The tire–pavement contact problem is one of the important problems in the field of pavement engineering ^[1][2][3]. Tire–pavement contact behavior is essential to understanding issues such as pavement skid resistance ^[4][5]轮胎-路面接触涉及摩擦学[10]、声学[11]、接触力学[12, noise ^[6]13]、轮胎动力学和其他多学科领域[14]，在路面工程领域引起了广泛的兴趣。轮胎与路面接触过程也是路面防滑性恶化[15, rolling resistance ^[7], and driving safety and comfort ^[8][9]. Tire–pavement contact involves tribology ^[10], acoustics ^[11], contact mechanics ^[12][13], tire dynamics, and other multidisciplinary fields ^[14] and has attracted widespread interest in the field of pavement engineering. The tire–pavement contact process is also the process of pavement skid resistance deterioration ^[15][16], pavement disease formation ^[17], and tire performance decline ^[18]. Therefore, the study of tire–pavement contact behavior is of great significance for improving pavement performance, enhancing pavement life, and enhancing vehicle energy saving and environmental protection ^[19][20].16]、路面病害形成[17]和轮胎性能下降[18]的过程。因此，研究轮胎与路面的接触行为对于改善路面性能、延长路面寿命、增强车辆节能环保具有重要意义[19\u201220]。此外，只有清楚地了解轮胎与路面的相互作用，才能获得真实的接触应力和路面荷载分布数据。只有这样，我们才能设计出更经济、更耐用的路面，并进行摩擦分析。

2. Tire–Pavement Contact Characteristics轮胎-路面接触特性

Tire–pavement contact behavior is 据了解，轮胎与路面的接触行为有助于优化轮胎设计和路面结构设计。这有助于提高路面性能和轮胎的整体性能。研究人员通过轮胎-路面接触特性表征了轮胎-路面接触行为[2,28]。轮胎-路面接触特性主要是根据接触面积定义的几何特性和根据应力分布定义的机械特性[29\understood to help optimize tire design and pavement structure design. This can help improve pavement performance and the overall performance of tires. Researchers have characterized tire–pavement contact behavior through tire–pavement contact characteristics ^[2][28]. Tire–pavement contact characteristics are mainly geometric characteristics defined according to the contact area and mechanical characteristics defined according to the stress distribution ^[29][30]. The definition, understanding, and application of tire–pavement contact characteristics vary among researchers because of differences in the study subjects and methods.201230]。由于研究对象和方法的差异，轮胎-路面接触特性的定义、理解和应用因研究对象而异。

2.1. Geometric Characteristics几何特性

The geometric characteristics of tire–pavement contact mainly refer to the contact area and contact shape. There is no clear definition of contact characteristics in the field of pavement engineering轮胎-路面接触的几何特性主要是指接触面积和接触形状。在路面工程领域，接触特性没有明确的定义; however, the geometric characteristics of tire–pavement contact are summarized and defined in the field of tires, and “Tire Terms and Their Definitions” (但是，轮胎与路面接触的几何特性在轮胎领域进行了总结和定义，《轮胎术语及其定义》（GB/T 6326-2005) ^[31] define the tread contact length (）[31]定义了胎面接触长度（L）、胎面接触宽度（W）、接触系数（L), tread contact width (/W), coefficient of contact (L/W), contact area (）、接触面积（C-A), and footprint area (）和占地面积（F-A), as shown in Figure ），如图1.所示。 The tire–pavement contact area is usually assumed to be circular or rectangular with uniform pressure distribution. This can simplify mechanical calculations and reflects tire–pavement contact behavior to a certain extent, and is widely used in pavement design ^[32]. However, measurements and modeling data show that the vertical stress distribution at the tire–pavement interface is not uniform, and the contact area is not regularly circular ^[29] or rectangular ^[33][34]. Tire pattern and pavement texture influences are ignored in this assumption, so researchers have conducted extensive research on contact geometric characteristics ^[35][36]. 轮胎与路面的接触区域通常被认为是圆形或矩形，压力分布均匀。这可以简化力学计算，在一定程度上反映轮胎与路面的接触行为，在路面设计中得到广泛应用[32]。然而，测量和建模数据表明，轮胎-路面界面处的垂直应力分布不均匀，接触面积不是规则的圆形[29]或矩形[33,34]。在这种假设中，轮胎花纹和路面纹理的影响被忽略了，因此研究人员对接触几何特性进行了广泛的研究[35,36]。Pillai et al. ^[37] used the tire footprint to determine the tire–pavement contact area and obtained two simple predictive equations for tire–pavement contact area based on tire deflection and tire and wheel dimensional parameters found on the tire sidewall, as shown in Equations (等[37]利用轮胎足迹确定轮胎-路面接触面积，根据轮胎挠度和轮胎胎侧的轮胎和车轮尺寸参数，得到了两个简单的轮胎-路面接触面积预测方程，如公式（1) and (）和（2), with an error between the calculated and measured footprint areas within 15%. Ge and Wang ^[38] established a tire–pavement contact finite element model using ）所示，计算和测量的足迹面积之间的误差在15%以内。Ge和Wang[38]利用ABAQUS to simulate the tire–pavement contact process and obtain a contact area equation based on tire pressure and wheel load, as shown in Equation (建立了轮胎-路面接触有限元模型，模拟了轮胎-路面接触过程，并得到了基于轮胎压力和车轮载荷的接触面积方程，如式（3). A quantitative expression of tire contact characteristics under vehicle load was obtained, as shown in Figure ）所示。获得了车辆负载下轮胎接触特性的定量表达式，如图2. 所示。 where 式中，A is tire footprint area为轮胎足迹面积; r, 、s, and和 a are tire radius, wheel diameter, and aspect ratio, respectively分别是轮胎半径、车轮直径和纵横比; and d is tire deflection. D为轮胎挠度。 where其中 δ is tire footprint area, 是轮胎足迹面积，10³ mm毫米; p is tire pressure, 为胎压，Mpa; and F is wheel load, 为车轮载荷，kN.。 Tielking et al. [39] found that the contact area between the tire and the pavement increases as the wheel load increases, and the effect of a single wheel load on the contact area is lower. Based on experiments, Weissman et al. [40] found that the width of the tire footprint remained essentially constant due to the stiffness constraint of the tire sidewall, and that the wheel load mainly affected the length of the tire footprint. Yu et al. [2] conducted a static tire–pavement contact test using super-low-pressure (LLW) Fujifilm Holdings Corporation (FUJI) pressure film paper. As the mean profile depth (MPD) increases, the actual tire–pavement contact area decreases, and as the tire load increases, the contact area gradually increases. However, when the tire load exceeds 250 N, the tire–pavement contact area does not broadly change and even shows a slight decrease. This is mainly because the contact width becomes larger when the load is too large but the contact length is significantly reduced. In summary, it can be seen that the geometric characteristics of tire–pavement contact are related to the wheel load, pavement texture, tire type, etc. Research has mostly used the footprint method for static tire–pavement contact geometric characteristic analysis, lacking dynamic contact studies, while more direct simplification is used in pavement design.

2.2. Mechanical Characteristics

Tire–pavement contact creates stresses and forces. These tire–pavement contact stresses and forces provide the driving force when the vehicle accelerates, the lateral force when it rotates, and the braking force when it decelerates, and it can be seen that the contact behavior is directly related to vehicle performance [41] and pavement performance ^[42][43][42,43]. Therefore, it is significant to conduct contact mechanical characterization studies. When a tire is in contact with pavement, the tire is subjected to a complex load through the complex deformation of the tread and carcass. This complex load is generally described in the study of tire–pavement contact dynamics as the six tire forces, which are vertical force, longitudinal force, lateral force, aligning torque, lateral tilt moment, and rolling resistance moment. Some of these forces are shown in Figure 3. Due to the large deformation of a tire in mutual contact with pavement coupled with the environment and load, these forces are coupled with each other and affect each other ^[39][44][39,44]. The vertical forces are of most concern in pavement studies. 垂直力是路面研究中最关注的问题。Marshek et al. ^[45] attempted to test the pressure distribution footprint of diagonal truck tires using pressure-sensitive films, and their results showed that the contact pressure was non-uniformly distributed and that the contact pressure at the tire shoulder was significantly greater than the tire air pressure. 等[45]试图用压敏膜测试对角线卡车轮胎的压力分布足迹，结果表明接触压力分布不均匀，胎肩处的接触压力明显大于轮胎气压。Wang et al. ^[46] analyzed the non-uniformity of vertical contact stresses and found that the non-uniformity of stress distribution decreases with increasing load but increases with increasing inflation pressure. 等[46]分析了垂直接触应力的不均匀性，发现应力分布的不均匀性随载荷的增加而减小，而随充气压力的增加而增加。Gong et al. ^[47] used a high等[47]使用高精度压力传感器测试了不同力下的轮胎-precision pressure sensor to test the tire–pavement contact pattern and stress under different forces, as shown in Figure 路面接触模式和应力，如图4. It can be seen that with an increase in force, the contact area and the region of stress concentration gradually increase. The distribution of vertical contact stresses is not uniform.所示。可以看出，随着力的增加，接触面积和应力集中区域逐渐增大。垂直接触应力的分布不均匀。 For longitudinal forces, 对于纵向力，Tielking et al. ^[39] analyzed longitudinal contact stresses and vertical contact stresses as a function of vehicle speed. They found that vehicle speed had almost no effect on the vertical contact stress but had a significant influence on the longitudinal contact stress等[39]分析了纵向接触应力和垂直接触应力与车速的关系。他们发现，车速对垂直接触应力几乎没有影响，但对纵向接触应力有显著影响; the longitudinal stress on the pavement and the tire changed direction twice from the stationary state to the rolling state. 路面和轮胎上的纵向应力从静止状态到滚动状态两次改变方向。Douglas et al. ^[48] tested the distribution of vertical and longitudinal pressures between the tire and the pavement under different tire pressures and loads. 等[48]测试了不同轮胎压力和载荷下轮胎与路面之间的垂直和纵向压力分布。他们的测试是一个全面的实验室测试，证实了Their test was a full-scale laboratory test and confirmed Tielking’s analysis of the contact stresses. For lateral forces, Hugo et al. ^[49] found that lateral forces can cause pavement cracking. Research on the aligning torque, lateral tilt moment, and rolling resistance moment has mostly been conducted in the field of vehicle engineering. In summary, it can be seen that the mechanical characteristics of tire–pavement contact are closely related to pavement performance and vehicle performance, and there are certain rules. elking对接触应力的分析。对于侧向力，Hugo等[49]发现侧向力会导致路面开裂。对准力矩、横向倾斜力矩和滚动阻力力矩的研究主要在车辆工程领域进行。综上所述，可以看出，轮胎与路面接触的力学特性与路面性能和车辆性能密切相关，有一定的规律性。