## 4 Results and Discussion
### VCCD Damage Curve Results  
Figures 7-15 present the VCCD damage curves derived from the amplitude sweep tests, illustrating the fatigue behavior of various unmodified and modified bitumen samples. In these graphs, the \(x\)-axis represents the damage intensity (dimensionless), which quantifies the accumulated damage in the binder under cyclic loading. The \(y\)-axis shows the pseudo-stiffness parameter (C), also dimensionless, reflecting the degradation in material stiffness over the course of loading. These axis definitions have been added to clarify the interpretation of the fatigue performance results presented. The observed trends demonstrate how different modifiers influence the rate of stiffness reduction and the material's  
Figure 6: Step load mode results. resistance to damage progression. In Figure 7, the unmodified bitumen sample exhibits a relatively steep damage curve, indicating a rapid damage progression with applied strain. This steep increase suggests a limited capacity for resisting cumulative damage, making the unmodified bitumen more susceptible to cracking and structural breakdown under repeated loading. Without additives, the base bitumen lacks mechanisms for dissipating stress effectively, leading to faster accumulation of micro-damage, which would reduce its longevity in high-demand applications. Figure 10: VECD damage curve from amplitude sweep for modified samples (4% AB). Figure 9: VECD damage curve from amplitude sweep for modified samples (5% SBS). Figure 11: VECD damage curve from amplitude sweep for modified samples (5% AB). Figure 12: VECD damage curve from amplitude sweep for modified samples (6% AB). Figure 14: VECD damage curve from amplitude sweep for modified samples (4% WCO). Figure 13: VECD damage curve from amplitude sweep for modified samples (3% WCO). Figures 8 and 9 illustrate the performance of bitumen samples modified with 4% and 5% styrene-butadiene-styrene (SBS), showing noticeably less steep damage curves. Notably, the 5% SBS sample in Figure 9 demonstrates a gradual slope, indicating slower damage accumulation than the unmodified sample. This improved resistance to cumulative damage is likely due to SBS's ability to form a resilient polymer network within the bitumen, enhancing its capacity to absorb and dissipate strain energy effectively. The polymeric structure of SBS contributes both elasticity and toughness, making it suitable for applications where durability under repetitive loading is critical. Consequently, SBS-modified samples resist micro-damage formation more effectively, extending the material's lifespan in high-stress environments. In Figures 10-12, the damage curves for bitumen modified with animal bone ashes (AB) also reveal a reduction in slope compared to the unmodified bitumen, with the 6% AB-modified sample (Figure 12) exhibiting the most gradual slope. This indicates that higher AB concentrations significantly enhance resistance to cumulative damage. AB's reinforcement effect likely stems from its ability to increase the elastic properties of bitumen, enabling more effective recovery from each load cycle. This elasticity allows AB-modified bitumen to withstand better the stresses associated with repeated loading, thus slowing the deterioration process. These results suggest that AB-modified bitumen offers substantial durability improvements, making it especially beneficial for applications that demand sustained structural integrity under continuous loading. Figures 13-15 display the VECD damage curves for bitumen samples modified with waste cooking oil (WCO) at 3%, 4%, and 5% concentrations. Although WCO modifications show some improvement in damage resistance compared to the unmodified sample, their curves are steeper than those of SBS- and AB-modified samples. Among the WCO-modified samples, the 4% WCO sample (Figure 14) exhibits the best performance, demonstrating a wider range of damage intensity and more gradual reduction in modulus.