## 5 Conclusions  
This study considered three simplified pavements comprising aggregates of different grain sizes as the research object to develop a 3D finite element tyre-pavement contact model in ABAQUS 2021. First, the contact stress and contact area distribution characteristics of each simplified pavement and the occlusal depth of the tyre-pavement system were analysed under steady-state rolling conditions. Subsequently, the horizontal braking force and cumulative occlusal depth of each simplified pavement were analysed at different vehicle speeds under steady-state braking conditions, and a correlation analysis between these parameters was conducted. The results of this study can be summarised as follows:  
1. Under steady-state rolling conditions, the overall shape of the contact area between the tyre and each simplified pavement was similar; however, the peak contact stresses on the simplified pavement increased with its _MTD_, whereas pavements with larger _MTD_ values exhibited smaller contact areas.
2. Under steady-state rolling conditions, the mean occlusal depth of the simplified pavement was positively correlated with the aggregate grain size. However, the cumulative occlusal depth did not exhibit any correlation with the aggregate grain size and ranked from largest to smallest as aggregate grain sizes 9, 7, and 13 mm. These results indicate that a simplified pavement with a smaller aggregate grain size exhibited a larger overall deformation of the tyre tread, implying that the grain size of the pavement aggregate bulge affects pavement skid resistance during the later stages.
3. Under steady-state braking conditions, the effect of the contact interaction between the tyre and simplified pavement aggregates was ranked in order of superiority as aggregate grain sizes of 9, 7, and 13 mm, indicating that during the late stages of pavement skid resistance, the two smaller aggregates provided superior performance. Consequently, to ensure the durability of pavement skid resistance, more consideration should be given to aggregates with grain sizes in the 7-9 mm range during pavement design.
4. The squares of linear correlation coefficients between the horizontal braking force and pavement cumulative occlusal depth were 0.921, 0.941, 0.889, and 0.894 for vehicle speeds of 30, 60, 90, and 120 km/h, respectively, indicating that the cumulative occlusal depth can be confidently used for the assessment of pavement skid resistance.  
Note that this study was limited to the use of specific tyre and simplified pavement models. In future research, experimental studies will be conducted on pavements with actual aggregate compositions using different types of tyres. These limitations notwithstanding, the conclusions of this study indicate a clear direction for application and can contribute to the development of skid resistance design methods for asphalt pavements.  
Conceptualization, Z.L. and W.C.; methodology, Z.L.; software, W.C.; validation, W.W., Z.L. and Y.L.; formal analysis, W.C.; investigation, Y.L.; resources, W.W.; data curation, Y.L.; writing--original draft preparation, W.C.; writing--review and editing, Z.L.; visualization, Y.L.; supervision, W.W.; project administration, W.W.; funding acquisition, Z.L. All authors have read and agreed to the published version of the manuscript.  
This study received no external funding.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
The authors declare no conflict of interest.