## 3 Results and Discussion
### Performance of Studied Asphal Mixtures
#### 3.4.4 Fatigue Cracking Resistance of Studied Asphalt Mixtures  
In order to assess the fatigue cracking performance of the studied mixtures, 4 point bending beam tests were carried out at 20 \({}^{\circ}\)C. The results of those tests are presented in Figure 12.  
Figure 11: Master curves of the stiffness modulus and phase angle of the studied mixtures for a reference temperature of 20 \({}^{\circ}\)C.  
In Figure 12, it can be observed that the fatigue performance of the mixtures with PEX is not higher than that of the mixtures without PEX and a similar binder content. However, an increase of 0.5% in the binder content of the 50/70 pen bitumen is enough to improve the fatigue performance of the mixture (M3). This behaviour can be explained by the nature of the polymer that is contained in the PEX (plastomer), which does not perform in the same way as the elastomer used in the PMB 45/80-60 mixtures (M2 and M5). In fact, the mixture with the best fatigue performance was M2, which contains only the natural aggregates and the elastomer modified binder.  
From the fatigue life equations (fatigue cracking laws) of the studied mixtures, two main fatigue performance parameters, \(\epsilon_{6}\) and N100, were calculated (as specified in EN 12697-24 standard) and are presented in Table 5.  
The \(\epsilon_{6}\) results, representing the strain level at which the mixture would fail after 1 million cycles, showed that for the same binder type and content (comparing M1 and M3), the addition of PEX slightly reduced the fatigue resistance. The increased binder content used in mixture M4 was not enough to assure a fatigue performance equivalent to that of mixture M1, although the \(\epsilon_{6}\) value was not significantly lower.  
As previously observed in Figure 12, the mixture with the best \(\epsilon_{6}\) value is M2, due to the increased flexibility given by the elastomeric additive used in the binder modification. However, if the binder content is increased by 0.5% a considerable amount of PEX could be introduced in the mixture, as aggregates, without compromising the performance of the mixture (M5), demonstrating that the use of PEX could be an interesting solution in ecological and technical terms.  
Regarding the N100 values, which are the number of cycles corresponding to a test carried out at 100 microstrain, the mixtures produced with the PMB 45/80-60 binder are those that present the highest performance, which confirms the results presented in Figure 12. For those mixtures, the addition of  
Figure 12: Fatigue cracking laws of the studied mixtures.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Fatigue Parameter**} & \multicolumn{5}{c}{**Mixture**} \\ \cline{2-6}  & **M1** & **M2** & **M3** & **M4** & **M5** \\ \hline \(\epsilon_{6}\) & 156 & 252 & 117 & 129 & 242 \\ N100 (\(\times\) 10\({}^{6}\)) & 6.9 & 45.9 & 2.1 & 3.0 & 140.0 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Fatigue parameters, N100 and \(\epsilon_{6}\), of the studied mixtures.  
PEX, associated with a small increase in the binder content, resulted in the best performing mixture (M5), while in the mixtures produced with the conventional 50/70 pen bitumen, the addition of PEX did not have the same effect, even when a higher binder content was used.