## 2 Material and Methods
### Testing Program  
Table 3 summarizes the penetration, softening point, penetration index, storage stability, ductility, loss on heating, and viscosity tests performed in this research to determine the properties of the conventional asphalt binder. The softening point and penetration values were used to compute the penetration index (_PI_) using Formula (1).  
\[PI=\frac{1952-500 loglog\;PEN-20 SP}{50 loglog\;PEN-SP-120}, \tag{1}\]  
where _PI_ is the penetration index, _PEN_ is the penetration value (0.1 mm), and _SP_ is the softening point value (\({}^{\circ}\)C). The viscosity and penetration values were used to compute the penetration viscosity number (_PVN_) using Formula (2).  
\[PVN=\frac{4.258-0.7967\;log\;P-loglog\;V}{(0.795-0.1858\;log\;P)} \tag{2}\]  
where _PVN_ is the penetration viscosity number, \(V\) is the viscosity in centistokes measured at 135 \({}^{\circ}\)C (cp), and \(P\) is the penetration value at 25 \({}^{\circ}\)C (0.1 mm).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Binder** & **ID** & \begin{tabular}{c} **Asphalt Binder** \\ **(\%)** \\ \end{tabular} & \
\begin{tabular}{c} **Crumb** \\ **(\%)** \\ \end{tabular} &
\begin{tabular}{c} **Warm Mix Additive** \\ **(\%)** \\ \end{tabular} \\ \hline Virgin 60/70 & V & 100 & - & - \\ \hline Crumb rubber & CR & 100 & 5 & - \\ \hline Sasobit & SA & 100 & - & 1.5 \\ \hline Cecabase & CE & 100 & - & 0.44 \\ \hline Rediset & RE & 100 & - & 1.5 \\ \hline Sasobit + crumb rubber & SECR & 100 & 5 & 1.5 \\ \hline Cecabase + crumb rubber & CECR & 100 & 5 & 0.44 \\ \hline Rediset + crumb rubber & RECR & 100 & 5 & 1.5 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Composition of the modified and virgin asphalt binders.  
Figure 2: The high-shear mixer for blending the modified asphalt binders.  
[PERSON] [38] introduced the concept of stiffness modulus, which represents the ratio between a consistent uniaxial stress and the resultant uniaxial strain at a specified time. By examining the outcomes of tests conducted on 47 bitumens, [PERSON] constructed a graphical tool, known as a nomograph, designed to ascertain the stiffness of asphalt binder, accounting for temperature and loading time (or frequency), given knowledge of the softening temperature and penetration. For the practical determination of binder stiffness, the BitProps program is a useful tool. This program utilizes a digitized version of [PERSON]'s nomograph, developed by [PERSON] and [PERSON] [39], facilitating the ease of calculation. The study evaluated the stiffness characteristics of eight distinct asphalt binders, both unmodified and modified, across varying temperature conditions: low, intermediate, and high. This assessment employed five distinct loading scenarios, considering outcomes from penetration and softening point tests. The selected temperatures for this investigation corresponded to the low, intermediate, and high temperature ranges observed in Kuala Lumpur, Malaysia. Figure 3 shows the flowchart of the research.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Asphalt Binder Test (Unit)** & **Test Standard** & **Specification** \\ \hline Penetration at 25 \({}^{\circ}\)C (0.1 mm) & ASTM D5 & 60–70 \\ \hline Softening point (\({}^{\circ}\)C) & ASTM D36 & 48–52 \\ \hline Penetration index & - & \(-\)2 to 2 \\ \hline Penetration viscosity number & - & - \\ \hline Storage stability (\({}^{\circ}\)C) & ASTM D5892 & \(<\)2.2 \\ \hline Ductility at 25 \({}^{\circ}\)C (cm) & ASTM D113 & Min. 100 \\ \hline Loss on heating (\%) & AASHTO T240 & Max. 1.00 \\ \hline Viscosity at 120 and 135 \({}^{\circ}\)C (cp) & ASTM D4402 & - \\ \hline Stiffness modulus (MPa) & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 3: The physical properties tests conducted in this research.  
Figure 3: The flowchart of the study.