## 4 Results and Discussion
### Complex Viscosity and Loss Factor (Tan \(\delta\)) Results
The loss factor (tan \(\delta\)) in the 5% SBS sample is also lower at 15 \({}^{\circ}\)C, indicating a more elastic response, while at 25 \  
Overall, the 5% SBS-modified bitumen shows better performance in terms of flexibility and viscosity reduction compared to the 4% SBS-modified bitumen, particularly at higher temperatures. The higher SBS content enhances the bitumen's ability to resist deformation at low temperatures while maintaining flexibility at higher temperatures, improving its resistance to block cracking. In the 5% animal bone ash-modified sample (Tables 7-10), the trends are similar but with slightly higher viscosity values compared to the 4% sample. This indicates increased stiffness as the concentration of animal bone ash rises, particularly at 15 \({}^{\circ}\)C, where the bitumen becomes more resistant to deformation, suggesting a greater tendency to crack under stress. The tan \(\delta\) values also reflect this, with lower values at 15 \({}^{\circ}\)C, showing that the material behaves more elastically, and higher values at 25 \({}^{\circ}\)C, where it behaves more viscously. For the 6% animal bone ash-modified sample (Tables 7-10), the complex viscosity values are the highest among the three concentrations, particularly at 15 \({}^{\circ}\)C, which indicates the stiffest behavior and the greatest resistance to flow. This increased stiffness makes the bitumen more prone to cracking, especially in colder conditions. The loss factor (tan \(\delta\)) remains lower at 15 \({}^{\circ}\)C, indicating a more solid-like response, while at 25 \({}^{\circ}\)C, the bitumen exhibits slightly higher tan \(\delta\) values, reflecting more viscous behavior and better flow characteristics at higher temperatures. In summary, increasing the concentration of animal bone ash in the bitumen leads to higher viscosity and greater stiffness, particularly at lower temperatures (15 \({}^{\circ}\)C), which can increase the risk of cracking under stress. At higher temperatures (25 \({}^{\circ}\)C), the bitumen becomes more flexible and fluid-like, though the overall stiffness increases as the  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Bitumen** & \multirow{2}{*}{**Unmodified**} & \multirow{2}{*}{**4\% SBS**} & \multirow{2}{*}{**5\% SBS**} & \multirow{2}{*}{**4\% AB**} & \multirow{2}{*}{**5\% AB**} & \multirow{2}{*}{**6\% AB**} & \multirow{2}{*}{**3\% WCO**} & \multirow{2}{*}{**4\% WCO**} & \multirow{2}{*}{**5\% WCO**} \\
**Type** & & & & & & & & & & \\ \hline
**Ang  
concentration of animal bone ash rises. The 4% animal bone ash offers a balance between stiffness and flexibility, while 6% animal bone ash shows the greatest increase in stiffness and susceptibility to cracking under cold conditions. In the 3% WCO-modified sample (Tables 7-10), the complex viscosity decreases with increasing angular frequency, demonstrating the shear-thinning behavior characteristic of bitumen. At 15 \({}^{\circ}\)C, the viscosity is higher than at 25 \({}^{\circ}\)C, indicating that the bitumen is stiffer and more resistant to deformation at lower temperatures. The loss factor (tan \(\delta\)) is lower at 15 \({}^{\circ}\)C, reflecting more elastic (solid-like) behavior, while at 25 \({}^{\circ}\)C, tan \(\delta\) values are higher, indicating more viscous behavior and better flexibility. For the 4% WCO-modified sample (Tables 7-10), the trends are similar, but the complex viscosity is slightly lower compared to the 3% WCO sample, especially at 25 \({}^{\circ}\)C. This indicates improved flexibility with the increase in WCO concentration. The tan \(\delta\) values remain consistent, with the bitumen showing more viscous behavior at 25 \({}^{\circ}\)C and more elastic behavior at 15 \({}^{\circ}\)C. This suggests that increasing WCO concentration allows the bitumen to maintain a more flexible, fluid-like behavior at higher temperatures while maintaining sufficient stiffness at lower temperatures.