## 3 Results and Discussion
### Ultimate Strain  
Table 5 and Figures 7 and 8 display the ultimate strain results versus test temperature for AC-13 and SMA-13 under different degrees of aging. As shown in Figures 7 and 8, the ultimate strain of both SMA-13 and AC-13 gradually descends with the increase in aging degree at the same test temperature. The reason for this phenomenon may be that during thermos-oxidative aging, long-term exposure to a high temperature increases the kinetic energy of light molecules in asphalt and further widens the diffusion rate gap between light and heavy molecules, thus weakening the intermolecular attraction and reducing the stability of asphalt mortar or even the overall structure of the asphalt mixture [37]. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & \multirow{2}{*}{**Input**} &  
16%. For SMA-13 at 10 \({}^{\circ}\)C and 20 \({}^{\circ}\)C, the ultimate strain decreases slightly, by 3% (10 \({}^{\circ}\)C) and 8% (20 \({}^{\circ}\)C), under STOA conditions, and when aging degree reaches LTOA2d, there is a sharper descent with a decrease gradient of 23% (10 \({}^{\circ}\)C) and 21% (20 \({}^{\circ}\)C). However, when the degree of aging further decreases, the descent of the ultimate strain slows down and becomes steadier, with a decrease gradient of 9% (10 \({}^{\circ}\)C) and 17% (20 \({}^{\circ}\)C). For SMA-13 at 30 \({}^{\circ}\)C and 40 \({}^{\circ}\)C, the descent of the ultimate strain exhibits slight fluctuations, with an average decrease gradient of 5% (STOA), 18% (LTOA2d), 8% (LTOA5d) and 30% (LTOA8d). With the elevation of test temperature, the ultimate strain under each aging degree shows an increasing trend for both AC-13 and SMA-13. The cause of this phenomenon may be explained as follows: the Brownian motion in asphalt molecules becomes more active, and free volume between molecules increases under the impact of rising temperature, which reduces the viscous flow of asphalt mortar and the eventual enhancement in ultimate strain [38]. For AC-13 under STOA and LTOA8d conditions, the ultimate strain grows nearly proportionally by an average increase rate of 26% (STOA) and 61% (LTOA8d) with every increase of 10 \({}^{\circ}\)C. Comparatively, for AC-13, under the other aging conditions, ultimate strain increases unsteadily. However, when test temperature climbs from 30 \({}^{\circ}\)C to 40 \({}^{\circ}\)C, the sharpest variation in ultimate strain can be seen, with an average increase rate of 80% (UA), 85% (LTOA2d) and 182% (LTOA5d). For SMA-13, the increasing tendency of the ultimate strain is weakened with the elevation of test temperature. For SMA-13 under LTOA5d conditions, ultimate strain steadily increases, with an average increase rate of 50% with every rise of 10 \({}^{\circ}\)C, when the discussed test temperature is in the range of from 10 \({}^{\circ}\)C to 30 \({}^{\circ}\)C. When test temperature increases from 30 \({}^{\circ}\)C to 40 \({}^{\circ}\)C, the average increase rate drops to only 10%. At the same time, for SMA-13 under the other four aging conditions, ultimate strain lifts by 42% (UA), and only 37% (STOA), 55% (LTOA2d) and 28% (LTOA8d), with the elevation of test temperature from 10 \({}^{\circ}\)C to 20 \({}^{\circ}\)C. With further elevations in test temperature, the ultimate increasing tendency becomes flat, with an average increase rate of 7% (UA), 8% (STOA), 16% (LTOA2d), 10% (LTOA8d). Moreover, it is apparent that the ultimate strain of SMA-13 is higher than that of AC-13. This can be explained by the following causes: one is that the contact action between coarse aggregates is more prominent in SMA-13 than AC-13. Furthermore, the lignin fiber in SMA-13 can fully contact and fuse with asphalt to form a wet surface under its large surface area and excellent bitumen-absorbing property, which strengthens the viscosity of the bitumen film wrapped around the aggregate [39, 40].