# Performance Evaluation of Steel Slag Asphal Mixtures for Sustainable Road Placement Rehabilitation
## 3 Results and Discussion
### Stiffness and Fatigue Resistance  
The results of the stiffness tests, stiffness modulus and phase angle, are presented in Figure 5, where the bars represent average values, and the error marks the respective standard deviation. As expected, the increase of the loading frequency caused an increase of the stiffness modulus and a decrease of phase angle. In general, the behavior of all the studied asphalt mixtures was similar, highlighted by a visual overlap of the error marks.  
Generally, the stiffness of the asphalt mixture is highly dependent on the type of bitumen and binder content. If these variables remain unchanged, as well as the mixture type and compaction conditions (i.e., voids content), one can expect similar stiffness results. Furthermore, the percentages of aggregate substitution (20% and 35%) are moderate, thus a significant change in behavior is not to be expected. The differences observed in the stiffness results can be explained by the production (specimen mixing and compaction) and experimental variability.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Property**} & \multicolumn{3}{c}{**Asphalt Mixture**} \\ \cline{2-4}  & **0\% SSA** & **20\% SSA** & **35\% SSA** \\ \hline Binder content (\% by mass) & 4.70 & 4.70 & 4.53 \\ Binder content (\% by volume) & 10.81 & 11.47 & 11.47 \\ Stability (kN) & 8.497 & 12.940 & 16.775 \\ Flow (mm) & 3.81 & 4.52 & 4.53 \\ Marshall quotient (kN/mm) & 2.2 & 3.0 & 4.0 \\ Bulk density SSD (Mg/m\({}^{3}\)) & 2.377 & 2.526 & 2.626 \\ Maximum density (Mg/m\({}^{3}\)) & 2.485 & 2.622 & 2.714 \\ Air voids content (\%) & 4.34 & 3.64 & 3.26 \\ Void in the mineral aggregate VMA (\%) & 15.18 & 15.17 & 15.20 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Marshall and volumetric properties.  
The result of the fatigue resistance test, for each tested specimen, was the number of cycles (fatigue life) for the respective loading strain being applied. The individual test results were used to derive fatigue lines. Figure 6 presents the obtained fatigue lines, where it can be observed that the incorporation of SSA was not detrimental to the fatigue resistance of the asphalt mixture.  
The fatigue lines can be written according to the following equation:  
\[\log(N)=A_{0}+A_{1}\times\log(\varepsilon) \tag{1}\]  
where: \(N\) is the fatigue life (number of cycles to reach the failure criterion), \(\varepsilon\) is the applied loading strain, \(A_{0}\) and \(A_{1}\) are constants (determined by linear regression in the log-log space). When plotted in a log-log space, \(A_{1}\) corresponds to the slope of the fatigue line. Table 4 presents the parameters determined for the fatigue lines, \(\varepsilon_{6}\) (strain correspondent to fatigue life of one million cycles) and \(R^{2}\) (coefficient of determination).  
Regarding fatigue resistance, the behavior among the asphalt mixtures can be considered approximately similar. The asphalt mixtures with SSA performed slightly better than the reference mixture. However, this can be partially explained by the variability of this type of test and a small difference in the volumetric binder content, which is a bit higher in the case of SSA asphalt mixtures (Table 3).  
Figure 5: (a) Stiffness modulus; (b) phase angle.  
Figure 6: Fatigue lines.