## 3 Results and Discussion
### Thermal Cracking Property (Low Temperature)  
The inclusion of LC significantly affects the stiffness. An example is the binder containing 10% TLA and 5% CRM, which exhibits a decrease in stiffness from 195.00 MPa to 177.00 MPa upon the inclusion of 1.5% LC. Similarly, the binder containing 20% TLA and 5% CRM experiences a decrease in value from 238.00 MPa to 185.00 MPa with LC. The observed pattern remains consistent in different binder formulations, including those containing 10% and 20% TLA combined with 10% CRM, where the addition of LC leads to a decrease in stiffness and is shown in Figures 6 and 7 and Table 12. These observations suggest that the use of LC effectively reduces the hardness of the binder, making it less likely to develop cracks and enhancing its ability to withstand stress over time.  
The m-value is a significant parameter that indicates the flexibility of a binder. Higher values indicate better performance, especially in terms of resistance to thermal cracking. The original/base binder, PG 64-22, possesses an m-value of 0.33. TLA incorporation results in a decrease in the m-value to 0.278 and 0.292 for TLA concentrations of 10% and 20% respectively, indicating a decrease in flexibility. Nevertheless, the addition of 5% CRM raises the m-value to 0.34, thereby improving the flexibility of the binder. The impact of LC is especially noticeable in its capacity to enhance the m-value in comparison to binders modified solely with PG 64-22 and TLA. However, LC does not exhibit significant influence when combined with CRM, as it demonstrates a decreasing trend. As an illustration, the binder containing 10% TLA and 5% CRM exhibits a reduction in m-value from 0.397 to 0.33 when 1.5% LC is added. In the binder containing 20% TLA and 5% CRM, a comparable  
Figure 7: m-Value at \(-12\)\({}^{\circ}\)C of the modified asphalt binders after RTFO + PAV aged condition.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & & & & & & & \\ \hline \multicolumn{12}{c}{**RTFO + PAV**} \\ \hline \multicolumn{12}{c}{**Combination**} & \multicolumn{1}{c}{
\begin{tabular}{c} **PG64-** \\ **22** \\ **10\%TLA** \\ **22** \\ **10\%TLA** \\ **20\%TLA** \\  
pattern is seen where the m-value decreases from 0.322 to 0.25 with LC. The detrimental effect of LC on the m-value remains consistent across different formulations, demonstrating a decrease in flexibility and a reduction in resistance to thermal cracking when compared to a combination of CRM co-modified with TLA and petroleum binder (PG 64-22).  
To summarize, the inclusion of LC as a warm mix additive has a beneficial impact on both stiffness and m-value in high-performance binders. The majority of the binder co-modified with LC exhibits a higher m-value exceeding 0.30, with the exception of the combination of 20% TLA and 5% CRM. LC decreases the rigidity of the binder, reducing its susceptibility to cracking and enhancing its resilience under stress, particularly in formulations containing higher levels of TLA and CRM. At the same time, LC improves the m-value, which shows increased flexibility and resistance to thermal cracking. This is important for achieving good performance in colder climates. The data substantiates the utilization of LC in warm mix asphalt compositions to attain high-performance binders with enhanced durability and elasticity, effectively harmonizing rigidity and pliability to fulfill diverse performance requirements in paving applications.