## 3 Experimental Design of Composite-Modified Asphal
### Determination of Compound Modifier Dosing
#### 3.3.3. Rheological Properties of Modified Asphalt
Comparison of the rutting factor data between original and short-term aged samples reveals that aging can enhance the rutting factor and improve resistance to high-temperature deformation of asphalt. The trend of high-temperature performance remains consistent for several asphalts. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Temperature\({}^{\text{f}}\)C** & **20C** & **3R20C** & **6R20C** & **9R20C** & **12R20C** \\ \hline
58 & 20.67 & 23.46 & 29.58 & 31.77 & 33.52 \\ \hline
64 & 13.28 & 15.35 & 19.07 & 20.77 & 21.63 \\ \hline
70 & 8.44 & 10.05 & 12.34 & 13.69 & 14.88 \\ \hline
76 & 5.32 & 6.47 & 7.99 & 8.82 & 9.80 \\ \hline
82 & 3.35 & 4.16 & 5.19 & 4.67 & 6.69 \\ \hline
88 & 2.11 & 2.66 & 3.36 & 3.46 & 3.90 \\ \hline
94 & 1.35 & 1.71 & 2.26 & 2.47 & 2.76 \\ \hline
100 & 0.88 & 1.11 & 1.40 & 1.67 & 1.82 \\ \hline \end{tabular}
\end{table} 
Table 11: Rutting factor of original samples (kPa). Figure 4: The G* and \(\delta\) of short-term aged samples. To quantify the correlation between the rutting factor and temperature more accurately, this study uses Origin 2017 and regression Equation (1) to fit the curve. The fitting results are presented in Table 13.  
\[\text{G}^{\star}/\text{sin}\delta=Ae^{BT} \tag{1}\]  
where \(T\) is the test temperature, \(A\) and \(B\) are constants related to the properties of the asphalt material. Based on the fitted results, Equation (1) shows correlation coefficients A and B higher than 0.9900, accurately describing the variation of the rutting factor with temperature. The similar values of B indicate a general consistency in the trend of several asphalts with temperature. (2) Frequency scan \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Asphalt**} & \multicolumn{3}{c}{**Original Samples**} & \multicolumn{3}{c}{**RTOFT Samples**} \\ \cline{2-7}  & **A** & **B** & \(\mathbf{R}^{2}\) & **A** & **B** & \(\mathbf{R}^{2}\) \\ \hline
20C & 1674.8 & \(-\)0.076 & 0.9999 & 1892.1 & \(-\)0.075 & 0.9948 \\ \hline
3R20C & 1641.8 & \(-\)0.073 & 0.9999 & 1992.2 & \(-\)0.073 & 0.9993 \\ \hline
6R20C & 1989.3 & \(-\)0.073 & 0.9998 & 2305.9 & \(-\)0.069 & 0.9998 \\ \hline
9R20C & 1969.5 & \(-\)0.071 & 0.9986 & 2393.3 & \(-\)0.07 & 0.9921 \\ \hline
12R20C & 1914.3 & \(-\)0.07 & 0.9988 & 2615.7 & \(-\)0.069 & 0.9966 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: The curve fitting parameters of G\({}^{\star}\)/sin\(\delta\) with T.  
Figure 5: Comparison of rutting factors between original and short-term aging samples. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Temperature/\({}^{\circ}\)C** & **20C** & **3R20C** & **6R20C** & **9R20C** & **12R20C** \\ \hline
58 & 25.67 & 29.16 & 36.16 & 39.07 & 45.60 \\ \hline
64 & 15.95 & 18.84 & 23.59 & 25.62 & 32.26 \\ \hline
70 & 9.65 & 12.15 & 15.71 & 17.75 & 20.41 \\ \hline
76 & 5.69 & 7.71 & 10.17 & 12.13 & 13.94 \\ \hline
82 & 3.60 & 5.00 & 6.76 & 8.03 & 10.05 \\ \hline
88 & 2.29 & 3.19 & 4.33 & 5.34 & 6.56 \\ \hline
94 & 1.61 & 2.24 & 2.79 & 2.65 & 3.88 \\ \hline
100 & 1.15 & 1.32 & 1.79 & 2.22 & 2.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Rutting factor of short-term aged samples (kPa). The frequency scan test was conducted to reflect the changes in the viscoelasticity of asphalt pavements under vehicle loading. This test involves applying continuously varying frequencies to asphalt samples and obtaining their dynamic mechanical response spectra as well as various viscoelasticity parameters. Table 14 presents the parameters obtained from the frequency scan test. The complex shear modulus G* is composed of two components: the elastic energy storage modulus G\({}^{\prime}\) (G\({}^{\prime}\) = G* cos\(\delta\)) and the viscous loss modulus G\({}^{\prime\prime}\)(G\({}^{\prime\prime}\) = G* sin\(\delta\)). Specifically, G\({}^{\prime}\) represents the energy stored in asphalt during deformation, while G\({}^{\prime\prime}\) characterizes the energy dissipated by the asphalt during thermal shear.