## 6 Conclusions and Findings  
In this research, the performance of three different fiber types--LF, PF and BF--was compared with the SBS-7% mixture in terms of indirect tensile strength, stiffness modulus and DSR values. Furthermore, indirect tensile strength tests were conducted at various loading rates, ranging from 10 MPa/s to 70 MPa/s. Stiffness modulus values were calculated across various frequency ranges: 5 Hz, 3.5 Hz, 1.9 Hz and 1.2 Hz. Moreover, finite element modeling was performed using the modified [PERSON]'s logit model to simulate material decay in terms of rutting and fatigue damage.  
When comparison is performed among all fiber types, BF modified mixtures exhibit the highest stiffness modulus, outperforming PF and LF by 7% and 12%, respectively. In terms of mixture strength without fiber reinforcement, SBS-7% provides the least indirect tensile strength when compared to fiber-modified mixtures, with a 16% reduction in strength compared to LF modified mixtures. Therefore, further improvement in stiffness modulus under higher-temperature conditions can be observed when the fibers are used. As observed from the experimental results, the reduction in stiffness modulus for SBS-7% is 35% when compared to BF modified mixtures, with a higher phase angle and lower resistance to permanent deformation for the SBS-7% mixture. Furthermore, the use of fibers further enhances the cohesion and interlocking between bitumen and aggregates, leading to higher deformation resistance of asphalt mixtures. The presence of fibers further enhances the interlocking between binder and aggregates, leading to increased permanent deformation resistance. Fiber-modified asphalt mixtures reduce fatigue damage by an average of 25%. Furthermore, BF modified asphalt mixtures outperform LF mixtures by 12% in terms of the number of passes to fatigue damage.  
BF modified asphalt mixtures exhibit a high complex shear modulus, followed by PF modified asphalt mixtures. Performance gains in terms of indirect tensile strength and complex shear modulus can be observed for fiber-reinforced mixtures compared to the SBS-7%-only mixture. Therefore, the use of fibers in high-volume applications for large-scale road construction projects makes them an excellent candidate for improving both high- and low-temperature performance of asphalt mixtures. The findings are as follows.  
Figure 11: Rut depth at 1.6 million passes for different scenarios.  
A higher magnitude of rutting parameter g*/sin exists for fiber-modified asphalt mixtures, resulting in higher rutting resistance when compared to the SBS-7% only asphalt mixture.
* BF modified asphalt mixture exhibits the least sensitivity to phase angle variations among the fiber-modified asphalt mixtures (PF and LF), thereby providing high permanent deformation resistance.
* The number of passes to rutting damage increases by 28% when the performance of BF is compared with that of SBS-7%.  
Conceptualization, M.F. and R.N.; methodology, M.F. and R.N.; software, M.F.; validation, M.F.; formal analysis, M.F.; investigation, M.F.; resources, M.F.; data curation, M.F.; writing--original draft preparation, M.F.; writing--review and editing, R.N.; visualization, M.F.; supervision, M.F.; project administration, M.F. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available in this current article.  
The authors declare no conflicts of interest.