## 3 Results and Analysis
### Contact Angle Measurement Test and Analysis  
#### 3.2.1 Contact Angle Measurement Test  
According to material surface theory, surface free energy in a vacuum was the energy that separated a solid or liquid to create a new interface. Gibbs free energy refers to the difference between the initial and final free energy of a certain system, which was represented by \(\Delta\)G. According to Gibbs free energy, the asphalt-aggregate model in the dry condition and the asphalt-water-aggregate adhesion-cracking model in the wet condition were established, as shown in Figure 13.  
[PERSON] et al. [39] assumed that the dispersion force between the liquid and solid interface can be expressed by the geometric mean of the dispersion components of the free energy on liquid and solid surfaces. On this basis, [PERSON] et al. [40] further developed this method to make it applicable to polar components. Adhesion work between asphalt and aggregate is calculated as follows:  
\[\begin{array}{c}W_{as}=2\sqrt{\gamma_{a}^{d}\gamma_{a}^{d}}+2\sqrt{\gamma_{a}^ {+}\gamma_{s}^{-}}+2\sqrt{\gamma_{a}^{-}\gamma_{s}^{+}}\\ W_{asw}=2\left(\begin{array}{c}\sqrt{\gamma_{a}^{d}\gamma_{s}^{d}}-\sqrt{ \gamma_{a}^{d}\gamma_{w}^{d}}-\sqrt{\gamma_{s}^{d}\gamma_{w}^{d}}+\gamma_{w}^ {d}+\sqrt{\gamma_{w}^{+}}(\sqrt{\gamma_{w}^{-}}-\sqrt{\gamma_{a}^{-}}-\sqrt{ \gamma_{s}^{-}})\\ +\sqrt{\gamma_{w}^{-}}(\sqrt{\gamma_{w}^{+}}-\sqrt{\gamma_{a}^{+}}-\sqrt{ \gamma_{s}^{+}})+\sqrt{\gamma_{a}^{+}\gamma_{s}^{-}}+\sqrt{\gamma_{a}^{-} \gamma_{s}^{+}}\end{array}\right)\end{array} \tag{3}\]  
where \(W_{as}\) is the adhesion work between asphalt and aggregate under dry conditions (mJ/m2); \(W_{asw}\) is the adhesion work between asphalt and aggregate under wet conditions (mJ/m2); \(\gamma_{a}^{N}\) is the surface free energy between the asphalt and water interface (mJ/m2); \(\gamma_{a}^{s}\) is the surface free energy between the asphat-aggregate interface (mJ/m2); \(\gamma_{a}^{d}\) is the dispersion component of the surface free energy of water (mJ/m2); \(\gamma_{S}^{d}\) is the dispersion component of the surface free energy of aggregate (mJ/m2); \(\gamma_{a}^{d}\) is the dispersion component of the surface free energy of asphalt (mJ/m2); \(\gamma_{S}^{+}\) is the Lewis acid component of the surface free energy of aggregate (mJ/m2); \(\gamma_{s}^{-}\) is the Lewis basic component of the surface free energy of aggregate (mJ/m2); \(\gamma_{a}^{+}\) is the Lewis basic component of the surface free energy of asphalt (mJ/m2); \(\gamma_{a}^{-}\) is the Lewis basic component of the surface free energy of asphat (mJ/m2); and \(\gamma_{w}^{-}\) is the Lewis basic component of the surface free energy of water (mJ/m2).  
The water stability index \(W^{\prime}\)[41] was defined, and its calculation is shown in Equation (4). The larger \(W^{\prime}\) was, the less the adhesion work of the material was affected by water, and the better its surface adhesion ability was:  
\[W^{\prime}=\left|\frac{W_{asw}}{W_{as}}\right|\times 100\% \tag{4}\]  
where \(W^{\prime}\) is the water stability index; \(W_{as}\) is the adhesion work between the asphalt and aggregate under dry conditions (mJ/m2); and \(W_{asw}\) is the adhesion work between the asphalt and aggregate under wet conditions (mJ/m2).