# Laboratory Evaluation and Finite Element Modeling of SBS and Basalt Fiber Modified Mixtures
## 2 Experimental
### Dynamic Stability, and Marshall and Flexural Testing  
The mixing methodology consists of using a dry mix of a stone matrix asphalt SMA-13 asphalt mixture, where 0.3% basalt fiber and aggregates are premixed before bitumen is added to the mixture and heated to 165 \({}^{\circ}\)C for 2 h. This process removes excessive moisture from raw materials and improves workability during sample preparation. Mineral filler is later added to asphalt and mixed at a rate of 500 rotations/min at 165 \({}^{\circ}\)C. The 7% SBS asphalt mixture was procured directly from the manufacturer. For rutting performance evaluation of the mixtures, rutting tests are carried out using wheel tracking apparatus developed by the company Infratest (Infrastest, Berlin, Germany) as per the American Society for Testing and Materials ASTM D8292. Tests are carried out at 60 \({}^{\circ}\)C, with the size of the specimen being 300 mm \(\times\) 300 mm \(\times\) 50 mm. The equipment used is shown in Figure 1.  
Wheel speed is set at 45 passes/min and a load of 0.7 MPa is applied. For permanent deformation evaluation, dynamic stability function is used, as shown in Equation (1). \[\text{DS}\equiv\frac{(t_{2}-t_{1})\times N}{d_{2}-d_{1}}\times C_{1}\times C_{2} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c} \hline
**PG Grade** & **Penetration at** & **Softening** & **Separation** & **Elastic** & **Ductility** & **Viscosity** \\
**25 \({}^{\circ}\)C [0.1 mm]** & **Point [\({}^{\circ}\)C]** & [\({}^{\circ}\)C] & **Recovery [\%]** & [\({}^{\circ}\)C] & **[135 \({}^{\circ}\)C Pa:s]** \\ \hline
76-22 with 3\% SBS & 72 & 79 & 1.5 & 74 & 42.1 & 0.82 \\
0.3\% basalt fiber & 76 & 84 & 1.8 & 68 & 37.4 & 0.74 \\
76-22 with 7\% SBS & \multicolumn{1}{c}{} & & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Properties of asphalt mixtures. \begin{table}
\begin{tabular}{c c c} \hline
**Property** & **Unit** & **Value** \\ \hline Diameter & \(\mu\)m & 16.1 \\ Length & mm & 4–6 \\ Elastic modulus & GPa & 83.2 \\ Heat resistance & \% & 92.1 \\ Elongation & \% & 4 \\ Ferrous content & \% & 7.43 \\ Acidity content & \% & 3.6 \\ Fracture strength & MPa & 2359 \\ Relative density & g/cm\({}^{3}\) & 2.72 \\ \hline \end{tabular}
\end{table} 
Table 2: Properties of basalt fiber. \begin{table}
\begin{tabular}{c c c c} \hline
**Sieve Size [mm]** & **Percentage Passing [\%]** & **Control Point [\%]** & **Restricted Zone [\%]** \\ \hline
16 & 100 & - & - \\
13.2 & 94.9 & 90–100 & - \\
9.5 & 78.4 & Less than 90 & - \\
4.75 & 46 & - & - \\
2.36 & 36.4 & 28–58 & 39.1 \\
1.18 & 25.8 & - & 25.6–31.6 \\
0.6 & 19.4 & - & 19.1–25.1 \\
0.3 & 15.2 & - & 15.5 \\
0.15 & 11.8 & - & - \\
0.075 & 8.4 & 2–10 & - \\ \hline \end{tabular}
\end{table} 
Table 3: Aggregate properties. where DS is the dynamic stability in times/mm, \(t_{1}\) and \(t_{2}\) are test timings (min), \(d_{1}\) and \(d_{2}\) are rutting depths at timings \(t_{1}\) and \(t_{2}\) (mm), \(N\) is the wheel speed at 45 passes/min, and \(C_{1}\) and \(C_{2}\) are experimental coefficients of value 1.0. Furthermore, percentage rut depth can be calculated with regards to the dynamic stability as shown in Equation (2). \[PRD\equiv\frac{\Delta L}{D}\times 100 \tag{2}\]  
where \(\Delta L\) is the rutting depth at specimen timing in mm and \(D\) is the thickness of the specimen in mm. For low-temperature performance evaluation, the bending beam test is used. The test is carried out at \(-10\)\({}^{\circ}\)C using a sample size of 200 mm \(\times\) 25 mm \(\times\) 30 mm, as per ASTM D8237-21. The equipment used in shown in Figure 2.  
The loading rate is set at 50 mm/min in order to determine the low-temperature cracking resistance; the failure strain is calculated using Equation (3). \[\varepsilon_{B}\equiv\frac{6h_{2}l}{L^{2}} \tag{3}\]  
where \(h_{2}\) is the height of specimen in mm, \(l\) is the deflection in mm, and \(L\) is the span of the specimen in mm. Furthermore, the fatigue damage evaluation can be performed using a half sine wave load at 10 Hz with the temperature kept at 25 \({}^{\circ}\)C using Equation (4).