## 4 Results and Discussion  
### G-R Index Results  
The G-R Index analysis provides important insights into the cracking susceptibility of modified bitumen at two temperatures, 15 \({}^{\circ}\)C and 25 \({}^{\circ}\)C, under stress levels of G-R = 180 kPa and G-R = 600 kPa. At 15 \({}^{\circ}\)C, the bitumen exhibited a higher complex shear modulus (1 G*1), indicating increased stiffness and elasticity, which heightens the risk of block cracking, especially under higher stress. The shift of the curve towards the block cracking region suggests that the material's rigidity at lower temperatures increases its susceptibility to cracking under applied stress. In contrast, at 25 \({}^{\circ}\)C, the bitumen showed more viscous behavior, with a lower complex shear modulus, resulting in greater flexibility and reduced susceptibility to block cracking (Figure 1). The curve remains within the no block cracking region, although it begins to approach the damage zone under higher stress (G-R = 600 kPa), reflecting the material's reduced stiffness at higher temperatures but vulnerability under extreme stress. The differing behaviors at these temperatures stem from the temperature-dependent viscoelastic properties of bitumen, which stiffens at lower temperatures and softens at higher ones. Stress levels also play a key role, as higher stress increases the likelihood of cracking due to the material's limited ability to store energy elastically under these conditions. It should be noted that Figures 1-4 were generated directly by the DSR software (v. 1.35.1394) and, as such, do not allow the inclusion of standard deviation bars or user-inserted data annotations. Figure 1: G–R index unmodified bitumen. Figure 3: _Cont_. Figure 2: G–R index SBS modified samples (**a**) 4% SBS, (**b**) 5% SBS. The G-R Index plots for SBS-modified bitumen samples at 4% and 5%, as shown in Figure 2, reveal how varying concentrations of styrene-butadiene-styrene (SBS) affect the bitumen's resistance to block cracking across different stress levels and temperature conditions. These plots (a and b) correspond to SBS concentrations of 4% and 5%, respectively, and demonstrate the material's behavior in terms of flexibility, stiffness, and overall performance under applied stress. In the 4% SBS sample (Figure 2a), the bitumen shows improved flexibility compared to unmodified bitumen, as indicated by its position in the no block cracking region at both 15 \({}^{\circ}\)C and 25 \({}^{\circ}\)C under lower stress (G-R = 180 kPa). At 25 \({}^{\circ}\)C, the bitumen maintains its flexibility, staying in the no block cracking zone for most of the phase shift range. However, under higher stress conditions (G-R = 600 kPa), the material begins to approach the damage zone, reflecting some reduction in elasticity but still showing resilience compared to unmodified bitumen. The increased SBS content enhances the bitumen's ability to deform without cracking, but at low temperatures, particularly at 15 \({}^{\circ}\)C, the material moves closer to the block cracking region, indicating increased stiffness under these conditions. Overall, the 4% SBS-modified bitumen offers significant improvement in flexibility, especially at higher temperatures, though some vulnerability to cracking remains at low temperatures and high stress. The 5% SBS sample (Figure 2b) performs even better, demonstrating further improvement in flexibility and resistance to cracking. At both 15 \({}^{\circ}\)C and 25 \({}^{\circ}\)C, the bitumen largely stays in the no block cracking zone, even under the higher stress level of G-R = 600 kPa. The higher SBS content enhances the elasticity of the material, allowing it to store more energy elastically, which reduces the risk of block cracking. At 25 \({}^{\circ}\)C, the bitumen shows superior resistance to entering the damage zone, even under high stress, remaining flexible throughout the entire phase shift range.