## 3 Results and Discussion
### Relaxation Characteristics of the Three Asphalt Mixtures
#### 3.3.3 Analysis of Relaxation Characteristics of Three Asphalt Mixtures  
Figure 7 shows the trend of the relaxation parameters of the three asphalt mixtures obtained by the Burgers model with the test temperatures. It can be seen from Figure 7 that the relaxation strength of the three asphalt mixtures increases with the decrease of the test temperature. From 50 \({}^{\circ}\)C to 0 \({}^{\circ}\)C, the relaxation strength of the asphalt mixtures increases slowly. However, from 0 \({}^{\circ}\)C to \(-20\)\({}^{\circ}\)C, the relaxation strength of the asphalt mixtures increases rapidly. This indicates that from 50 \({}^{\circ}\)C to 0 \({}^{\circ}\)C, the properties of the asphalt mixtures change from viscosity to viscoelasticity, which has a little effect on the relaxation strength of the asphalt mixtures. However, after the temperature drops to a certain extent, the properties of the asphalt mixtures change from viscoelasticity to elasticity, which causes the relaxation strength of the asphalt mixtures to increase rapidly. Further, it can be seen from the trend of the relaxation time with the test temperature that, as the temperature decreases, the relaxation time of the asphalt mixtures is shortened. This is due to the fact that the properties of the asphalt mixtures change from viscoelasticity to elasticity, and the elasticity is continuously increased, so that the time for releasing the internal stress of the asphalt mixture is shortened. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{8}{c}{**Temperatures (\({}^{\circ}\)C)**} \\ \cline{2-9}  & **50** & **40** & **30** & **20** & **10** & **0** & **\(-\)10** & **\(-\)20** \\ \hline \(E_{e}\) (MPa) & 23.27 & 17.76 & 18.77 & 0.87 & 6.45 & 26.72 & 89.20 & 0.0973 \\ \(E_{1}\) (MPa) & 712,357 & 32,995.2 & 57,986.4 & 175.7 & 13,056.4 & 14,422.0 & 3977.79 & 38,069.22 \\ \(E_{2}\) (MPa) & 531,625 & 32,995.21 & 38,731.11 & 175.65 & 10,995.88 & 2304.55 & 3977.79 & 3977.78 \\ \(E_{3}\) (MPa) & 509.51 & 55.19 & 95.80 & 175.64 & 10,898.08 & 2304.55 & 2766.72 & 3977.69 \\ \(E_{4}\) (MPa) & 17.54 & 46.09 & 95.80 & 174.82 & 2118.32 & 2304.55 & 2766.60 & 3977.69 \\ \(E_{5}\) (MPa) & 10.93 & 14.13 & 27.08 & 73.08 & 66.70 & 2304.55 & 2766.60 & 1822.42 \\ \(E_{6}\) (MPa) & 3.08 & 5.31 & 7.45 & 20.88 & 66.33 & 28.68 & 2591.78 & 1822.42 \\ \(E_{7}\) (MPa) & 3.08 & 5.31 & 7.44 & 11.28 & 14.78 & 28.68 & 0.0152 & 1822.42 \\ \(E_{8}\) (MPa) & 3.06 & 5.31 & 7.12 & 11.27 & 14.68 & 28.68 & 0.0151 & 1510.65 \\ \(E_{9}\) (MPa) & 2.89 & 4.84 & 4.76 & 11.04 & 14.60 & 28.25 & 0.0100 & 0.0120 \\ \(E_{10}\) (MPa) & 2.83 & 2.62 & 3.59 & 8.40 & 14.54 & 9.20 & 0.0100 & 0.0108 \\ \(E_{11}\) (MPa) & 2.62 & 2.60 & 2.86 & 8.37 & 2.91 & 9.14 & 0.0100 & 0.0103 \\ \(E_{12}\) (MPa) & 0.99 & 2.59 & 0.96 & 1.21 & 2.57 & 8.09 & 0.0100 & 0.0101 \\ R\({}^{2}\) & 0.9872 & 0.9857 & 0.9896 & 0.9864 & 0.9733 & 0.9823 & 0.9712 & 0.9525 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The fitting parameters of DBFAM based on the generalized Maxwell model. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{8}{c}{**Temperatures (\({}^{\circ}\)C)**} \\ \cline{2-9}  & **50** & **40** & **30** & **20** & **10** & **0** & **\(-\)10** & **\(-\)20** \\ \hline \(E_{e}\) (MPa) & 12.76 & 29.27 & 35.32 & 22.50 & 1.40 & 84.99 & 15.74 & 0.0123 \\ \(E_{1}\) (MPa) & 950.05 & 7617.25 & 588.95 & 4469.53 & 6536.74 & 6702.77 & 37  
It can also be seen from Figure 7 that the relaxation strength \(G_{1}\) of DBFAM is the largest, that of SBSAM is the smaller, and that of AM is the smallest. The relaxation strength \(G_{2}\) of SBSAM is the largest, that of DBFAM is the smaller, and that of AM is the smallest.