## 3 Results and Discussion
### Fatigue Resistance  
[PERSON] et al. [38] indicated that traditional design methods, such as the Marshall method, can provide mixtures with an acceptable performance. However, the lack of flexibility in the design values can lead to ill-adapted mixtures. Taking into account in-service conditions (as fatigue performance) leads to an improvement of the overall performance of the pavement. Traffic loads are cyclical and the repeated passage of these loads induces a fatigue process [39]. Fatigue is of importance for concrete structures subjected to repetitive loading, such as bridges [40] or railway slab tracks under traffic loads [41]. However, there is still a lack of common criteria about the necessary number of tests or sample size. For high-strength concrete, the studies are still limited [42; 43]. However, in bituminous mixes, there are several standardized methods for determining the fatigue characteristics of asphalt concrete mixtures--uniaxial tension/compression; 2, 3, and 4 point bending; and indirect-tension tests [44].  
In this research, the fatigue resistance was obtained through a four point besting test carried out on strain control and with a repetitive sinusoidal loading configuration, as can be seen in Figure 8a. Figure 8b illustrates an example of the fatigue results on AC-PA, AC-WC, and AC-MT samples. Since the load and displacement were continuously measured during the test, parameters like dynamic modulus, phase angle, and dissipated energy could easily be calculated and plotted, as can be seen in the example of Figure 8b. Shown are the dynamic modulus, phase angle, and dissipated energy as a function of number of test cycles for typical tests. It is apparent that the dynamic modulus decreases with the number of cycles. The phase angle increases with the number of cycles, demonstrating the degradation of the mix, as well as its loss of rigidity. Over the length of the test, which simulates the useful life of the road service, the energy dissipated per cycle is reduced as the sample suffers from fatigue effects.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mixture Properties** & **AC-PA** & **AC-WC** & **AC-MT** \\ \hline \(\rho_{d}\) (kg/m\({}^{3}\)) & 2897 & 2745 & 2774 \\ Correction factor \(\alpha\) & 0.915 & 0.965 & 0.955 \\ Minimum bitumen content & 4.12 & 4.34 & 4.30 \\ (\%) & 4.54–3.68\% & 4.72–4.11\% & 5.89–5.11\% \\ \(IT  
Table 7 summarizes the mean fatigue testing results for the dynamic modulus; phase angle; and the initial, final, and accumulated dissipated energies of each of the mixes as a function of bitumen content. Additionally, the number of cycles necessary for a 50% reduction in the initial value of the dynamic modulus is presented [45]. As may be observed from the results at a low bitumen content, the phase angles are low, indicating the fragility of these mixes. At a low bitumen content, the mineral skeleton of the mix is unable to support deflections greater than 150 \(\upmu\)m/m, which causes failure at a lower number of cycles. However, with an increase in the amount of bitumen content, the mix becomes more flexible, increasing the viscous component, as may be seen in the increasing values of the phase angle. This improvement increases the number of cycles necessary to induce fatigue in the mix.  
In the AC-WC mix, the mix with a 3% bitumen content broke during the pre-testing phase. With a higher bitumen content, the dynamic modulus was approximately constant, with values similar to those of the AC-PA mix. The AC-MT mix had slightly lower dynamic modulus values than the control.  
The AC-WC and AC-MT mixes took a greater number cycles to fatigue, around 20-25% higher, with a bitumen content greater than 5% and 5.5%, respectively.  
Figure 8: (**a**) Four-point bending beam fatigue testing equipment used for testing the samples. (**b**) Some examples of the typical test results for fatigue testing of the studied mixes.