## 4 Results and Discussion
### Establishment of Moisture Damage Model of Aggregate-Bitumen Interface Shear Strength
According to the test results and numerical calculation results, the relationship between aggregate-bitumen interface shear strength and interfacial moisture content can be obtained, as shown in Figure 11.0  
According to Table 4, it can be clearly found that the fitting result is better at higher temperatures, indicating that acquired data is relatively stable at higher temperatures and has better regularity, and \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Asphalt Category** & **Test Temperature** & **Regression Equation** & \multicolumn{4}{c}{**Equation Parameters**} & \multirow{2}{*}{**SS\({}_{\text{e}}\)**} & \multirow{2}{*}{**R\({}^{2}\)**} \\ \cline{4-7} BA & \(10\)\({}^{\circ}\)C & & \(0.193\) & \(0.276\) & \(0.721\) & \(0.0001\) & \(0.99\) \\ BA & \(-10\)\({}^{\circ}\)C & \(\text{SS}=2.806\) & \(0.066\) & \(14.71\) & \(0.03\) & \(0.96\) \\ NHSSMA & \(10\)\({}^{\circ}\)C & \(e^{a-b\sqrt{\phi}}-c\) & \(-0.221\) & \(0.764\) & \(0.084\) & \(0.0001\) & \(0.99\) \\ NHSSMA & \(-10\)\({}^{\circ}\)C & & \(3.897\) & \(0.029\) & \(46.94\) & \(0.023\) & \(0.98\) \\ \hline \end{tabular}
\end{table} 
Table 4: Fitting results of the relationship between aggregate-bitumen interface shear strength and interfacial moisture content. Figure 12: Moisture content of shear specimen at 4 h immersion time. Figure 13: Fitting curve of interfacial moisture content with immersion time. the dispersion of data is slightly larger at lower temperatures. In order to establish aggregate-bitumen interface shear strength damage model of modified and unmodified asphalt binder, a residual shear strength index (RSS) is proposed. The residual shear strength is calculated as follows. \[\text{RSS}=\frac{SS_{n}}{SS_{0}}\times 100,\]  
where RSS is residual aggregate-bitumen interface shear strength, \(SS_{0}\) is the aggregate-bitumen interface shear strength when interfacial moisture content is 0, \(SS_{n}\) is the aggregate-bitumen interface shear strength at different interfacial moisture content. Figure 14 shows fitting curve of 10 \({}^{\circ}\)C residual aggregate-bitumen interface shear strength of BA with interfacial moisture content. The regression equation of damage model and the corresponding value of each model is shown in Table 5. The moisture damage model of aggregate-bitumen interface shear strength is effective, because all R\({}^{2}\) of the regression equation are above 0.9. In order to compare the model parameters and analyze physical meaning, the model parameter \(a\) is defined as shear strength damage degree, and the value of \(b\) represents the aggregate-bitumen interface shear strength damage rate. It can be clearly seen from Table 5 that the damage degree of NHSSMA is larger than BA in the test temperature range, which indicates that the modified asphalt is more sensitive to interfacial moisture, especially at lower temperature. Interestingly, NHSSMA is more sensitive to interfacial moisture, but it can still provide greater aggregate-bitumen interface shear strength than BA at any interfacial moisture content. This may be due to the fact that the incorporation of the nano hydrophobic silane silica does not change the moisture-sensitive properties of aggregate-bitumen interface, but it can improve the viscosity of asphalt, thus the incorporation of nano hydrophobic silane silica improves the bond strength between asphalt and aggregate in a moisture environment. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Asphalt** & **Test** &
\begin{tabular}{c} **Regression** \\ **Equation** \\ \end{tabular} & \multicolumn{2}{c}{**Equation Parameters**} & \multirow{2}{*}{\(\text{\bf{SS}}_{\text{e}}\)} & \multirow{2}{*}{\(\text{\bf{R}}^{2}\)} \\ \cline{4-5}
**Category** & & & & & \\ \hline BA & \(10\)\({}^{\circ}\)C & & 0.014 & 0.866 & 21.85 & 0.99 \\ BA & \(-10\)\({}^{\circ}\)C & & 0.039 & 0.791 & 189.2 & 0.93 \\ NHSSMA & \(10\)\({}^{\circ}\)C & & 0.0008 & 0.899 & 3.035 & 0.99 \\ NHSSMA & \(-10\)\({}^{\circ}\)C & & 0.025 & 0.866 & 118.8 & 0.95 \\ \hline \hline \end{tabular}
\end{table}