## 4 Results and Discussion
### Performance of Asphalt Binders
#### 4.2.3 DSR Test  
The \(|\)G*\(|\) and \(\delta\) were obtained from the five temperatures by high-temperature FS. Based on the time-temperature superposition, master curves were constructed for four kinds of asphalt binders (Figure 9). Overall, the curves have similar shapes and trends. As can be seen from Figure 9a, \(|\)G*\(|\) increased as the reduced frequency increased, and the control binder had higher \(|\)G*\(|\) compared to the others. In other words, the addition of the CaCO\({}_{3}\) NFs caused a slight decrease in the \(|\)G*\(|\). It can be explained by the fact that the CaCO\({}_{3}\) NFs begin flowing with the increasing temperature, which softens the texture of asphalt binder, thus reducing the overall high-temperature stiffness of the asphalt binder. In Figure 9b, the \(\delta\) gradually decreased with increasing reduced frequency. When the reduced frequency and CaCO\({}_{3}\) NFs content increased continuously, the \(\delta\) decreased, and the \(\delta\) values' gap gradually increased. This indicates that the modifier addition reduced the viscous component of the modulus under load, and increased the portion of the recoverable deformation. The \(|\)G*\(|\)/sin \(\delta\) is an index of the high-temperature stability of asphalt binder, and a higher \(|\)G*\(|\) and lower \(\delta\) indicate a better resistance to rutting performance. The asphalt binders' \(|\)G*\(|\)/sin \(\delta\) values at five temperatures and test frequencies were calculated, as detailed in Figure 10. Overall, the \(|\)G*\(|\)/sin \(\delta\) increased with increasing frequency, and decreased with increasing temperature. Further observations found that the modifier addition caused the \(|\)G*\(|\)/sin \(\delta\) to decrease slightly, and the influence gradually weakened as the temperature increased. Taking the above analysis into consideration, the CaCO\({}_{3}\) NFs had a slight negative effect on the high-temperature performance of asphalt binder. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Test Items**} & \multicolumn{4}{c}{**Dosage (\%)**} \\ \cline{2-5}  & **0** & **1** & **3** & **5** \\ \hline Penetration (25 \({}^{\circ}\)C, 0.1 mm) & 81.8 & 82.1 & 82.9 & 83.0 \\ Ductility (5 \({}^{\circ}\)C, cm) & 7.4 & 8.9 & 10.8 & 12.0 \\ Softening Point (\({}^{\circ}\)C) & 46.2 & 45.9 & 45.8 & 45.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Test results for three key parameters of the asphalt binders. High-temperature TS test results still showed similar changing trend of the four binders, as shown in Figure 11. With increasing temperature, the \(|\)G\({}^{\bullet}|\) and \(\delta\) gradually decreased and increased, respectively. The \(|\)G\({}^{\bullet}|\) decreased with increasing modifier content, but the influence was not obvious. In the temperature range of 30-50 \({}^{\circ}\)C, the \(\delta\) values' gap increased with the increasing content, and the gap reduced gradually as the temperature increased, corresponding to the changes in the FS test. Besides, the trend of the \(|\)G\({}^{\bullet}|\)/sin \(\delta\) was similar to that for \(|\)G\({}^{\bullet}|\). In summary, the results of the TS tests were similar to the above FS test, further confirming that the modifier slightly reduced the asphalt binder's resistance to rutting performance. Figure 11: Temperature sweep of asphalt binders at 30–80 \({}^{\circ}\)C: (**a**) \(|\)G\({}^{\bullet}|\); (**b**) \(\delta\); (**c**) \(|\)G\({}^{\bullet}|\)/sin \(\delta\). Figure 10: High-temperature rutting factor \(|\)G\({}^{\bullet}|\)/sin \(\delta\) of asphalt binders at: (**a**) 28, 40 \({}^{\circ}\)C; and (**b**) 52, 64, and 76 \({}^{\circ}\)C.  
Similarly, the \(|\)G*\(|\) and \(\delta\) were obtained from the three temperatures by low-temperature FS. As mentioned earlier, based on the time-temperature superposition, master curves were constructed for the asphalt binders, and are plotted in Figure 12. The minimum \(|\)G*\(|\) and maximum \(\delta\) generally appeared at the maximum frequency.