# Laboratory Evaluation and Finite Element Modeling of SBS and Basalt Fiber Modified Mixtures
## 3 Finite Element Modeling
### Fatigue and Rutting Damage Analysis  
Fatigue damage occurs as a result of repeated numbers of axle passes. Fatigue damage starts with hairline longitudinal cracks under the wheel paths and gradually leads to alligator cracking. Fatigue damage occurs when 45% of the pavement surface is covered  
Figure 6: Loading and boundary condition details. \begin{table}
\begin{tabular}{c c c} \hline
**Depth** & **76-22 with 7\% SBS** &
\begin{tabular}{c} **76-22 with 3\% SBS and** \\ **0.3\% BF** \\ \end{tabular} \\ \hline
50 mm & 2.59 & 2.31 \\
450 mm & 2.24 & 2.20 \\
800 mm & 0.023 & 0.019 \\ \hline \end{tabular}
\end{table} 
Table 9: Von Mises stress values for each scenario. Figure 7: Simulation results for SBS-7% mixture. with alligator cracking. The Asphalt Institute's model can be used to evaluate the number of passes leading to fatigue damage from the horizontal tensile strain under the asphalt layer using Equation (6). \[N_{f}=0.0796\times\varepsilon_{t}^{-3.291}\times E^{-0.854} \tag{6}\]  
where \(N_{f}\) is the number of load repetitions to fatigue damage, \(\varepsilon_{t}\) is the horizontal tensile strain at the bottom of the asphalt layer and \(E\) is the elastic modulus of the asphalt mixture. Putting damage in the pavement occurs as a result of further densification and shear deformation of the asphalt mixture, usually in high-temperature conditions. The Asphalt Institute provides a relationship between the number of passes to rutting damage and the vertical compressive strain, as shown in Equation (7). \[N_{f}=1.365\times 10^{-9}\times\varepsilon_{c}^{-4.477} \tag{7}\]  
where \(N_{f}\) is the number of load repetitions to rutting damage and \(\varepsilon_{c}\) is the vertical compressive strain on top of subgrade. As observed from Table 10, the 3% SBS with 0.3% BF mixture significantly outperforms the 7% SBS mixture in terms of number of passes to damage for rutting and fatigue cracking. For the BF mixture, \(\varepsilon_{t}\) and \(\varepsilon_{c}\) stay at 15.3 and 374.8, respectively, showing the least strains compared with the SBS-7% mixture. The number of passes to fatigue damage for BF remains at 9.34 \(\times\) 10\({}^{10}\); however, for the same amount of damage, SBS-7% requires only 7.48 \(\times\) 10\({}^{10}\) passes. Furthermore, in terms so rutting damage, the 7% SBS mixture only requires 8.26 \(\times\) 10\({}^{6}\) passes. The number of passes to fatigue damage for both mixture types are shown in Figure 8. As observed, the 3% SBS with 0.3% BF mixture exhibits a higher number of passes with an \(\varepsilon_{t}\) value of 15.3 compared with 18.2 for the 7% SBS mixture. Furthermore, a 25% increase in number of passes can be observed for the 3% SBS with 0.3% BF mixture when compared with the 7% SBS mixture; the addition of basalt fiber further improves the cohesion as well as interlocking of aggregates, thereby providing further resistance to fatigue damage. Fatigue damage of the asphalt mixtures is shown in Table 11. As observed, the addition of 0.3% basalt fiber enhances the performance of the asphalt mixtures, where the k value is increased by 28% and the n value increases by 25% when compared with the SBS only-modified mixture. The use of basalt fiber decreases the stress concentration in asphalt mixtures by creating a stable film for increased cohesion between aggregates and bitumen, thereby forming a highly elastic mixture where a higher number of loading cycles is required for the specimen to become damaged. Furthermore, the addition of basalt fiber can be employed as a part of enhancing anti-fatigue properties of asphalt mixtures. The number of passes to rutting damage is shown in Figure 9. As observed, the least number of passes is exhibited by the 7% SBS mixture, showing only 8.26 \(\times\) 10\({}^{6}\) passes for the same amount of damage compared with 1.01 \(\times\) 10\({}^{7}\) passes for the 3% SBS with 0.3% BF mixture. The 7% SBS mixture exhibits 47% higher rutting damage when compared with the 3% SBS with 0.3% BF mixture.