## 5 Results and Discussions
### Temperature Susceptibility of THFS Modified Asphalt Binder  
#### 5.5.1 Resistance to Rutting at High Temperature  
Figure 3 illustrates the _G\({}^{\circ}\)/sin\(\delta\)_ values of asphalt binders versus test temperatures.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Items** & **0\% THFS** & **4\% THFS** & **6\% THFS** & **8\% THFS** & **10\% THFS** \\ \hline
25 \({}^{\circ}\)C Penetration/0.1 mm & 85.0 & 58.7 & 56.8 & 54.0 & 49.6 \\ Softening Point/\({}^{\circ}\)C & 51.0 & 48.2 & 49.0 & 49.4 & 50.1 \\
10 \({}^{\circ}\)C ductility/cm & 51.8 & 11.3 & 10.2 & 9.9 & 9.7 \\
135 \({}^{\circ}\)C RV/mPa-s & 365.8 & 465.7 & 567.7 & 582.3 & 627.4 \\ \hline Residue & Residual penetration ratio/\% & 64.0 & 53.2 & 51.3 & 47.9 & 46.5 \\ After RTFOT & 10 \({}^{\circ}\)C Residual ductility/cm & 10.0 & 4.3 & 3.8 & 3.6 & 3.2 \\ \hline \multicolumn{5}{c}{Performance Grade (PG)} & 58–22 & 64–22 & 64–22 & 64–16 & 64–16 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Physical properties of Asphalt Binders with Different THFS Contents.  
According to the test results in Figure 3, the \(G^{*}\)/\(sin\delta\) values of asphalt binders decreased across the test temperature ranges(46 \({}^{\circ}\)C to 76 \({}^{\circ}\)C with a 6 \({}^{\circ}\)C increment). Under the identical condition of THFS content, there was a major decrease in \(G^{*}\)/\(sin\delta\) value at low temperatures, but a minor decrease was observed at high temperatures. Moreover, the \(G^{*}\)/\(sin\delta\) had a good exponential correlation with the test temperature with a high correlation coefficient \(R^{2}\) ranging from 0.9981 to 0.9989 and is given in Equation (1)  
\[G^{*}\)/\(sin\delta=A\cdot\mathrm{e}^{B\cdot T} \tag{1}\]  
where: \(G^{*}\)/\(sin\delta\) is the rutting parameter of asphalt binder, kPa;  
\(T\) is the temperature, \({}^{\circ}\)C;  
\(A\) and \(B\) are the regression coefficients.  
When taking the logarithm of Equation (1), there was a good linear relationship between \(lg\) (\(G^{*}\)/\(sin\delta\)) and test temperature \(T\) and is shown in Equations (2) and (3).  
\[lg(G^{*}\)/\(sin\delta)=GTS\cdot T+C \tag{2}\]  
\[GTS=\frac{lg(G^{*}/\sin\delta_{1})-lg(G^{*}/\sin\delta_{2})}{T_{1}-T_{2}} \tag{3}\]  
\(GTS\) is the slope of \(lg\) (\(G^{*}\)/\(sin\delta\)) with respect to the test temperature \(T\), which can be used to characterize the temperature susceptibility of asphalt binder at high temperatures. A higher absolute \(GTS\) value indicates that asphalt binder is more sensitive to high temperatures. The \(GTS\) values of asphalt binders are listed in Figure 4.  
From the test results in Figure 4, it could be observed that the absolute \(GTS\) values of THFS modified asphalt binders were lower than that of SK-90 and decreased with the increase in THFS content. It showed that the addition of THFS resulted in decreased temperature susceptibility of asphalt binder. The asphalt binder with higher THFS content was less sensitive to temperature. However, for THFS modified asphalt binders, the \(G^{*}\)/\(sin\delta\) values were higher than that of SK-90 under identical conditions of temperature and increased gradually as THFS content increased. This observation could be attributed to THFS had a higher asphaltene content, resulting in asphalt binder with a higher RV, greater stiffness, and hardness compared to SK-90, which improved the resistance to permanent deformation.  
Figure 3: \(G^{*}\)/\(sin\delta\) Values of Asphalt Binders over Temperatures.