## 3 Results and Discussion
### Fatigue Cracking Property (Intermediate Failure)  
The statistical analysis findings of different modified asphalt binders, which were exposed to RTFO and PAV aging processes and evaluated at a temperature of 25 \({}^{\circ}\)C, are presented in Table 8. The tested combinations encompass various compositions of PG64-22, TLA, and CRM. The resistance to aging of each combination is evaluated for statistical significance (\(\alpha\) = 0.05) and classified as either significant (S) or non-significant (N).  
The characteristic G*.sin\(\delta\), expressed in kilopascals (kPa), is a crucial predictor of an asphalt binder's vulnerability to fatigue cracking. Greater values indicate an increased propensity for fatigue cracking, with a threshold of 5000 kPa signifying a notably elevated risk. The virgin binder, PG64-22, exhibits a G*.sin\(\delta\) value of around 3000 kPa, suggesting a moderate sensitivity to fatigue cracking. By increasing the TLA by 10%, the value rises to around 5000 kPa, surpassing the critical threshold and indicating a notable rise in the danger of fatigue cracking. When the TLA content is increased to 20%, the G*.sin\(\delta\) value rises to over 7000 kPa, surpassing the critical threshold and suggesting a significant vulnerability to fatigue cracking.  
Implementing a 5% CRM leads to a marginal elevation in the G*.sin\(\delta\) value compared to the original binder. This suggests a slight rise in the probability of fatigue cracking. The combination of 10% TLA and 5% CRM results in an elevated G*.sin\(\delta\) value, indicating enhanced rigidity and an elevated likelihood of fatigue cracking. Raising the TLA content to 20% while incorporating 5% CRM yields a further elevated value, perpetuating the pattern of heightened risk. Significantly, the use of 10% CRM alone reduces the G*.sin\(\delta\) value in comparison to 5% CRM, suggesting enhanced resistance to fatigue cracking. The combination of 10% TLA and 10% CRM has a G*.sin\(\delta\) value that is lower than that of 10%  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & \multicolumn{6}{c}{**PAV Condition at 25 \({}^{\circ}\)C**} \\ \hline  & & & & & & & & & & & & \\ \multirow{6}{*}{**Combination**} & \multirow{2}{*}{**PG64-22**} & \multirow{2}{*}{**PG64-22**} & \multirow{2}{*}{**PG64-22**} + & \multirow{2}{*}{**CRM 55\%**} & \multirow{2}{*}{**105\%TLA**} & \multirow{2}{*}{**20\%TLA**} & \multirow{2}{*}{**20\%TLA**} & \multirow{2}{*}{**CRM 10\%**} & \multirow{2}{*}{**10\%TLA**} & \multirow{2}{*}{**20\%TLA**} + & \multirow{2}{*}{**CRM 10\%**} & \multirow{2}{*}{**10\%TLA**} & \multirow{2}{*}{**20\%TLA**} + \\  & & & & & & & & & & & \\  & PG64-22 + 10\%TLA & - & - & - & S & S & S & S & S & S \\  & CRM5\% & - & - & - & - & S & S & S & S & S \\  & & & - & - & - & - & S & S & S & S \\  & & - & - & - & - & - & S & S & S TLA alone, but higher than that of CRM 10% alone. This indicates a balanced influence between TLA and CRM. Nevertheless, the combination of 20% TLA and 10% CRM still yields a substantial G*.sin\(\delta\) value, suggesting that an increased TLA content in conjunction with CRM poses a significant danger of fatigue cracking, as illustrated in Figure 5 below.  
In general, the use of TLA leads to an increase in stiffness and a higher likelihood of fatigue cracking. However, the use of CRM can mitigate this risk by enhancing elasticity. Nevertheless, combinations that surpass the 5000 kPa threshold present a significant danger for fatigue cracking. Hence, it is imperative to achieve a meticulous equilibrium between TLA and CRM components in order to maximize fatigue performance. Increased CRM content typically enhances flexibility and decreases the likelihood of fatigue cracking. However, additional comprehensive investigations and performance assessments under real-life loading conditions are necessary to identify the optimal combinations for specific uses, while ensuring that G*.sin\(\delta\) values remain below the critical threshold of 5000 kPa.