## 3 Test Setup  
Similar to asphalt binder, the rheological properties of asphalt mastics also depend on temperature and loading frequency or time [24]. Therefore, the time-temperature sweep (TTS) test was carried out using the dynamic shear rheometer (DSR) to obtain the complex modulus (G\({}^{\circ}\)) and phase angle (8) at different temperatures and loading frequencies. As Figure 1d shows, A 8 mm parallel plate geometry with a 2 mm gap was used in the TTS test at temperature of 5 \({}^{\circ}\)C, 15 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, and 35 \({}^{\circ}\)C for the mastic samples. The loading frequencies for all test temperatures were the same, including 0.2, 0.4, 0.6, 0.8, 1, 2, 4, 6, 8, 10, 20 and 30 Hz. A constant shear strain amplitude of 0.01% was applied during the dynamic loading within the linear visco-elastic zone of the mastics. According to the time-temperature equivalence principle, the \(|G^{\ast}|\) at different temperatures and frequencies could be shifted to one master-curve under one reference temperature by the WLF function as Equation (2) shows. Given that, the composition of the mastics is complex compared to the neat asphalt binder, including different filler contents and different modified asphalt binders, the shape parameter m\({}_{\rm e}\) of the master-curve may not be equal to 1, so the CAM model [25] was used to fit the complex modulus mastercurve of the mastics as Equation (3) exhibits. Equation (4) shows the calculation of the parameter \(R\).  
\[\log\alpha_{T}=\frac{C_{1}(T-T_{0})}{C_{2}+T-T_{0}} \tag{2}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Properties** & **70\#** & **PG70-22** & **PG76-22** \\ \hline Penetration (25 \({}^{\circ}\)C, 100 g, 5 s) (0.1 mm) & 70 & 65 & 51 \\ \hline Ductility (cm, 5 cm/min, 5 \({}^{\circ}\)C) & 25 & 38.1 & 33 \\ \hline Softening point (\({}^{\circ}\)C) & 47 & 62.4 & 82 \\ \hline \(|\)G\({}^{\bullet}\)/sin\(\delta\) (Original sample) & 1.513 (58 \({}^{\circ}\)C) & 1.991 (70 \({}^{\circ}\)C) & 1.880 (76 \({}^{\circ}\)C) \\  & 0.773 (64 \({}^{\circ}\)C) & 0.956 (76 \({}^{\circ}\)C) & 0.652 (82 \({}^{\circ}\)C) \\ \hline \(|\)G\({}^{\bullet}\)/sin\(\delta\) (After RTFOT) & 5.027 (58 \({}^{\circ}\)C) & 2.881 (70 \({}^{\circ}\)C) & 2.831 (76 \({}^{\circ}\)C) \\  & 1.923 (64 \({}^{\circ}\)C) & 1.194 (76 \({}^{\circ}\)C) & 1.321 (82 \({}^{\circ}\)C) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Rheological properties of three different binders.  
Figure 1: Sample preparation procedures: (**a**) mixing by the homogenizer; (**b**) Completed asphalt mastics; (**c**) Mastic plates after oven aging; (**d**) Samples out of the silicon mold.  
\[G^{*} =G_{e}^{*}+\frac{G_{g}^{*}-G_{e}^{*}}{\left[1+\left(f_{c}/f^{\prime} \right)^{k}\right]^{m_{e}/k}} \tag{3}\] \[R =\log\frac{2^{m_{e}/k}}{1+(2^{m_{e}/k}-1)G_{e}^{*}/G_{g}^{*}} \tag{4}\]  
where: \(T\) = test temperature, \({}^{\circ}\)C; \(\alpha_{T}\) = the shifted factors at temperature \(T\); \(C_{1}\), \(C_{2}\) = fitting coefficient; \(T_{0}\) = the reference temperature, \({}^{\circ}\)C; \(G_{g}^{*}\) = glass modulus, Mpa; \(G_{e}^{*}\) = the modulus of equilibrium, Mpa; \(f_{c}\) = crossover frequency, Hz; \(m_{e}\), \(k\) = shape parameters; \(f^{\prime}\) = reduced frequency, Hz. \(G^{*}\) = predicted complex modulus, Mpa; \(R\) = the width of the relaxation spectrum.