1、附录 1：外文文献翻译对柔性路面面层开裂的三维有限元分析Hasan Ozer, Imad L. Al-Qadi* and Carlos A. Duarte美国伊利诺伊大学厄本那香槟分校，土木与环境工程系, IL 61801摘要：靠近路面表层的开裂是导致道路寿命缩短的主要因素之一。重交通荷载、施工缺陷、表层混合料的特征是导致路面表层开裂的主要原因。此外，形状不规则的轮胎与路面的接触力有可能在路面表层附近产生极其复杂的应力状态。在这种条件下预测裂纹扩展需要对多种路面结构状态如应力、应变、位移做高精度计算。广义有限元方法（GFEM）提供了一个计算框架，当使用一个扩展的策略时，裂缝在有限单元网格中可能
2、沿任意方向发展。此扩展方法在 GFEM中也能提高多项式近似计算的精度。使用 GFEM 时会对地表层裂缝执行三维分析，建立持久路面结构的大型三维模型，在不同位置插入裂缝。拥有集料规模缺陷的持久路面结构的数值试验揭示了双轮胎下路面断裂的复杂情形。关键词：由上而下产生裂缝（top-down crack） ；广义有限元法；混合模型；持久路面；1. 简介靠近上面层的裂缝，即自上而下开展的裂缝（top-down cracking，以下简称“上贯缝” ） ，一直被认为是柔性路面的主要损坏形式之一。随着长效路面，即人们所认为的持久路面建设率的增加，这种损坏现象也随之增加。这些路面常为了增加寿命而有较厚的沥青混
3、合料层。在这种情况下，裂缝只限于表面。然而，人们还没有弄明白靠近路面表层的结构层。研究“上贯缝”的学者在没有识别裂缝产生的位置的情况下，就导致开裂的原因达成共识。不规则的轮胎接触压力、横向组件与温度荷载时主要因素。由于粘结剂的老化和分离，刚度梯度的变化成了另一个增加裂缝发展的因素。许多学者通过现场调查研究了这一复杂的现象。利用多种数值方法分析、实验室模拟和大规模的测试，De freitas et al.在2005年识别出了几个导致上贯缝产生的原因，开始利用实验室、三维有限元法（FE）评估了其中的一些原因。这些原因包括粘结剂种类、粘结剂用量、集料等级、孔隙率大小、温度。在车轮轮迹带装置下，表层裂
4、缝同车轮下路面的极端永久变形有关。当时发现层间分离对产生表面裂缝影响最大。裂缝发生在行车道上。在另一个试验中，Rolt（2000）进行了一个大规模的路面设计试验，来分析粘结层老化对于路面产生裂缝的影响。这项研究仅做了热带地区试验。研究得出在此热带环境下下，多种粘结层的老化是产生上贯缝的基本原因。Tsoumbanos （2006）在澳大利亚墨尔本地区检查了永久路面的工作性能。根据研究调查，上贯缝逐渐成为永久路面主要的失效模式。表面裂缝限制在路面层4060mm深度之内。从调查网站取得的核心数据显示表面裂缝从垂直线沿特定角度发展。Kim 等人(2009b) 利用轴对称粘弹有限元（ FE）模型研究了表
5、层沿纵向轮迹带的开裂。在轮胎下发现关键的拉伸应变，采用了基于能量耗散的模型来预测上贯缝。根据这个模型，在预设的关键位置重复加载来计算能量的耗散。当耗散能量达到某一阈值时，裂缝就会产生。Myers和 Roque（2011）利用断裂力学和有限元（FE）模型分析了表面轮迹带裂缝的产生。根据这项研究的成果，裂缝发展的原因首先来至于张力，路面结构和轴载谱对裂缝影响也很重要。将不同长度的裂缝插入二维有限元模型中，由这个研究中改进的有限元模型进行敏感性分析。根据敏感性分析，热拌沥青混合料（HMA）的厚度和刚度对裂缝的影响最小，但轮胎和地面的横向作用应力被认为是导致横向开裂的主要原因。Sangpetngam（
6、2004）等人使用边界元法（BEM）预测裂缝在柔性路面的产生。在距轮迹边缘 952.5mm 处的表面插入 12.7mm 长的裂缝，使用模型 I 的应力强度因子（SIF）K I 作为产生裂缝的因素来计算。根据敏感度分析的结果，发现热拌沥青混合料层的刚度变化是使裂缝扩张的很大的原因。这些人同时谈到BEM 模型在解决裂缝插入困难当中的优势。Wang（2007）等人建议根据机械经验法（mechanistic empirical）将贯裂缝融入路面设计协议书中，在佛罗里达州机械经验法被认为是路面失效的主要模式。他们使用散失能量比的概念来描述路面损坏及产生裂缝程度。层状弹性理论被用来预测应力及位移的发生，由
7、此导致裂缝的产生。Al-Qadi （2008）等人，包括 Elseifi（2005,2006） 、Wang和 AL-Qadi（2009） 、Yoo 和 Al-Qadi（2007）等，研究了新一代的双轮宽胎荷载对路面开裂特别是近表层失效的影响。将真实的轮胎荷载与 3D 动态和粘弹模型相结合，分析了剪应力在表面开裂的产生的作用。对纵贯缝的分析以及将其纳入路面设计协议中是一项重大的挑战。主要的挑战是准确确定裂缝产生位置并精确计算出不规则轮胎接触下的应力应变。传统的条状或带状分析无法对路面裂缝的产生提供必要的条件。轮胎与路面的接触在路面表面及接近荷载的位置越来越重要。结果可能是产生极其复杂的拉伸与压缩
8、相混合的破坏模式。此外，由于接近表面的粘结剂因氧化而老化，其刚度的变化成为导致路表面及附近的情形变的更加复杂的又一因素。老化不但改变了表面材料的刚度，而且改变了破裂的特征。因此，真实的车轮荷载应力分析及三维模型分析对于计算交通荷载的应力是必不可少的。其次，这个用于计算应力、预测裂缝产生发展的模型应该可以分析混合模式的断裂问题。广义有限元（GFEM）模型、扩展有限元模型（XFEM） ，与标准有限元方法不同，主要用于解决具有复杂形状、复杂应力状态以及多尺度应用程序的问题。这些方法也被称为是统一分区（partition of unity PoU）法，它们有可能克服困难，解决网格设计和有限元计算法无法
9、攻克的例如裂缝不连续、材料接口等难题。早期用于解决三维开裂难题的 GFEM、XFEM 模型可以分别在Duarte、Oden（1996a） 、Duarte et al.（2000，2001 ） 、Belytschko et al.（2001）等人的工作找到。本研究的主要目的是分析较厚的路面结构下，靠近表层的结构层（表层下结构层）在双轮配置的荷载下的开裂问题。用 GFEM 作为数值工具查找三维格栅中裂缝的准确位置。假定路面结构层在总体规模上存在缺陷，这些缺陷以半便士形或圆形按不同的位置以不同方向插入路表层下的结构层。这些裂缝规模不足全球总量的 1%。在这项研究中假定了材料的弹性性质，采用了线弹性断
10、裂力学理论。将这一方法（GFEM）扩展到粘弹性材料是一个正在研究的项目。注：本文节选原文对道路有限元原理及发展历史的介绍部分附录 2：外文文献原文A three-dimensional generalised finite element analysis for the near-surface cracking problem in flexible pavementsHasan Ozer, Imad L. Al-Qadi* and Carlos A. DuarteDepartment of Civil and Environmental Engineering, University o
11、f Illinois at Urbana Champaign, Urbana, IL 61801, USADepartment of Civil and Environmental Engineering, University of Illinois at Urbana Champaign, Urbana, IL 61801, USA Near-surface cracking is one of the major distress types which results in reducing pavement service life. Heavy traffic loads, con
12、struction deficiencies, and surface mixture characteristics are among the predominant factors contributing to nearsurface cracking. In addition, non-uniform tire-pavement contact stresses have a potential to generate extremely complex stress states near the surface. Prediction of crack initiation un
13、der these conditions requires high accuracy in the computation of state variables in pavement structure such as stresses, strains and displacements in the pavement. The generalised finite element method (GFEM) provides a computational framework in which arbitrary orientation of cracks in a finite el
14、ement mesh is possible when using an enrichment strategy. The enrichment strategy in the GFEM can also increase the accuracy of the solution using higher-order polynomial approximations. A 3D analysis of near-surface cracking is performed using the GFEM. A 3D large-scale model of a long-lasting pave
15、ment is built, and cracks at various locations near the surface are introduced. Numerical experiments of a long-lasting pavement structure with defects at the aggregate scale illustrate the complex fracture conditions on and near the surface in the vicinity of a dual tire configuration.Keywords: top
16、-down; GFEM; mixed-mode; long-lasting; pavement1. IntroductionNear-surface cracking, also known as top-down cracking, in flexible pavements has been recognised as one of the major modes of distress types. This phenomenon increases with the increasing rates of constructing long-lasting pavement, also
17、 known in the market as perpetual pavement. These pavements usually have a relatively thick asphalt mixture layer to extend pavement life. In this case, cracking is only confined to the surface. However, the mechanisms of near-surface cracking have not yet been clearly understood. Consensus among th
18、e researchers who studied top-down cracking addresses several major factors contributing to near-surface cracking, without identifying the location of the crack initiation. Non-uniform tire contact stresses with transverse components and thermal loads are among the major driving forces. Stiffness gr
19、adients due to ageing of binder and segregation are other contributing factors that can aggravate near-surface cracking.Many researchers studied this complex phenomenon by conducting field surveys, utilising various numerical methods and performing laboratory and large-scale tests. De Freitas et al.
20、 (2005) identified several factors on topdown cracking initiation and evaluated some of these factors using laboratory tests and a 3D finite element (FE) analysis. These factors were identified as binder type, binder content, aggregate gradation, air void content and temperature. Surface cracks were
21、 associated with the excessive permanent deformations under the wheels of a wheel-tracking device. A comprehensive field survey was conducted by Harmelink et al. (2008) to identify causes, effects and cures for top-down cracking in asphalt pavements. Segregation was found to be the most influential
22、factor for the initiation of cracking on the surface. Cracks appeared in the driving lanes. In another experimental study, Rolt (2000) performed large-scale pavement design experiments to analyze the effects of binder ageing on surface initiated cracks. This study was limited to tropical environment
23、s. Severe binder ageing in tropical environments was identified as the primary cause of top-down cracking. Tsoumbanos (2006) inspected the performance of long-lasting pavements in Melbourne, Australia. Top-down cracking appeared to be the predominant distress mechanism based on the survey conducted
24、in this study. Surface cracking was limited to the top 4060mm in the pavement. The cores taken from various survey sites showed that the surface cracks propagated at a certain angle from the vertical.Kim et al. (2009b) investigated surface initiated longitudinal wheel-path cracking using a viscoelas
25、tic axisymmetric FE model. A critical tensile strain was identified right under the tires. A dissipated energy-based model was used to predict top-down cracking. According to this model, dissipated energy was computed under repeated applications of loading at the predefined critical locations. Crack
26、 initiation was predicted when the dissipated energy reached a certain threshold. Myers and Roque (2001) analysed surface-initiated wheel-path cracks using fracture mechanics and an FE model. According to the findings from this study, crack propagation mechanism is primarily tensile, and the influen
27、ce of pavement structure and load spectra is significant. Cracks at different lengths were inserted into a 2D FE mesh. A sensitivity analysis was conducted using the FE model developed in this study. Hot-mix asphalt (HMA) thickness and stiffness were among the least influential factors according to
28、the sensitivity analysis. However, transverse contact stresses between tire and pavement surface was identified as the primary contributors to top-down cracking.Sangpetngam et al. (2004) used the boundary element method (BEM) to predict the initiation of surface cracks in flexible pavements. A crack
29、 of 12.7mm was inserted on the surface and 952.5mm away from the tire edge. Mode-I stress intensity factor (SIF) KI was computed as the crack driving force. According to the results from a sensitivity analysis, stiffness gradient in the HMA layer was recognised as an influential factor increasing th
30、e magnitude of crack driving forces. The authors also commented on the advantages of the BEM considering the crack front meshing difficulties. Wang et al. (2007) proposed a mechanistic empirical approach to integrate top-down cracking into the design protocols of pavements, which was recognised as t
31、he predominant mode of distresses in the State of Florida. The authors used a dissipated energy ratio concept as an indicator of damage and cracking in pavements. Layered elastic theory was used to predict stresses and displacements, and hence crack initiation. The effects of dual and new generation
32、 wide base tire configuration on pavement cracking and particularly near surface failure were studied by Al-Qadi et al. (2008), Elseifi et al. (2005, 2006),Wang and Al-Qadi (2009) and Yoo and Al-Qadi (2007). Realistic tire pressures were used in conjunction with a 3D dynamic and viscoelastic FE mode
33、l. The analysis in these studies addressed the effects of shear stresses and their significant role in the initiation of surface cracks.The analysis of top-down cracking and its integration into a pavement design protocol poses significant challenges. The major challenges are to identify the critica
34、l locations of crack initiation and to develop accurate computation of stresses and strains under nonuniform contact stresses. The conventional beam or platelike analysis does not provide necessary conditions for crack initiation on the surface of a pavement. Tire pavement interaction becomes increa
35、singly important on the surface and in the proximity of loading. The outcome can be extremely complex stress conditions to generate mixed-mode tensile or compressive fracture. In addition, stiffness gradation due to oxidative ageing of binder near the surface is another factor that may complicate th
36、e conditions at the surface and at its proximity. Ageing not only changes the stiffness of the surface materials but also alters the fracture properties. Therefore, a 3D analysis with realistic tire configuration and contact stresses is essential to capture the effects generated by traffic loading.
37、Second, the method employed to compute stresses and predict crack initiation/propagation should be capable of analyzing mixed mode fracture problems.The generalized FE method (GFEM) and the extended FE method (XFEM) are the two alternatives to the standard FE method (FEM) for problems with complex g
38、eometry, loading conditions and also multi-scale applications. These methods are also known as partition of unity (PoU) methods. They are promising candidates to overcome mesh design and computational issues of the FEM for the problems with discontinuities such as cracks, material interfaces and so
39、on. Early developments on the GFEM and XFEM for solving 3D fracture problems can be found in the works of Duarte and Oden (1996a), Duarte et al. (2000, 2001) and Belytschko et al. (2001), respectively.The objective of this study is to analyse near-surface cracking under a dual tire configuration on
40、a relatively thick pavement structure. The GFEM is utilised as the numerical tool to find critical locations for crack initiation in a 3D mesh. The pavement structure is assumed to have existing defects at the aggregate scale. These defects are in the form of half-penny and circular cracks inserted
41、at different locations and orientations on and near the surface. These cracks are in a scale of nearly less than 1% of the global scale of the problem domain. Linear elastic fracture mechanics theories in conjunction with elastic material properties are used in this study. The extension of the proposed approach to viscoelasticity is a subject of an ongoing study.
