# Dynamic Characteristic Master Curve and Parameters of Different Asphalt Mixtures
## 4 Master Curves of Different Asphalt Mixture  
Table 4 shows the material types and volume indexes of several kinds of asphalt mixtures. The data of the dynamic modulus and phase angle were obtained on an AMPT tester. The master curve parameters were analyzed by Equations (1) and (2), and the main curve diagram of the mixture at 40 \({}^{\circ}\)C was drawn. (1) Figure 11A shows the modulus master curve of the asphalt mixtures. Due to the difference in aggregate gradation, asphalt content, and volume index of asphalt mixtures, the difference in the dynamic modulus is obvious; due to the different form and properties of the asphalt binder, the shape of the modulus master curve is obviously different, and the shape parameters (\(\beta\)) are also different. Figure 12 shows that grade 50, grade 70, and grade 90 petroleum asphalt is obviously different from SBS and MAC-modified asphalt, and the modulus is more sensitive to frequency. At the same time, it is also different from the binder form of emulsified asphalt (containing cement) and foamed asphalt (containing cement). The existence of emulsified asphalt and foamed asphalt combined with cement can improve the low-frequency ultimate modulus of the mixture. The dynamic characteristics of different asphalt mixtures are determined by the factors of mixture and binder. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Code** & **Asphalt Type** & **Mixture Type** & **Pb, \%** & **Vv, \%** & **VMA, \%** & **VFA, \%** \\ \hline ZH50-AC20 & Pen-grade 50 & HMA, AC20 & 4.3 & 4.6 & 14.2 & 67.32 \\ ZH70-AC20 & Pen-grade 70 & HMA, AC20 & 4.4 & 4.4 & 14.1 & 68.54 \\ ZH90-AC20 & Pen-grade 90 & HMA, AC20 & 4.3 & 4.4 & 14.4 & 68.47 \\ SBS-SMA13 & SBS modified & HMA, SMA13 & 6 & 4.2 & 17.1 & 75.6 \\ asphalt & MAC-AC20 & MAC modified & HMA, AC20 & 4.4 & 4.3 & 13.4 & 68.3 \\ ZH70-AC-25 & Pen-grade 70 & HMA, AC25 & 4.1 & 4.1 & 12.6 & 68 \\ MAC-LSTM30 & MAC modified & HMA, LSPM30 & 3.2 & 15.2 & 23.5 & / \\  & asphalt & & & & & \\ SBS-AC13 & SBS modified & HMA, AC13 & 6.2 & 2.4 & 15.2 & 82.9 \\ E-CRM & Emulsified asphalt & Cold recycling & 3.5 (plus 1.5\%cement) & 10.2 & / & / \\ F-CRM1 & Formed asphalt & Cold recycling & 3 (plus 1.5\%cement) & 11.5 & / & / \\ F-CRM2 & Formed asphalt & Cold recycling & 3 (plus 1.5\%cement) & 12.0 & / & / \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Material types and volume indices of several asphalt mixtures. Figure 10: Relationship between relaxation time (\(\tau\)) and temperature. (2) Figure 11B shows the phase angle master curve of the mixture. Table 5 shows the phase angle master curve parameters. Due to the different forms and properties of the binder, the phase angle master curve of the mixture is obviously different. Among them, the change range of phase angle (A) of foam cold-recycled asphalt mixture is much smaller than that of other asphalt mixtures and emulsified asphalt mixtures. Figure 13 shows that its A/\(\omega\) value is the smallest, reflecting the weakest viscoelastic characteristics, and tends to be rigid, which is related to the cement cementitious state and the non-continuous distribution of foamed asphalt on the aggregate surface. Although the cold-recycled mixture of emulsified asphalt has a lower initial phase angle (\(\delta_{0}\)), it shows more significant viscoelasticity and the variation range of FWHM (\(\omega\)) and phase angle height (A) is larger than that of foamed asphalt. This is related to the continuous distribution of emulsified asphalt among aggregate particles, shown in Figure 14. For the binder of the hot-mix asphalt mixture, SBS-modified asphalt mixture SBS-AC13 has the best viscoelastic performance, and its A/\(\omega\) ratio is the highest. Figure 11: Comparison of master curves of different asphalt mixtures. (**A**) Dynamic modulus master curve, (**B**) Phase angle master curve. Figure 12: Comparison of shape parameters (\(\beta\)) of modulus master curves.