## 3 Simulation Analysis of Tire-Asphalt Pavement Frictional Contact
### Pavement Braking Effect  
Tire slip ratio is directly correlated to the tangential deformation found in the tire-pavement contact zone. Therefore, the tangential displacement of the pavement surface, along the direction of tire movement (Figure 7), is primarily used to investigate pavement deformation under various slip ratios. Figure 8 illustrates the pavement's tangential deformation response under three types of tire slip ratios. The comparison shows that pavement tangential deformation varies most significantly with the alternation of slip ratios. For example, consider a 7% slip ratio; the tangential deformation is generally no more than 0.1 mm, whereas the deformation could reach 1 mm as the slip ratio reaches 10% or higher. The figure also depicts the impact of pavement modulus on tangential interaction, which should not be ignored. It can be observed that in highly elastic pavement (high-E), the tangential resistance to tire rolling is more significant than that of other pavements (low-E and med-E) under the same slip ratio. Therefore, it can be concluded that changes in tire-pavement tangential behavior caused by slight alterations in pavement resilience can be neglected due to their negligibility in comparison to slip ratio.  
Figure 8: Tangential deformation of pavement surface layer under different slip ratios of tires.  
Figure 7: Vertical route of the tire movement.  
Figures 9 and 10 respectively present the correlation of contact area and pavement braking force under different slip ratios. As the slip ratio increases from 7 to 10%, the contact area enlarged, intensifying the tire-pavement friction, causing an upward trend in the braking force applied by the pavement. When the slip ratio raised from 10 to 14%, the contact area began to reduce, accounting for degradation of the tire adhesion effect. According to Figure 6, the braking force also declined along with increasing slip ratio. The two figures illustrate that tire-pavement contact area is related to pavement braking force. In other words, tire adhesion has a substantial impact on the braking force applied by asphalt pavements.  
Figure 11 also shows that the braking force coefficient of pavement does not always enlarge with increases in slip ratio; this coefficient will decrease after reaching its peak value. Using the tire modeled in this research, it was found that pavement type has the most significant braking impact at a slip ratio value near 10%. Furthermore, with reduction in contact area, the effect of pavement type on braking diminished with slip ratios greater than 10%. However, it can be observed that for the most elastic pavement (high-E), the corresponding braking force coefficient is greater than the other two types of less elastic pavement. As the slip ratio was further improved, the braking effect of the high elastic pavement began to degrade, nonetheless, this pavement's braking effect is superior to that of the other pavements. Therefore, it can be concluded that the enhancement of pavement elasticity will give rise to the braking efficiency of the tires under different slip ratios.  
Figure 10: Braking force of pavement under different slip ratios.  
Figure 9: Tire-pavement contact area under different slip ratios.