的基础上研究开发了一个预测模型。Mohseni（1998）拟议修订了沥青粘结
47、剂性能分级选择系统，特别是低温应用。本研究中，依据的数据来自路面长期性能-季节性监测计划（LTPP-SMP） ，提出修改模型确定低温和高温构件性能的粘合剂。Bosscher 等人（1998）进行了一项研究，使用不同的性能分级沥青粘合剂来验证的算法（Kennedy 等人,1994）和粘合剂规格界限。分析的重点是从气象数据上发展的一个统计模型估计路面温度的高低。需要注意的是，虽然目前可用的方法与一些修改已经取得了不同的成功，在实践中使用的路面工程，现有方法的准确性和可靠性受到质疑，既然提出了相关规定沥青混合料性能常数的值为多少，表面对流条件和太阳辐射情况。具体来说，Bosscher 等人（1998
48、）认为，统计/概率模型正确预测路面设计温度环境温度高于 30 摄氏度，复合问题的准确性和可靠性估计使用当前可用的建议。方法论环境热能在路面的相互作用暴露的热环境条件直接影响沥青路面的温度分布。主要的传热方式是入射的太阳辐射和长波辐射，热量在路面和天空之间，自由和强迫对流和传导内的路线，如图 1 所示。太阳辐射强度（或太阳辐照）是依赖于昼夜周期，纬度，和入射角之间的表面和太阳的光芒。热量或长波辐射辐射在路面和天空之间传导。这一机制通常有一个冷却效果，尤其是在夜间。路面的表面能量平衡要求路面表面传导的热量总和必须等于路面热量的总和。绝热的底面可以假定足够厚的路面规定路基路面结构层之间不传热。同样，侧表面的路面（路面边缘）被认为是绝热的足够大的横向扩张由于空间的温度变化在垂直方向将远远大于水平变化在路面边缘，和传热通过路面边缘表面可以被忽略。图 1、沥青表面能量平衡_有限差分网格代表性的有限差分网格中使用的模型
