# Mechanism of HCB-Modified Asphalt and Dynamic Properties of Mixtures
## 6 Dynamic Properties of HAM
### Dynamic Response Parameter Analysis  
Dynamic modulus and phase angle are considered the important parameters to characterize the viscoelasticity of asphalt mixtures, which can reflect the actual force and dynamic response of asphalt pavement [20,21]. Under different temperatures, the dynamic moduli and phase angle of HAM and BAM with the variation of loading frequencies are exhibited in Figures 9 and 10.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**BA**} & \multicolumn{2}{c}{**CB-Modified Asphalt**} & \multicolumn{2}{c}{**HCB-Modified Asphalt**} \\ \cline{2-7}
**Test Indicators** & \begin{tabular}{c} **Before** \\ **Aging** \\ \end{tabular} & \begin{tabular}{c} **After** \\ **Aging** \\ \end{tabular} & \begin{tabular}{c} **Before** \\ **Aging** \\ \end{tabular} & \begin{tabular}{c} **Before** \\ **Aging** \\ \end{tabular} & \
\begin{tabular}{c} **After** \\ **Aging** \\ \end{tabular} &
\begin{tabular}{c} **Before** \\ **Aging** \\ \end{tabular} \\ \hline Penetration (25 \({}^{\circ}\)C)/(1/10 mm) & 83 & 46 & 81 & 48 & 73 & 47 \\ Ductility (5 \({}^{\circ}\)C)/cm & 7.4 & 0 & 7.3 & 0 & 8.1 & 4.5 \\ Softening point (R\&B)/\({}^{\circ}\)C & 44.5 & 51.5 & 46.2 & 52.4 & 47.4 & 52.8 \\ Penetration ratio (\%) & - & 56.4 & - & 62.7 & - & 64.7 \\ Softening point increase (\({}^{\circ}\)C) & - & 7.0 & - & 6.2 & - & 5.4 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Properties of asphalt binders before and after aging.  
As shown in Figure 9, the variation tendency of the dynamic modulus for two mixtures remained the same, i.e., both of the dynamic moduli slid progressively with the increase of temperature. The dynamic modulus of HAM was evidently larger than that of BAM at lower temperatures (4.4 \({}^{\circ}\)C and 21.1 \({}^{\circ}\)C), which suggests that adding HCB can increase the nondeformability of an asphalt mixture; polar oxygen-containing functional groups enhance the elasticity of asphalt. The difference of dynamic moduli for the two mixtures slid progressively with the increase of temperature; in particular, both of the dynamic moduli were almost the same at 54.4 \({}^{\circ}\)C, which suggests that the viscoelasticities of the mixtures were similar at higher temperature. In addition, the dynamic moduli increased progressively with the growth of loading frequency, whereas the increase was different in different frequency ranges (0.1-1 Hz). The dynamic moduli increased sharply at a lower frequency range (0.1-1 Hz), and it was smaller and smaller at higher loading frequencies (5-25 Hz). The higher the frequency, the shorter the duration of the load, and the smaller the creep deformation of the asphalt mixture.  
As shown in Figure 10, the variation tendency of phase angles for two mixtures remained the same. As the loading frequency decreased, the phase angle increased progressively at the lower temperature of 4.4 \({}^{\circ}\)C, and at 21.1 \({}^{\circ}\)C, and the increase of phase angle of the HAM asphalt mixture was relatively small. HCB can enhance the elasticity of asphalt mixtures, while there was no apparent difference in phase angle between the two asphalt mixtures at higher temperatures.  
Figure 10: Phase angles of mixtures.  
Figure 9: Dynamic moduli of mixtures.