## 3 Lab Testing Protocol
### Indirect Tensile Strength and Stiffness Modulus Evaluation  
Indirect tensile strength tests were performed on Marshall-prepared specimens. Diameter of specimens was kept at 101.6 mm \(\pm\) 0.25 mm and height was kept at 63.2 mm \(\pm\) 1.3 mm. ITST was carried out using cooper equipment. The specimen was set in a temperature controlled environment with the temperature kept at 15 \({}^{\circ}\)C. Tests followed the protocols mentioned as per ASTM D6931-17 [35]. Using this equipment, the split ensile strength and flexural tensile strength can be evaluated. The split tensile strength \(R_{T}\) is obtained using Equation (1). \[R_{T}=0.006287P_{T}h \tag{1}\]  
where \(R_{T}\) is the indirect tensile strength (MPa), \(P_{T}\) is the maximum force value (N) and \(h\) is the height of the specimen. Flexural strength can be obtained using Equation (2). \[R_{B}=\frac{3 LP_{B}}{2 bh^{2}} \tag{2}\]  
where \(L\) is specimen span (mm), \(b\) is the width of the control frame (mm), \(h\) is the height of control frame (mm), and \(P_{B}\) is the maximum load at fracture (N). Stiffens modulus of asphalt mixture is a significant parameter used to evaluate the high- and low-temperature performance of asphalt mixtures against rutting and fatigue damage, respectively. Tensile strains at the bottom of the layers can be further controlled with a better stiffness modulus of asphalt mix. Therefore, ITSM was used to evaluate the stiffness moduli of specimens by using 15 load pulses with a 3 s duration. Five subsequent load pulses and average value were used to determine the stiffness modulus. The stiffness modulus can be calculated from Equation (3). \[S_{m}=\frac{F\times(v+0.27)}{z\times h} \tag{3}\] \begin{table}
\begin{tabular}{c c c c c} \hline
**Type** & **Relative Density** & **Void Ratio (\%)** & **VFA (\%)** & **Stability (kN)** & **Flow (mm)** \\ \hline SBS-7\% & 2.321 & 4.41 & 70.5 & 14.02 & 3.2 \\ LF & 2.487 & 4.47 & 71.2 & 14.78 & 3.8 \\ BF & 2.689 & 4.65 & 74.1 & 15.89 & 3.3 \\ PF & 2.591 & 4.52 & 73.2 & 15.24 & 3.6 \\ \hline \end{tabular}
\end{table} 
Table 4: Marshall test results. where \(S_{m}\) is the indirect tensile stiffness modulus in MPa, \(F\) is the peak vertical load in N, \(z\) is the average amplitude of 5 repeated horizontal deformations in mm, \(h\) is the mean thickness of the specimen in mm and \(v\) is the Poisson's ratio. For the determination of indirect tensile strength, 3 samples of each variation were prepared and tested under dry and saturated conditions. For saturated conditions, samples were placed in a freezer for 16 h at \(-\)18 \({}^{\circ}\)C. The samples were then placed in warm water for 24 h at 60 \({}^{\circ}\)C and then in a water bath for 2 h at 25 \({}^{\circ}\)C in order to complete the freeze-thaw cycle. The ITST was performed at 25 \({}^{\circ}\)C at a constant rate of 50.8 mm/min. As observed from Table 5, higher tensile strength is exhibited by 0.3% BF, followed by 0.3% PF. Lignin fiber, however, shows the least tensile strength under both dry and saturated conditions among the fiber-modified asphalt mixtures. The use of SBS-7% only mixture, however, shows the least performance in terms of indirect tensile strength under both saturated and dry conditions. The difference between tensile strength values under saturated and dry conditions is smaller in case of 0.3% BF when compared to 0.3% LF and SBS-7%, indicating higher resistance to moisture-induced damage and permanent deformation. Lignin fibers show decreased tensile strength as a result of saturation when subjected to indirect tensile strength testing protocol. Due to the organic nature of the material, saturation leads to a decrease in cohesion between bitumen and aggregates, thereby leading to lower tensile strength when subjected to freeze and thaw cycles. The stiffness moduli for different asphalt mixtures are shown in Table 6. As observed, the addition of fiber further enhances the deformation resistance and stiffness moduli of asphalt mixtures.