# Determining the Compaction Temperature of Warm-Mix Anti-Rutting Asphal Mixture
## 3 Viscosity-Temperature Curve of Warm-Mix Anti-Rutting Asphalt
### Viscosity-Temperature Curve  
According to the test requirements of (JTG E20-2011) T0702, the Brookfield rotational viscosity test was conducted on warm-mix anti-rutting asphalt with different warm-mix-agent amounts (0%, 1%, 2%, and 3%) at four different temperatures (115, 135, 155, and 175 \({}^{\circ}\)C). The test results are shown in Table 6.  
Using the results from the Brookfield viscosity tests, the viscosity-temperature curves for modified asphalt with anti-rutting agent contents of 6% are plotted, as shown in Figure 5. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test** & **0\% Sasobit** & **1\% Sasobit** & **2\% Sasobit** & **3\% Sasobit** \\
**Temperature** & **Warm-Mix** & **Warm-Mix** & **Warm-Mix** & **Warm-Mix** \\
**(\({}^{\circ}\)C)** & **Agent** & **Agent** & **Agent** & **Agent** \\ \hline
115 & 5.315 & 4.662 & 4.450 & 4.228 \\
135 & 1.917 & 1.432 & 1.276 & 1.188 \\
155 & 0.685 & 0.347 & 0.324 & 0.308 \\
175 & 0.235 & 0.155 & 0.144 & 0.132 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Viscosity of modified asphalt under 6% anti-rutting agent (Pa-s). Figure 5: Viscosity–temperature curves of modified asphalt at 6% anti-rutting agent. The Brookfield rotational viscosity decreases exponentially as the test temperature increases. This is due to the increase in intermolecular movement of the asphalt material at high temperatures, resulting in a decrease in viscosity. The test data in the viscosity-temperature curves were fitted to obtain the fitted equations for the viscosity-temperature curves at different Sasobit warm-mix agent:  
\[0\text{s}:\text{y} =1804.9096*\exp(-0.05064*\text{x})-0.01984(\text{R2}=0.99999) \tag{1}\] \[1\text{s}:\text{y} =4468.1296*\exp(-0.05966*\text{x})-0.01705(\text{R2}=0.99946)\] (2) \[2\text{s}:\text{y} =6764.2861*\exp(-0.06374*\text{x})+0.02014(\text{R2}=0.99976)\] (3) \[3\text{s}:\text{y} =7265.4267*\exp(-0.06482*\text{x})+0.02540(\text{R2}=0.99985) \tag{4}\]  
where 0s, 1s, 2s, and 3s represent the contents of Sasobit warm-mix agent as 0%, 1%, 2%, and 3%. Based on the fitting equations, the mixing and compaction temperatures of the warm-mix anti-rutting asphalt mixture with different warm-mix agent contents under the condition of 6% anti-rutting agent content can be calculated backward. When the anti-rutting agent content is 6%, the mixing temperatures of the warm-mix anti-rutting asphalt mixture with 0%, 1%, 2%, and 3% warm-mix agent contents are 180.88 \({}^{\circ}\)C, 168.96 \({}^{\circ}\)C, 168.18 \({}^{\circ}\)C, and 166.92 \({}^{\circ}\)C. Compared with the anti-rutting asphalt mixture without the addition of warm-mix agent, the mixing temperatures of the warm-mix anti-rutting asphalt mixture with agent contents of 1%, 2%, and 3% decrease by 6.59%, 7.02%, and 7.72%. The compaction temperatures are 171.86 \({}^{\circ}\)C, 161.23 \({}^{\circ}\)C, 159.55 \({}^{\circ}\)C, and 158.28 \({}^{\circ}\)C. Compared with the anti-rutting asphalt mixture without the addition of warm-mix agent, the compaction temperatures of the warm-mix anti-rutting asphalt mixture with agent contents of 1%, 2%, and 3% decrease by 6.19%, 7.16%, and 7.90%. These data are calculated based on the relationship between temperature and viscosity. A comprehensive analysis of the viscosity-temperature curves of warm-mix anti-rutting composite-modified asphalt reveals the following: The addition of warm-mix agent can reduce the viscosity of modified asphalt. After the addition of warm-mix agent (\(\leq\)3%), the mixing and compaction temperatures obtained from the viscosity-temperature curve generally decrease by 6% to 8%. It can be seen that as the amount of warm-mix agent increases, and the mixing and compaction temperatures obtained from the composite-modified asphalt viscosity-temperature curve both show a decrease, but the degree of decrease is not significant.