## 2 Contact Theory  
During the normal vehicle driving process, tyre-pavement contact can be divided into three general regions, as shown in Figure 1. Region I denotes before contact (where the tyre and pavement are about to make contact); Region II denotes stable contact (where the tyre and pavement are in full contact); and Region III denotes after contact (where the tyre and pavement experience contact detachment). When the vehicle brakes, the impact force generated in contact Region I and the adhesion friction generated in contact Region III contribute less to the tyre's overall friction, and the vehicle's braking force comes from contact Region II. Consequently, this study focused on the contact behaviour in Region II (full contact state). The contact behaviour in Region II primarily comprises type-pavement aggregate contact interaction. Because the tyre's internal inflatable structure and tread material stiffness are considerably lower than those of the pavement aggregate, the tyre produces a localised wrapping of the raised aggregate on the pavement during the rolling process. When the vehicle brakes, the speed of the outer edge of the tyre line is less than the vehicle's driving speed; consequently, the tyre and raised aggregate produce an \"occlusual braking\" effect. This effect can be explained by the hysteresis effect (\(F_{th}\)) of the aggregate as well as the adhesion (\(F_{a}\)) between the tread and pavement materials [20; 21], as shown in Figure 2. The hysteresis effect is primarily a result of the resistance provided by the occlusion of the tread with the raised pavement aggregates and the surface friction generated by the relative slip between them. Because the adhesion interaction between materials has a small effect on the overall friction behaviour, its magnitude is negligible [22; 23]. Consequently, this study ignored the effect of adhesion and focused on the contact interaction between the tyre and pavement aggregates. Additionally, research and practice have shown that during the early stages of road use, different pavement types can provide excellent skid resistance, although their macro-textures vary considerably. With repeated traffic loads, pavement aggregate angles and surface microtextures are repeatedly abraded to present a smoother surface; therefore, the skid resistances of different pavements will exhibit different degrees of attenuation. However, pavement aggregate grain size is a critical factor affecting pavement macrotexture [24; 25; 26]. Consequently, attention must be paid to the effect of aggregate grain size on pavement skid resistance. To analyse the contact interaction between a tyre and aggregates of different grain sizes in this study, hemispherical shells were used to simulate abraded coarse aggregates, as shown in Figure 3.  
Figure 1: Schematic of the tyre–pavement contact region. Figure 2: Analysis of tyre–pavement contact interaction. To model the local package behaviour produced by the process of rolling type deformation on pavement raised aggregates, this study proposed the concept of \"occlusal depth\", which refers to the package depth of a tyre on pavement raised aggregate. Within the occlusal range of the tyre and aggregate, the occlusal depth (\(H\)) of a single aggregate is expressed using the difference between the vertex elevation value of the aggregate (\(Z_{1}(x_{1},y_{1})\)) and the critical point elevation of the aggregate (\(Z_{2}(x_{2},y_{2})\)), as shown in Figure 3. It can be calculated as follows:  
\[H=Z_{1}(x_{1},y_{1})-Z_{2}(x_{2},y_{2}) \tag{1}\]  
where \(H\) denotes the occlusal depth of a single aggregate, \(Z_{1}(x_{1},y_{1})\) denotes the vertex elevation in the occlusal range, and \(Z_{2}(x_{2},y_{2})\) denotes the critical point elevation in the occlusal range.