## 3 Experimental Design of Composite-Modified Asphal
### Determination of Compound Modifier Dosing
#### 3.3.3. Rheological Properties of Modified Asphalt
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Asphalt** & \(G_{0}\) & \(G_{1}\) & \(\eta_{0}\) & \(\eta_{1}\) & \(R^{2}\) \\ \hline
20C & 640.088 & 88.650 & 52.602 & 25.249 & 0.99 \\ \hline
3R20C & 765.927 & 103.138 & 67.728 & 29.296 & 0.99 \\ \hline
6R20C & 1025.911 & 147.632 & 101.421 & 41.255 & 0.99 \\ \hline
9R20C & 1213.467 & 193.833 & 154.50 & 52.889 & 0.99 \\ \hline
12R20C & 1332.117 & 270.189 & 229.961 & 69.420 & 0.99 \\ \hline \end{tabular}
\end{table} 
Table 16: Fitting parameters of the Burgers equation. Figure 11: Burger model and creep recovery. Figure 10: \(J_{ur-diff}\) of different compound-modified asphalt. \[J_{DE} = \frac{1}{C_{1}}\bigg{(}1-e^{-\frac{C_{1}}{\eta_{1}}t}\bigg{)}\text{ is the coefficient of delayed elastic deformation during }1\text{ s loading};\] \[J_{V} = \frac{1}{\eta_{0}}t\text{ is the coefficient of viscous deformation compliance during }1\text{ s loading}.\] Then, the proportion of each part of deformation compliance to creep compliance is determined. \[\left\{ \begin{aligned} J_{E}\%&=J_{E}/J(t) \times 100\%=G_{0}^{-1}/\bigg{[}G_{0}^{-1}+G_{1}^{-1}\bigg{(}1-e^{-\frac{C_{1}}{ \eta_{1}}t}\bigg{)}+t\eta_{0}{}^{-1}\bigg{]}\times 100\%\\ I_{DE}\%&=J_{DE}/J(t)\times 100\%=G_{1}^{-1} \bigg{(}1-e^{-\frac{C_{1}}{\eta_{1}}t}\bigg{)}/\bigg{[}G_{0}^{-1}+G_{1}^{-1} \bigg{(}1-e^{-\frac{C_{1}}{\eta_{1}}t}\bigg{)}+t\eta_{0}{}^{-1}\bigg{]}\times 1 00\%\\ J_{V}\%&=J_{V}/J(t)\times 100\%=t\eta_{0}{}^{-1}/ \bigg{[}G_{0}^{-1}+G_{1}^{-1}\bigg{(}1-e^{-\frac{C_{1}}{\eta_{1}}t}\bigg{)}+t \eta_{0}{}^{-1}\bigg{]}\times 100\%\end{aligned} \right. \tag{7}\]  
Equation (7) represents the three components of asphalt viscoelastic compliance with loading time, as illustrated in Figure 12. The overall creep compliance of asphalt gradually increases as the stress loading time extends. The percentage of instantaneous elastic deformation \(J_{E}\) decreases rapidly after 0.1 s, while delayed elastic deformation \(J_{DE}\) and viscous flow deformation \(J_{V}\) increase rapidly. This implies that the high-temperature deformation of modified asphalt is primarily dominated by its viscous component. Meanwhile, an increase in rock asphalt admixture within the same loading time will correspondingly decrease the overall creep compliance of composite-modified asphalt while also reducing the degree of plastic deformation exhibited by the material. \(J_{E}\) decreases rapidly with increasing rock asphalt content during loading. The rubber-modified asphalt decreased the fastest, while the 12R20C composite-modified asphalt decreased the slowest. After unloading, the percentage of \(J_{E}\) increased by 4% (3R20C), 13% (6R20C), 35% (9R20C), and 74% (12R20C) compared with 20C for composite-modified asphalts. \(J_{DE}\) first increases and then decreases with the extension of stress loading time. The delayed elastic creep compliance of rubber powder-modified asphalt has the smallest proportion, while \(J_{DE}\) increases after adding rock asphalt under the same loading time. Compared to 20C, the \(J_{DE}\) of the final composite-modified asphalt increased by 6% (3R20C), 9% (6R20C), 18% (9R20C), and 20% (12R20C). The \(J_{V}\) of the composite-modified asphalt increased rapidly with increasing loading time, while its deformation recovery capacity decreased rapidly. The \(J_{V}\) gradually decreased under the same loading time with an increase in the mass of rock asphalt. Compared to 20C, the \(J_{V}\) percentage of 12R20C was reduced by 17%, effectively controlling permanent deformation. Rock asphalt enhances the high-temperature deformation resistance of asphalt by increasing its instantaneous and delayed elastic components while decreasing the viscous flow component. Notably, the increase in the proportion of instantaneous elastic components is more pronounced. Moreover, rock asphalt can gradually enhance the viscosity of asphalt and accelerate its hardening process, thereby enhancing instant elastic recovery after force application.