## 3 Results and Discussion
### Seismic Modulus by Ultrasonic Pulse Velocity Test  
Non-destructive testing (NDT) is an essential and effective method for evaluating the structural integrity of materials within asphalt and concrete pavements [86; 87]. Among the many existing non-destructive tests used, acoustic systems involve generating ultrasonic acoustic pulses on a sample and detecting them with a receiving sensor. The ultrasonic pulse velocity (UPV) test is a cost-effective and efficient method that requires minimal time and inexpensive equipment. While the UPV test has not been standardized for testing HMA, researchers have effectively utilized it to estimate the seismic modulus of asphalt mixtures and evaluate the influence of components [86; 88; 89; 90].  
UPV tests were performed on 48 Marshall samples following the ASTM C597 [53] standard. The UPV tester employed in this study generated ultrasonic pulses at a frequency of 54 kHz. The ultrasonic gel was applied to the contact area to avoid cavities and transmitted energy dissipation. The pulse and receiver probes were placed on opposite parallel surfaces of the Marshall samples to record the transmission time of the ultrasonic waves. Pulse velocities were calculated by dividing the height of the Marshall specimen by the transmission time. The test was carried out at 20 \({}^{\circ}\)C, with minimal displacement of the Marshall specimens and their corresponding strain. According to the standard test method for pulse velocity ASTM C597 [53], the seismic modulus can be determined using Equation (7) from the velocity of longitudinal stress waves, the material's elastic properties, and density. After determining the average velocities for each specimen, the following equation was used to calculate the dynamic modulus. [PERSON]'s ratio for this study was 0.36, which is considered according to the literature [91; 92].  
\[\mathrm{E}=\frac{\mathrm{V}^{2}\rho(1+\mathrm{\mu})(1-2\mathrm{\mu})}{1- \mathrm{\mu}} \tag{7}\]  
Here, E represents seismic modulus (MPa), V stands for the velocity (km/s), \(\mathrm{\rho}\) denotes the density of Marshall mixtures (kg/m\({}^{3}\)), and \(\mathrm{\mu}\) is the [PERSON]'s ratio.  
Table 16 summarizes the results of transmission time, velocity, and seismic modulus for the Marshall mixtures. Transmission time increased due to the increase in air voids in Marshall mixtures, resulting in a decrease in seismic modulus [86; 93]. The addition of Cecabase RT BIO10 increased the seismic modulus, improving the fatigue cracking performance of asphalt mixtures [94].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Experiment No** & **Density (kg/m\({}^{3}\))** & **Height (mm)** & \
\begin{tabular}{c} **Avg. Transmission** \\ **Time (10\({}^{-6}\) s)** \\ \end{tabular} & **Velocity (km/s)** &
\begin{tabular}{c} **Seismic Modulus** \\ **(GPa)** \\ \end{tabular} \\ \hline
1 & 2402 & 62.44 & 19.90 & 3.14 & 14.07 \\
2 & 2397 & 62.86 & 20.02 & 3.14 & 14.06 \\
3 & 2394 & 61.84 & 20.16 & 3.07 & 13.40 \\
4 & 2399 & 62.23 & 19.93 & 3.12 & 13.92 \\
5 & 2397 & 61.71 & 20.15 & 3.06 & 13.38 \\
6 & 2397 & 62.68 & 20.20 & 3.10 & 13.73 \\
7 & 2403 & 61.88 & 19.72 & 3.14 & 14.08 \\
8 & 2395 & 62.49 & 20.17 & 3.10 & 13.67 \\
9 & 2405 & 61.88 & 20.07 & 3.08 & 13.60 \\
10 & 2407 & 62.21 & 19.86 & 3.13 & 14.06 \\
11 & 2408 & 61.73 & 19.19 & 3.22 & 14.83 \\
12 & 2405 & 62.26 & 19.33 & 3.22 & 14.85 \\
13 & 2412 & 62.14 & 19.30 & 3.22 & 14.87 \\
14 & 2408 & 61.99 & 19.33 & 3.21 & 14.73 \\
15 & 2407 & 62.17 & 19.38 & 3.21 & 14.74 \\
16 & 2407 & 62.29 & 19.37 & 3.22 & 14.82 \\ \hline \hline \end{tabular}
\end{table}
Table 16: UPV and seismic modulus results.