## 3 Results and Discussion
### Fatigue Cracking Property (Intermediate Failure)  
Figure 5 and Table 11 depict the G*sin \(\delta\) values (kPa) for different compositions of PG 64-22 asphalt binder that have been modified with TLA, CRM, and LC. The G*sin \(\delta\) parameter plays a critical role in evaluating the susceptibility of asphalt binders to fatigue cracking. Higher values of this parameter indicate a higher probability of such cracking, which can significantly reduce the durability of pavements.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & & & & & \\ \hline \multirow{3}{*}{**Combination**} & \multirow{3}{*}{**PG64-**} & \multirow{3}{*}{**PG64-**} & \multirow{3}{*}{**PG64-**} & \multicolumn{3}{c}{**PG64-**} & \multicolumn{3}{c}{**PG64-**} & \multicolumn{3}{c}{**PG64-**} & \multicolumn{3}{c}{**PG64-**} & \multicolumn{3}{c}{**PG64-**} \\  
When using the PG 64-22 base binder, we measure a G*sin \(\delta\) value of 3400 kPa. This serves as a standard against which the effects of different modifications can be compared. When 10% TLA is added to PG 64-22, the G*sin \(\delta\) value increases to 5695 kPa. Increasing the TLA content to 20% further raises the value to 6550 kPa. The substantial increase demonstrates that while TLA improves the rigidity of the binder, it also elevates the likelihood of fatigue cracking. The inclusion of CRM also affects the characteristics of the binder. An example is when PG 64-22 is combined with 10% TLA and 5% CRM, resulting  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & & & & & \\ \hline \multicolumn{12}{c}{**PAV Condition at 25 °C**} \\ \hline \multirow{4}{*}{**Combination**} & \multirow{4}{*}{
\begin{tabular}{c} **PG64-** \\ 22 + 20\%TLA** \\ **PG64-** \\ **22 + 2** \\ **22 + 10\%TLA** \\ **22 + 10\%TLA** \\ **22 + 10\%TLA** \\ **22 + 10\%TLA** \\ **23 +  
in a G*sin \(\delta\) value of 7910 kPa, which is very high. While this formulation enhances performance, the significant rise in stiffness suggests a greater susceptibility to fatigue cracking. Moreover, when PG 64-22, 20% TLA, and 5% CRM are combined, the resulting G*sin \(\delta\) value is 5915 kPa, highlighting the significant increase in stiffness.  
The significance of LC in these formulations is particularly notable. LC is an asphalt additive that is specifically created to decrease the viscosity of the binder at lower temperatures. This makes it easier to mix and compact the asphalt during construction. The inclusion of LC consistently decreases the G*sin \(\delta\) values in different formulations, suggesting a positive impact on the rigidity of the binder. For instance, when PG 64-22 is combined with 10% TLA, 5% CRM and 1.5% LC, the G*sin \(\delta\) value is 4940 kPa, which is lower than the value obtained when LC is not present in the same formulation. In the same manner, the inclusion of LC in the mixture of PG64-22, 10% TLA, and 10% CRM results in a decrease in the G*sin \(\delta\) value from 4000 kPa to 3580 kPa. Adding LC to PG64-22, 20% TLA, and 10% CRM results in a decrease in the G*sin \(\delta\) value from 5950 kPa to 4430 kPa.  
From a scientific standpoint, the decrease in G*sin \(\delta\) values caused by LC signifies a reduction in the stiffness of the binder. This reduction is essential for minimizing the risk of fatigue cracking. This decrease in the value does not compromise the performance; instead, it harmonizes the requirement for exceptional performance with a diminished likelihood of cracking. Ultimately, the utilization of the warm mix additive LC has a beneficial impact on the creation of superior warm mix binders by decreasing the G*sin \(\delta\) values, which in turn reduces the likelihood of fatigue cracking.