## 3 Results and Discussions
### Dynamic Mechanical Analysis
#### 3.3.4 Master Curve  
Isotherms (\(-\)15 to 95 \({}^{\circ}\)C) obtained after the frequency sweep test were then shifted to a reference temperature (25 \({}^{\circ}\)C) using the superposition principle. Figure 14 shows shifting of isotherms for Base binder (BB). Shifting of all other binder configurations was carried out using the same procedure. Frequency was reduced using shift factors which were obtained using Equation (2). Activation Energy (E\({}_{\text{a}}\)) in Equation (2) was calculated while minimizing the sum of square of errors in theoretical and practical measured values of G* (Table 8). After obtaining a reduced frequency axis, G* values measured in the laboratory were plotted against this reduced frequency axis by horizontal translation of the curves obtained at different temperatures to a reference temperature.  
Afterwards, theoretically measured G* values were fitted to the actual measured values of G* using the solver function in excel by minimizing the sum of squares of errors and Mastercurves were obtained for each binder (BB, FR, UFO, FO) as shown in Figures 15 and 16. It is illustrated that waste oil rejuvenated asphalts (FR, UFO, FO) in the unaged condition had lower modulus values as compared to BB on low temperature side and hence were more capable of resisting fatigue or thermal cracking. Reduction of stiffness in case of FO and FR binders were higher compared to UFO. However, on the high temperature end, higher modulus values were desired to resist rutting. Waste-oil rejuvenated binders predicted slightly less rut resistance as compared to base binder.  
Figure 14: Superpositioning of unaged base binder (BB) (**a**) isotherms and (**b**) horizontal shifting using shift factors.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Binder Code**} & \multicolumn{2}{c}{**Ea (kJ/mol) 1**} \\ \cline{2-3}  & **Unaged** & **RTFO Aged** \\ \hline BB & 143.293 & 149.361 \\ FR & 137.983 & 146.175 \\ UFO & 141.774 & 137.443 \\ FO & 138.415 & 139.156 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Activation energy E\({}_{\text{a}}\) of binders.  
After RTFO aging, FO showed a slightly lower modulus compared to FR binder. UFO showed a much lower erroneous modulus after RTFO aging which was caused by the material breakage under the same testing criteria and should not be assessed as better fatigue resistance. The material breakage of UFO can be supported by its less activation energy compared to the unaged condition (Table 8). There was no significant difference on the high temperature end, among all binders, even after short term aging.  
In summary, this study evaluates the properties imparted to asphalt binder by mixing 2.5% of fresh and waste engine oil and the effect of filtering the waste oil before rejuvenation. Virgin asphalt binder employed in this research is locally used in South Korea for pavement construction. Laboratory experimentation incorporates RV, FTIR and DHR tests for rheological and chemical analysis of binders. RV test results showed that, initially, the decrement in asphalt viscosity after oil addition was more significant in fresh oil. However, after RTFO aging no significant difference was observed between fresh and waste engine oil. An increased amount of carbonyl functional group in rejuvenated asphalt  
Figure 16: Comparison of master curves for RTFO-aged samples.  
Figure 15: Comparison of master curves for unaged samples.  
molecules can be visualized through FTIR spectra. FO and UFO binder proved to be less age susceptible considering the deficiency of unsaturated hydrocarbons. DHR test data demonstrated improvement in low temperature properties at the expense of upper PG grade which was compromised by 1-3 \({}^{\circ}\)C. DHR data were further analyzed with a Modified Sigmoidal Model to construct Mastercurves for a comprehensive assessment of fatigue cracking and rutting resistance on a wide range of frequency and temperatures.