# Laboratory Evaluation and Finite Element Modeling of SBS and Basalt Fiber Modified Mixtures
## 2 Experimental
### Dynamic Stability, and Marshall and Flexural Testing
\[N_{f}\equiv k\bigg{(}\frac{1}{\sigma_{0}}\bigg{)}^{n} \tag{4}\]  
Figure 1: Infratest wheel tracking equipment. Figure 2: Low-temperature bending beam equipment. where \(N_{f}\) is the number of times of loading until specimen damage, \(\sigma_{0}\) is the initial bending tensile stress in MPa, and \(k\) and \(n\) are regression coefficients obtained during controlled stress mode. The Marshall test results for both variations of samples are shown in Table 4.  
Marshal tests were carried out on two sample variations. As observed in Table 4, higher gains in Marshall stability and a slightly low optimum binder content for the BF-modified asphalt mixture can be observed. Furthermore, a higher number of voids filled with asphalt exist for the BF-modified mixture due to the absorption of fiber. The addition of basalt fiber reduces the permanent deformation of asphalt mixtures with adequate flow parameters. Dynamic stability tests were conducted, with the results shown in Table 5. As observed from the table, dynamic stability further improves with the addition of 0.3% basalt fiber content, showing a 48% performance improvement, despite using 3% SBS in the mixture rather than 7% SBS. This is due to the fact that fibers reinforce the asphalt mixture by improving its stability and creates interlocking among the fibers, and the fibers aggregate to resist permanent deformation. The percentage rut depth for each scenario was calculated and is shown in Figure 3. As observed, the highest percentage is exhibited by the 7% SBS mixture, showing up to 4% of rut depth compared with only 2.5% for 3% SBS with 0.3% BF. The addition of basalt fiber further optimizes high-temperature stability, thereby increasing the rutting and permanent deformation resistance. Rutting performance is also further improved using a stone matrix asphalt mixture. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Type** & **Optimum Binder** & **Voids (\%)** & **Voids Filled** & **Voids in** & **Marshall** & **Flow** \\  & **Content (\%)** & & **with** & **Mineral** & **Stability** & **(0.1 mm)** \\ \hline
76-22 with 3\% SBS & & & & & & \\ and 0.3\% BF & 4.6 & 4.83 & 66.2 & 14.1 & 13.9 & 32.6 \\
76-22 with 7\% SBS & 4.3 & 4.95 & 65.1 & 14.3 & 11.2 & 30.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Marshall tests results. Figure 3: Percentage rut depth for each scenario. Low-temperature cracking resistance tests were conducted for a total of 5 specimens per each scenario and the results with average values are shown in Table 6. As observed, a higher component of flexural strain and flexural stress exists for the basalt fiber-modified mixture. The addition of basalt fiber allows the test sample to be repeatedly loaded with a higher accumulation of strains when compared with the SBS only-modified specimen. The addition of basalt fiber allows for higher fatigue durability and decreased stiffness modulus in low-temperature conditions. A visual comparison of some of the properties including dynamic stability, flexural tensile strength and failure strain is shown in Figure 4. As observed, the addition of 0.3% BF significantly increases the performance of the asphalt mixture in terms of improved permanent deformation resistance with a 47% higher magnitude of dynamic stability. Furthermore, in terms of low = temperature performance and higher use of load repetitions, the addition of 0.3% BF further optimizes the asphalt mixture, leading to a 16% increase in flexural tensile strength. The magnitude of failure strain also improves by 31% using the 0.3% BF with 3% SBS mixture.