## 3 Results and Discussion
### Analysis of CRI and Aging Coefficient
As shown in Figures 13 and 14, the aging coefficient of SMA-13 is higher than that of AC-13 by 1.4-36% when aging degree and test temperature remain the same, which means that SMA-13 is superior to AC-13 in terms of aging resistance. In addition, for both AC-13 and SMA-13, the aging coefficient under STOA condition is above 1, which demonstrates that STOA can have an increasing effect on the cracking resistance of AC-13 and SMA-13. For AC-13, the aging coefficient increases by 20%, 15%, 13%, 4%, respectively, at 10 \({}^{\circ}\)C, 20 \({}^{\circ}\)C, 30 \({}^{\circ}\)C and 40 \({}^{\circ}\)C; for SMA-13, this increases by 24%, 17%, 16%, 14%, respectively, at 10 \({}^{\circ}\)C, 20 \({}^{\circ}\)C, 30 \({}^{\circ}\)C and 40 \({}^{\circ}\)C. It is apparent that the increase amplitude of the aging coefficient of SMA-13 is bigger than that of AC-13, which demonstrates that the gaining effect of STOA is more prominent on SMA-13. Furthermore, it is not difficult to determine that the gaining effect can be lowered with the elevation of test temperature. Under LTOA conditions, the aging coefficient is below 1, and the aging coefficient decreases with the deepening of the degree of aging. This shows that LTOA conditions can have a weakening effect on the cracking resistance, and the weakening effect becomes increasingly prominent with the deepening of aging degree. For AC-13, the aging coefficient decreases by 2-23% (LTOA2d), 7-45% (LTOA5d), 10-63% (LTOA8d). For SMA-13, the aging coefficient decreases by 1-12% (LTOA2d), 2-25% (LTOA5d), 4-59% (LTOA8d). Additionally, the decrease amplitude of the aging coefficient of SMA-13 is smaller than that of the aging coefficient. \begin{table}
\begin{tabular}{c c c c} \hline
**Item** & **S\({}_{\mathbf{i}}^{+}\)** & **S\({}_{\mathbf{i}}^{-}\)** & **CRI** \\ \hline SMA13-STOA (30 \({}^{\circ}\)C) & 0.141363 & 0.168257 & 0.567763 \\ SMA13-LTOA2d (30 \({}^{\circ}\)C) & 0.162611 & 0.115018 & 0.444624 \\ SMA13-LTOA5d (30 \({}^{\circ}\)C) & 0.177390 & 0.100384 & 0.410339 \\ SMA13-LTOA8d (30 \({}^{\circ}\)C) & 0.213595 & 0.053093 & 0.272547 \\ AC13-UA (30 \({}^{\circ}\)C) & 0.175088 & 0.097908 & 0.414888 \\ AC13-STOA (30 \({}^{\circ}\)C) & 0.146474 & 0.127872 & 0.474235 \\ AC13-LTOA2d (30 \({}^{\circ}\)C) & 0.191802 & 0.077588 & 0.322393 \\ AC13-LTOA5d (30 \({}^{\circ}\)C) & 0.204788 & 0.083801 & 0.278172 \\ AC13-LTOA8d (30 \({}^{\circ}\)C) & 0.216290 & 0.087031 & 0.265904 \\ SMA13-UA (40 \({}^{\circ}\)C) & 0.175162 & 0.173909 & 0.478719 \\ SMA13-STOA (40 \({}^{\circ}\)C) & 0.161526 & 0.168348 & 0.545364 \\ SMA13-LTOA2d (40 \({}^{\circ}\)C) & 0.182497 & 0.122690 & 0.419226 \\ SMA13-LTOA5d (40 \({}^{\circ}\)C) & 0.191950 & 0.103701 & 0.355926 \\ SMA13-LTOA8d (40 \({}^{\circ}\)C) & 0.226150 & 0.048751 & 0.197862 \\ AC13-UA (40 \({}^{\circ}\)C) & 0.191654 & 0.153199 & 0.386046 \\ AC13-STOA (40 \({}^{\circ}\)C) & 0.171434 & 0.116590 & 0.399729 \\ AC13-LTOA2d (40 \({}^{\circ}\)C) & 0.184130 & 0.095429 & 0.296814 \\ AC13-LTOA5d(40 \({}^{\circ}\)C) & 0.207889 & 0.060709 & 0.211021 \\ AC13-LTOA8d (40 \({}^{\circ}\)C) & 0.241313 & 0.031141 & 0.143421 \\ \hline \end{tabular}
\end{table} 
Table 9: _Cont._of AC-13, which indicates that the weakening effect of LTOA is more prominent on AC-13. Similarly, it is not difficult to find that the gaining effect can be lowered by the elevation of test temperature. Meanwhile, a non-linear surface fitting method was applied to better describe the relationship between the aging coefficient and long-term aging duration and test temperature. Figure 15 and Table 10 depict the corresponding fitting result. The correlation coefficient of the fitting result of AC-13 and SMA-13 is 0.95 and 0.94, respectively, which reveals that the formula that is used can describe the relationship between the aging coefficient and the long-term aging duration and test temperature, where c denotes aging coefficient, d denotes long-term aging duration, and T denotes test temperature. Figure 14: Aging coefficient versus test temperature for SMA-13 under different degrees of aging.