## 4 Results and Discussion
### Temperature Sensitivity Analysis  
Asphalt is a viscoelastic-plastic material whose properties are affected by temperature. In detail, the rutting factors decrease with an increase in temperature. The temperature sensitivity is defined as the gradient of the rutting factors when the temperature changes. In order to analyze the temperature sensitivity of bio-asphalt, a line was utilized to describe the relationship between ln(G*/sin(\(\delta\))) and ln(T). A higher slope of the fitted line means that a higher temperature sensitivity of the asphalt is observed. Figure 8: The relationship between complex modulus and temperature. (**a**) Unaged; (**b**) RTFO aged. Figure 9: The relationship between rutting factors and temperature. (**a**) Unaged; (**b**) RTFO aged. Figure 10a,b shows the linear regression between \(\ln(\text{G}^{*}/\sin(\delta))\) and \(\ln(\text{T})\). As can be seen in Figure 10, \(\ln(\text{G}^{*}/\sin(\delta))\) and \(\ln(\text{T})\) were linear, and the fitted formulas were obtained; they are shown in Tables 2 and 3. As can be seen from Tables 2 and 3, all R\({}^{2}\) values were very close to 1, indicating very good linear fitting. Thus, the rutting factor logarithm of the matrix asphalt and bio-asphalt had good linear correlation with the temperature logarithm. The linear correlation could be characterized by the Equation (2):  
\[\ln\left(\text{G}^{*}/\sin\delta\right)=\text{A}\ \text{lnT}+\text{B} \tag{2}\]  
wherein, \(\text{A}<0\), \(\text{B}>0\); A and B could indicate the temperature sensitivity. As such, they were regarded as temperature sensitivity parameters, and the smaller the value of \(\mid\text{A}\mid\), the lower the sensitivity of the asphalt to temperature. Results could be drawn from Tables 2 and 3: the sequence of \(\mid\text{A}\mid\) for the unaged was \(\mid\text{A}\mid\) (\(50\#\)) \(>\mid\text{A}\mid\) (\(10\%\)) \(>\mid\text{A}\mid\) (\(5\%\)) \(>\mid\text{A}\mid\) (\(30\%\)), the sequence of \(\mid\text{A}\mid\) for the RTFO aged bio-asphalt was \(\mid\text{A}\mid\) (\(10\%\)) \(>\mid\text{A}\mid\) (\(30\%\)) \(>\mid\text{A}\mid\) (\(50\#\)) \(>\mid\text{A}\mid\) (\(5\%\)). For the unaged asphalt, the sensitivity did not show regularity, but the temperature sensitivity of bio-asphalt was lower than that of matrix asphalts. Among them, the temperature sensitivity of bio-asphalt with \(30\%\) content bio-oil was the lowest. For the RTFO-aged asphalt, the temperature sensitivity of bio-asphalt was not regular, but when the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Asphalt Type** & **Equation** & **R\({}^{2}\)** \\ \hline
50\#-base asphalt & \(\ln(\text{G}^{*}/\sin\delta)=-8.962\text{lnT}+39.312\) & 0.99907 \\
5\%-bio-asphalt & \(\ln(\text{G}^{*}/\sin\delta)=-8.526\text{lnT}+37.570\) & 0.99906 \\
10\%-bio-asphalt & \(\ln(\text{G}^{*}/\sin\delta)=-9.128\text{lnT}+40.376\) & 0.99848 \\
30\%-bio-asphalt & \(\ln(\text{G}^{*}/\sin\delta)=-8.989\text{lnT}+39.882\) & 0.99998 \\ \hline \hline \end{tabular} Note: RTFO is short for Rolling Thin Film Oven.  
\end{table} 
Table 3: Linear fitting results of different asphalt temperature sweep data for the RTFO-aged asphalt. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Asphalt Type** & **Equation** & **R\({}^{2}\)** \\ \hline
50\#-base asphalt & \(\ln(\text{G}^{*}/\sin\delta)=-8.962\text{lnT}+39.312\) & 0.99907 \\
5\%-bio-asphalt & \(\ln(\text{G}^{*}/\sin\delta)=-8.526\text{lnT}+37.570\) & 0.99906 \\
10\%-bio-asphalt & \(\ln(\text{G}^{*}/\sin\delta)=-9.128\text{lnT}+40.376\) & 0.99848 \\
30\%-bio-asphalt & \(\ln(\text{G}^{*}/\sin\delta)=-8.989\text{lnT}+39.882\) & 0.99998 \\ \hline \hline \end{tabular} Note: RTFO is short for Rolling Thin Film Oven.  
\end{table} 
Table 2: Linear fitting results of different asphalt temperature sweep data for the unaged asphalts. Figure 10: Linear regression between \(\ln\) (\(\text{G}^{*}/\sin\delta\)) and \(\ln\)T. **(a)** Unaged; **(b)** RTFO-aged. bio-oil content was higher than 10%, the temperature sensitivity was higher than that of the matrix asphalt.