## 3 Results and Discussions
### Results of the Water Boiling Method and Water Immersion Method  
The optimal material combination obtained by the surface free energy method with molecular dynamics simulations was PU-basalt. In order to verify this conclusion, the adhesion properties of PU with basalt were evaluated using the water boiling method and the water immersion method. As shown in Figure 17, the PU mixture has almost no spalling part, and the integrity of the PU adhesive film is favorable, which indicates that the adhesion properties between PU and basalt are excellent.  
The SEM results are shown in Figure 18. Compared to before water immersion, the interface between PU and basalt after water immersion showed cracks, but the width of the cracks was small. Moreover, as shown in Figure 19, the mass loss rate of the PU mixture at 72 h of immersion was less than 1%. The evaluation of the adhesion grade of the PU mixture referred to the section \"Adhesion grade of asphalt to aggregates\" in JTG E20-2011. The  
Figure 16: Calculation results based on MD: (**a**) adhesion work, (**b**) spalling work.  
Figure 17: PU mixtures: (**a**) after water boiling and (**b**) after water immersion.  
2. Interaction energies between PU, H\({}_{2}\)O, and H\({}_{2}\)SO\({}_{4}\) with the three minerals were calculated through MD simulation. In terms of aggregate type, the adhesion of PU with basalt was found to be superior to that with limestone, and limestone exhibited stronger hydrophilicity.
3. The adhesion work and spalling work obtained by surface free energy theory and molecular dynamics calculations have the same trend, and the results of the adhesion work and spalling work fully indicate that the adhesion properties of PU with basalt are better than with limestone. While the adhesion properties of PU with limestone and basalt decreased under acidic conditions, the adhesion properties of PU with basalt were better than those of limestone, indicating that the combination of PU-basal is more suitable for acid rain-prone areas. In addition, the water boiling method and water immersion method verified the rationality of the PU-basalt combination.
4. The surface free energy measurement based on the contact angle test and MD simulation provides a multiscale perspective on the adhesion properties between PU and aggregate, enhancing the feasibility of applying permeable PU mixtures. The study of factors affecting PU-aggregate adhesion properties contributes to the further optimization of PU mixture formulations. Moreover, the calculation results of the surface free energy method and MD simulation showed good correlation and were consistent with macroscopic performance tests, which can be extended to the study of the adhesion properties of other materials.  
Conceptualization, Z.Z. and J.J.; methodology, X.L.; software, J.J.; validation, Z.Z., J.J. and X.L.; formal analysis, J.J. and X.L.; investigation, Z.Z., Z.S. and J.W.; resources, X.L. and Z.S.; data curation, J.J. and X.L.; writing--original draft, Z.Z. and J.J.; writing--review and editing, Z.Z. and J.J.; supervision, Z.Z.; project administration, Z.Z.; funding acquisition, Z.Z. and J.J. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the Key R&D Project in Shaanxi Province (No. 2024 GX-YBXM-371) and Shaanxi Provincial Communication Construction Group (No. 17-06K).  
Not applicable.  
All data, models, and code generated or used during the study appear in the submitted article.  
Author [PERSON] was employed by the company Mount Taishan Traffic Planning & Design Consulting Corporation. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.