## 4 Prediction of Mechanical Properties
### Establishment of Prediction Model  
According to previous analysis results, the number of sizeable wet temperature cycles, the void ratio and the cut layer were selected as variables to establish the prediction equation for the strength modulus of the asphalt mixture under the action of sizeable wet temperature cycles. The fitted equation is shown in Equation (3), and the correlation coefficients are shown in Table 5.  
\[SB=a\cdot VV+b\cdot F+c\cdot T+d \tag{3}\]  
where \(S_{B}\) is the strength modulus (MPa), \(VV\) is the void ratio (%), \(F\) is the cut layer, \(T\) is the number of sizeable wet temperature cycles, and \(a,b,c\), and \(d\) are all correlation coefficients.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference Sequence** & \multicolumn{3}{c}{**Comparison Sequence**} \\ \hline \hline Degree of decay D & Number of sizeable wet temperature cycles & Void ratio & Depth of cut \\ \hline \hline
0.783 (1) & 0.619 (2) & 0.527 (3) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Grey correlation results.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Lamination** & **Void Ratio/\%** & \(a\) & \(b\) & \(c\) & \(d\) & \(\mathbf{R^{2}}\) \\ \hline
1 & 4.1 & 73.2 & 1785.43 & \(-6.19\) & 1785.43 & 0.974 \\
2 & 4.1 & 29.39 & 1433.6 & \(-5.42\) & 716.8 & 0.993 \\
3 & 4.1 & 14.71 & 1076.02 & \(-4.89\) & 358.67 & 0.987 \\
4 & 4.1 & 8.64 & 842.63 & \(-4.44\) & 210.66 & 0.964 \\
1 & 5.0 & 86.47 & 1729.45 & \(-7.12\) & 1729.45 & 0.934 \\
2 & 5.0 & 34.77 & 1390.89 & \(-6.88\) & 695.44 & 0.958 \\
3 & 5.0 & 17.48 & 1048.58 & \(-6.69\) & 349.53 & 0.985 \\
4 & 5.0 & 10.30 & 823.84 & \(-6.36\) & 205.96 & 0.985 \\
1 & 5.9 & 84.97 & 1699.44 & \(-8.33\) & 1699.44 & 0.952 \\
2 & 5.9 & 34.107 & 1364.29 & \(-7.68\) & 682.14 & 0.955 \\
3 & 5.9 & 17.11 & 1026.72 & \(-7.3\) & 342.24 & 0.952 \\
4 & 5.9 & 10.1 & 808.4 & \(-6.84\) & 202.1 & 0.961 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Coefficients of fitted equations.  
As shown in Table 5, the correlation coefficient of the regression equations under different conditions was greater than 0.95, and the regression equations were well correlated. On this basis, the comprehensive integrated correction coefficient \(\text{K}_{\text{VF}}\) of the void ratio and the cut layer was introduced. The prediction equation of the strength modulus with a void ratio of 4.1% for Cut Layer 1 was used as the basis, and the coefficients of the equations under the conditions of different cut layers and air voids were corrected and integrated, as shown in Equation (4). Subsequently, the prediction model parameters with a void ratio of 4.1% for Cut Layer 1 were used to calculate the equations with different cut layers and air voids, and the relationship between the relevant parameters was fitted. Finally, the integrated correction coefficient calculation equations for the prediction equations of the strength modulus of the AC-13-graded asphalt mixture under a sizeable wet temperature cycle are obtained in Equations (5)-(8).  
\[SB=K_{VF1}\cdot VV+K_{VF2}\cdot F+K_{VF3}\cdot T+l \tag{4}\]  
\[K_{VF1}=282.6\cdot VV-23.19\cdot F+488.7 \tag{5}\]  
\[K_{VF2}=-3317.08\cdot VV-308.53\cdot F+2189.61 \tag{6}\]  
\[K_{VF3}=-154.50\cdot VV-0.3344\cdot F+0.805 \tag{7}\]  
\[l=\frac{1785.43}{(0.888+2.778\cdot VV)\cdot(0.04825\cdot F^{2}+0.0565F+0.4575 )} \tag{8}\]  
where \(K_{VF}\) is the comprehensive correction coefficient for the void fraction and the cut layer.