## 3 Results and Discussion
### Analysis of CRI and Aging Coefficient  
Previous analyses have shown that different conclusions may be drawn when different indicators are used to evaluate the cracking resistance of the asphalt mixture. In order to make up for the defects in single-indicator evaluation, the above four indicators are combined to propose a comprehensive indicator. Table 8 shows the weight of each indicator, calculated by the entropy weight method, and Table 9 shows the calculation results of the entropy weight TOPSIS method. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Index** & **Entropy** & **Entropy Weight** \\ \hline Tensile strength & 0.942 & 0.259 \\ Ultimate strain & 0.936 & 0.286 \\ Pre-peak strain energy density & 0.958 & 0.187 \\ Post-peak strain energy density & 0.940 & 0.268 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Calculation results of entropy weight of four direct tension test indexes. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **S\({}_{1}^{+}\)** & **S\({}_{1}^{-}\)** & **CRI** \\ \hline SMA13-UA (10 \({}^{\circ}\)C) & 0.162751 & 0.108509 & 0.458683 \\ SMA13-STOA (10 \({}^{\circ}\)C) & 0.155920 & 0.116939 & 0.567867 \\ SMA13-LTOA2d (10 \({}^{\circ}\)C) & 0.167548 & 0.102847 & 0.456206 \\ SMA13-LTOA5d (10 \({}^{\circ}\)C) & 0.173033 & 0.100674 & 0.447181 \\ SMA13-LTOA8d (10 \({}^{\circ}\)C) & 0.176295 & 0.100589 & 0.438167 \\ AC13-UA (10 \({}^{\circ}\)C) & 0.186440 & 0.093445 & 0.447045 \\ AC13-STOA (10 \({}^{\circ}\)C) & 0.166225 & 0.129966 & 0.538652 \\ AC13-LTOA2d (10 \({}^{\circ}\)C) & 0.175259 & 0.129923 & 0.438717 \\ AC13-LTOA5d (10 \({}^{\circ}\)C) & 0.192069 & 0.144165 & 0.412537 \\ AC13-LTOA8d (10 \({}^{\circ}\)C) & 0.209025 & 0.154525 & 0.402688 \\ SMA13-UA (20 \({}^{\circ}\)C) & 0.136039 & 0.160869 & 0.587750 \\ SMA13-STOA (20 \({}^{\circ}\)C) & 0.128158 & 0.177350 & 0.686738 \\ SMA13-LTOA2d (20 \({}^{\circ}\)C) & 0.130483 & 0.162080 & 0.575787 \\ SMA13-LTOA5d (20 \({}^{\circ}\)C) & 0.153985 & 0.126742 & 0.502843 \\ SMA13-LTOA8d (20 \({}^{\circ}\)C) & 0.172785 & 0.108632 & 0.487106 \\ AC13-UA (20 \({}^{\circ}\)C) & 0.159100 & 0.110554 & 0.521773 \\ AC13-STOA (20 \({}^{\circ}\)C) & 0.152127 & 0.148879 & 0.602039 \\ AC13-LTOA2d (20 \({}^{\circ}\)C) & 0.155233 & 0.136729 & 0.500042 \\ AC13-LTOA5d (20 \({}^{\circ}\)C) & 0.178280 & 0.127625 & 0.440272 \\ AC13-LTOA8d (20 \({}^{\circ}\)C) & 0.189027 & 0.131564 & 0.393792 \\ SMA13-UA (30 \({}^{\circ}\)C) & 0.161795 & 0.162015 & 0.491779 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Calculation results of CRI for AC-13 and SMA-13. As shown in Table 8, the CRI of SMA-13 is larger than that of AC-13, suggesting that the former has superior cracking resistance to the latter. The main reason for this is that ultimate strain and post-peak strain energy density are given greater weight among the four indexes, as shown in Table 8. Furthermore, the CRI of AC-13 and SMA-13 under STOA conditions increases by 4-20% and 14-24%, respectively, compared with the unaging condition. The results show that STOA improves the cracking resistance of both AC-13 and SMA-13. In addition, the benefit is weakened with the increase in the test temperature. In contrast, the CRI under LTOA conditions is lower than that under unaging conditions for both AC-13 and SMA13, suggesting that long-term aging weakens their cracking resistance. Furthermore, this weakening effect becomes more pronounced as the test temperature increases. Figures 13 and 14 depict the aging coefficient results versus test temperature for AC-13 and SMA-13 under different degrees of aging. The aging coefficient is defined as the ratio of CRI under aging conditions compared to that under unaging conditions, which can eliminate the impact of CRI under unaging conditions. Figures 13 and 14 illustrate the aging coefficient versus test temperature for AC-13 and SMA-13, respectively.