## 3 Results and Discussion
### Rutting Property (G*/sin\(\delta\))  
To ensure the long-lasting and efficient performance of asphalt pavements, it is essential that the materials used demonstrate resistance to deformation and aging. The evaluation focuses on two essential parameters: the complex modulus (G*) and phase angle (\(\delta\)). More precisely, the assessment of the binder's performance under loading conditions involves measuring the ratio of G* (shear modulus) to sin\(\delta\) (phase angle). The findings of this research are displayed in Figure 3, and their significance is illustrated in Table 5.  
Figure 3: G*/sin\(\delta\) at 64 \({}^{\circ}\)C of the modified binders at original and RTFO conditions. The PG64-22 virgin binder had a G*/sin\(\delta\) value of around 1.5 kPa initially, which increased to 3 kPa after undergoing RTFO aging. The baseline measurements serve as a point of reference for assessing the impact of TLA and CRM adjustments. The addition of TLA to the PG64-22 binder greatly increased its rigidity. With a TLA content of 10%, the G*/sin\(\delta\) value rose to around 2 kPa for the binder in its original condition and 5 kPa after aging through RTFO. Upon increasing the TLA content to 20%, the G*/sin\(\delta\) values exhibited a further increase to 3 kPa (original) and 6.5 kPa (RTFO aged). This increase demonstrates that TLA, a type of natural asphalt, improves the ability of the binder to withstand high temperatures and resist rutting. This is because TLA possesses inherent qualities that boost the overall stiffness of the modified binder. The incorporation of CRM also enhanced the performance attributes of the PG64-22 binder. A 5% CRM concentration led to G*/sin\(\delta\) values of around 2.5 kPa (original) and 6 kPa (RTFO aged). The increase in CRM content to 10% resulted in G*/sin\(\delta\) values of around 3.5 kPa (original) and 8 kPa (RTFO aged). By integrating rubber particles, CRM enhances the elasticity and resistance to deformation of the binder, as it forms an elastic network inside the asphalt matrix. This network boosts the binder's capacity to regain its original shape after deformation, hence enhancing its resistance to forming ruts and increasing its longevity. The incorporation of both TLA and CRM into the PG64-22 binder resulted in more noticeable combination effects. A mixture consisting of 10% TLA and 5% CRM resulted in G*/sin\(\delta\) values of around 2.5 kPa (initial) and 6.5 kPa (after being aged using the RTFO method). After subjecting the sample to 20% TLA and 5% CRM, the G*/sin\(\delta\) values increased to approximately 3 kPa in the original state and 7 kPa after being aged using the RTFO method. The mixture, including 10% TLA and 10% CRM, showed G*/sin\(\delta\) values of roughly 4 kPa (original) and 9 kPa (RTFO aged). The greatest values were recorded with a blend of 20% TLA and 10% CRM, reaching around 5 kPa (original) and an impressive 18 kPa (RTFO aged). This notable improvement demonstrates a mutually beneficial effect in which TLA boosts the rigidity of the binder, while CRM improves its flexibility. The cumulative alteration results in a binder that exhibits exceptional performance at high temperatures, as demonstrated by the significant rise in G*/sin\(\delta\) values, particularly following RTFO aging. This synergy not only enhances the binder's ability to withstand deformation when subjected to a load, but also improves its resistance to aging, resulting in a more durable and dependable material for pavement applications. Overall, the addition of TLA and CRM to PG64-22 leads to a substantial enhancement in its performance, characterized by an increase in both stiffness and elasticity. TLA increases the rigidity and ability to withstand high temperatures, whereas CRM boosts flexibility and resistance to deformation. The simultaneous utilization of TLA and CRM produces a synergistic impact, yielding a binder with outstanding performance attributes, especially during the process of aging.