## 4 Results and Discussion
### Storage and Loss Modulus Results

Table 6: Loss modulus [kPa] at 25 \({}^{\circ}\)C.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Bitumen Type** & **Unmodified** & **4\% SBS** & **5\% SBS** & **4\% AB** & **5\% AB** & **6\% AB** & **3\% WCO** & **4\% WCO** & **5\% WCO** \\ \hline
**Angular Frequency** & \multicolumn{8}{c}{**Loss Modulus G\({}^{\prime\prime}\) [Pa]**} \\
**[rad/s]** & \multicolumn{8}{c}{**Loss Modulus G\({}^{\prime\prime}\) [Pa]**} \\ \hline
100 & \(9.12\times 10^{3}\) & \(1.31\times 10^{7}\) & \(1.20\times 10^{7}\) & \(8.51\times 10^{3}\) & \(1.32\times 10^{7}\) & \(6.97\times 10^{3}\) & \(6.97\times 10^{3}\) & \(4.60\times 10^{3}\) & \(7.61\times 10^{3}\) \\ \hline
68.1 & \(7.93\times 10^{3}\) & \(1.18\times 10^{7}\) & \(9.74\times 10 For unmodified bitumen, both G\({}^{\prime}\) and G\({}^{\prime\prime}\) show a larger decline at 25 \({}^{\circ}\)C compared to 15 \({}^{\circ}\)C. The reduced stiffness at higher temperatures can result in poorer performance in hot climates, where bitumen tends to soften and lose its ability to resist deformation. However, the modified bitumen samples exhibit improved resilience at both temperatures, especially in terms of retaining higher G\({}^{\prime}\) values. SBS-modified bitumen demonstrates significant enhancement in storage modulus at both 15 \({}^{\circ}\)C and 25 \({}^{\circ}\)C. While the elastic response (G\({}^{\prime}\)) and viscous response (G\({}^{\prime\prime}\)) decrease as the temperature increases, the reduction is less severe compared to unmodified bitumen. The 5% SBS-modified bitumen, in particular, retains a much higher G\({}^{\prime}\) at 25 \({}^{\circ}\)C than unmodified bitumen, indicating that SBS modification significantly enhances bitumen's ability to retain stiffness and elasticity even at elevated temperatures. This is beneficial for high-temperature performance, as roads constructed with SBS-modified bitumen would be less prone to rutting or deformation under traffic loading. Similarly, the bitumen samples modified with animal bone ash also show improved stiffness and elasticity at both temperatures. At 15 \({}^{\circ}\)C, the G\({}^{\prime}\) values for animal bone ash-modified bitumen are significantly higher than those of unmodified bitumen, with the 6% animal bone ash sample exhibiting the greatest improvement. However, the drop in G\({}^{\prime}\) when the temperature increases to 25 \({}^{\circ}\)C is more noticeable in animal bone ash-modified bitumen compared to SBS-modified bitumen. This suggests that while animal bone ashes enhance the elastic behavior of bitumen, their effectiveness diminishes more rapidly at higher temperatures compared to SBS. Moreover, although the increased stiffness provided by AB improves deformation resistance, it can also reduce the binder's ability to relax thermal stresses, particularly at lower temperatures. This limited relaxation capacity may lead to stress accumulation and an increased risk of thermal or fatigue cracking. Therefore, while 6% AB yields the highest stiffness, it may also introduce brittleness under cold conditions, highlighting the importance of optimizing the dosage to balance stiffness gains with flexibility and crack resistance. Bitumen modified with waste cooking oil shows the least improvement in G\({}^{\prime}\) and G\({}^{\prime\prime}\) at both temperatures. The addition of waste cooking oil seems to act more as a softening agent, which leads to better flexibility at lower temperatures (15 \({}^{\circ}\)C) but results in a more significant reduction in modulus at 25 \({}^{\circ}\)C. At 25 \({}^{\circ}\)C, waste cooking oil-modified bitumen demonstrates a more pronounced viscous behavior (higher G\({}^{\prime\prime}\)) compared to its elastic response (G\({}^{\prime}\)), indicating that the bitumen may become softer and more susceptible to deformation at higher temperatures, which may limit its applicability in hot climates.