其中 δ 是轮胎足迹面积，10³毫米;p为胎压，Mpa;F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.

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]. 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].

垂直力是路面研究中最关注的问题。Marshek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等[47]使用高精度压力传感器测试了不同力下的轮胎-路面接触模式和应力，如图4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。

对于纵向力，Tielking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;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Tielking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。