# Artificial Intelligence-Based Model for the Prediction of Dynamic Modulus of Stone Mastic Asphalt
## 5 Results and Discussion  
### Experimental Results  
Figure 4 shows the experimental results on the dynamic modulus \(|\)E\({}^{\bullet}|\) in highlighting the influence of the testing frequency, whereas Figure 5 shows similar results in highlighting the influence of the testing temperature. Considering a similar testing frequency, an increase of the testing temperature reduced the value of the dynamic modulus \(|\)E\({}^{\bullet}|\). Besides, at similar testing temperature, an increase of the testing frequency increased the value of the dynamic modulus \(|\)E\({}^{\bullet}|\). Specifically, the effects of the testing frequency and temperature on the experimental values \(|\)E\({}^{\bullet}|\) are clearly shown in Figures 4 and 5. The highest value of the dynamic modulus \(|\)E\({}^{\bullet}|\) for four types of mixtures was obtained with a temperature of 10 \({}^{\circ}\)C and a frequency of 25 Hz. The smallest value of the dynamic modulus \(|\)E\({}^{\bullet}|\) was obtained in the case of 60 \({}^{\circ}\)C and 0.1 Hz. At a testing temperature of 10 \({}^{\circ}\)C, the value of \(|\)E\({}^{\bullet}|\) of SMA-H was 1.22-1.33 times higher than HMA-H, whereas it was 1.01-1.42 times at 25 \({}^{\circ}\)C, 1.45-1.7 times at 45 \({}^{\circ}\)C and 1.01-1.08 times at 60 \({}^{\circ}\)C. For asphalt mixtures made by hot technology at a similar temperature, the difference was more pronounced with the higher frequency. The difference could be neglected at a testing temperature of 60 \({}^{\circ}\)C. At a testing temperature of 10 \({}^{\circ}\)C, the value of the dynamic modulus \(|\)E\({}^{\bullet}|\) of SMA-W was 1.11-1.22 times higher than HMA-W, whereas it was 1.01-1.15 times at a temperature of 25 \({}^{\circ}\)C, 1.09-1.22 times at a temperature of 45 \({}^{\circ}\)C, and 1.08-1.26 times at a temperature of 60 \({}^{\circ}\)C. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Values** & **Mixture** & **Technology** & **Frequency** & **Temperature** & **|E\({}^{\bullet}|\)** \\ \hline Unit & - & - & Hz & \({}^{\circ}\)C & MPa \\ Role & Input & Input & Input & Input & Output \\ Min & SMA & Warm & 0.1 & 10 & 277.440 \\ Median & - & - & 3 & 35 & 1438.637 \\ Average & - & - & 6.933 & 35 & 1709.439 \\ Max & HMA & Hot & 25 & 60 & 4762.255 \\ St.D. & - & - & 8.829 & 19.139 & 1234.724 \\ \hline \hline \end{tabular}  
St.D. = Standard Deviation; \(|\)E\({}^{\bullet}|\) = Dynamic Modulus  
\end{table} 
Table 4: Statistical analysis and summary of the input and output variables used in this study. Figure 4: Experimental results of dynamic modulus \(|\)E\({}^{\ast}|\) in function of the frequency, in the case of (a) SMA-W; (b) SMA-H; (c) HMA-W; and (d) HMA-H.  
Figure 5: Cont. Figure 5: Experimental results of dynamic modulus \(|\textbf{E}^{\prime}|\) in function of the test temperature for different frequencies: (**a**) 0.1 Hz; (**b**) 0.5 Hz; (**c**) 1 Hz; (**d**) 5 Hz; (**e**) 10 Hz; (**f**) 25 Hz. It could be concluded that, compared to the HMA, the SMA showed superior performance in terms of the dynamic modulus \(|\)E*\(|\). Besides, the warm technology exhibited higher dynamic modulus \(|\)E*\(|\) than using the hot technology. Considering SMA and the mixtures using the warm technique, similar observations were also reported in the literature [12]. Indeed, [PERSON] et al. showed that the SMA-W exhibited significant improvement compared with SMA-H. Moreover, the authors showed that, in terms of additives, Sasobit disclosed the highest performance compared with the control mix, Evotherm, and foamed asphalt. Besides, the curing time was proved to be another critical factor affecting the dynamic modulus. Several curing times using Sasobit were tested in the work, and the results showed that 1-day curing time was optimal. In this study, taking advantage of such a result, the curing time was directly chosen as one day. The analysis of the effect of curing time might be the objective of further research, as different natures of aggregates, filler, or bitumen might have a certain influence on the dynamic modulus.