## 3 Lab Testing Protocol
### Stiffness Modulus Based on Frequency Variations  
Furthermore, four different loading frequencies were used to evaluate the stiffness modulus under varying loading conditions at 1.2, 1.9, 3.5 and 5 Hz at 20 \({}^{\circ}\)C. The time-temperature superimposition principle is used as shown in Equation (4). \[log\propto_{T}=\frac{C_{1}\times\left(T-T_{ref}\right)}{C_{2}+\left(T-T_{ref} \right)} \tag{4}\]  
where \(\propto\) is the shift factor, \(T\) is the testing temeprature, \(T_{ref}\) is the reference emeprature and \(C_{1}\) and \(C_{2}\) are equaion parameters. Error margin was kept at a maximum value of 3%, both for the stiffness modulus evaluation at various frequencies and for indirect tensile strength at various loading rates. Error margin was further decreased by testing three samples for each scenario of frequency and loading rate. This component of research, with the use of different frequency variations for calculation of stiffness modulus, add further details to the research performed by [PERSON] et al. [14]. Furthermore, the optimization of shift factor was performed on the master curve and the shift factor was applied on phase angle master curve. The stiffness moduli values at 1.2, 1.9, 3.5 and 5 Hz are shown in Table 7. A gradual increase in stiffness moduli of the mixtures occurs with an increase in the loading frequency values. The highest accumulation of stiffness modulus is shown by BF mixtures, where the maximum value reaches 8442 MPa at 5 Hz and 8195 MPa at 1.9 Hz. PF and LF modified asphalt mixtures immediately follow the modulus values of BF, with magnitudes of 7918 MPa and 7503 MPa at 5 Hz, respectively. The SBS-7% mixture exhibits the maximum stiffness of 6902 MPa at 5 Hz, which corresponds to a 20% decrease in stiffness modulus compared to BF at 5 Hz and an 8% decrease in stiffness modulus compared to LF. The determination of stiffness modulus at variable frequencies provides a thorough insight into the performance of asphalt mixtures in terms of permanent deformation resistance. The graphical representation of stiffness modulus values at variable frequency ranges is shown in Figure 1. As observed, a gradual increase in stiffness modulus occurs for each mixture type when moving from 1.2 Hz to 5 Hz. The highest gain in stiffness modulus values is exhibited by BF modified asphalt mixture with maximum value ranging up to \begin{table}
\begin{tabular}{c c c} \hline \hline
**Mixture Types** & **Modulus (MPa)** & **f (Hz)** \\ \hline  & 6902 & 5 \\ SBS-7\% & 6532 & 3.5 \\  & 6241 & 1.9 \\  & 6103 & 1.2 \\ \hline  & 7548 & 5 \\ LF & 7498 & 3.5 \\  & 7325 & 1.9 \\  & 7219 & 1.2 \\ \hline  & 7918 & 5 \\ PF & 7725 & 3.5 \\  & 7647 & 1.9 \\  & 7587 & 1.2 \\ \hline  & 8543 & 5 \\ BF & 8354 & 3.5 \\  & 8236 & 1.9 \\  & 8195 & 1.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Stiffness modulus values at different loading frequencies. 8543 MPa at 5 Hz. BF modified asphalt mixture outperforms PF and LF modified asphalt mixtures by 7.5% and 125, respectively. The SBS-7% asphalt mixture exhibits the least accumulation of stiffness modulus values in all frequency ranges when compared to fiber-modified asphalt mixtures. Stiffness modulus increment slows down for LF when the loading frequency is greater than 1.9 Hz, thereby yielding almost identical modulus values at 3.5 Hz and 5 Hz. The performance of BF and LF modified asphalt mixtures remains almost identical when compared to BF modified asphalt mixtures. As observed, the increase in loading rate of up to 70 MPa/s further enhances the indirect tensile strength of each mixture type. A gradual increase in indirect tensile strength can be observed for base asphalt with 1.522 MPa at 10 MPa/s and a maximum strength of 3.483 MPa at 70 MPa/s. A similar pattern of increment in indirect tensile strength can be observed for modified mixtures. CR-20 exhibits the maximum accumulation of indirect tensile strength at 3.898 MPa at 70 MPa/s.