## 3 Results and Discussion
### Asphalt Mixtures Tests Results  
In relation to the water or moisture sensitivity of the studied asphalt mixtures, both in Europe and the US, a minimum tensile strength ratio (TSR) of 70% is recommended [31], although some conservative agencies refer to a TSR value of 80% [32; 33; 34]. The novel asphalt mixture studied in this work, with waste motor oil and SBS, showed a TSR value of 80%, which narrowly meets the recommended values to assure the needed durability of this mixture. In the previous study with bio-oil and ground rubber [6], the asphalt mixture presented a TSR value of 84%, which is also greater than 80%, and thus that mixture also fulfilled the requirements. Subsequently, the results of the fatigue cracking resistance test are summarized in Figure 3, namely for the new asphalt mixture with waste motor oil and SBS (B35/50 & MotorOil & SBS), the conventional mixture with B35/50 bitumen, and also for the asphalt mixture with bio-oil and ground rubber (PG64-22 & cryoMBO). Those results show the variation in the number of loading cycles (N\({}_{I}\)) before fatigue failure of each mixture (defined through the reduction of the stiffness to half of its initial value) as a function of the tensile micro strain (\(\mu\epsilon\)) applied in the fatigue test. Those results demonstrate that the new asphalt mixture with waste motor oil and SBS (B35/50 & MotorOil & SBS) is more resistant to fatigue than the conventional asphalt mixture (B35/50), at least in the range of the tensile strain values used in this test. The low viscosity of the waste motor oil and the high amount of SBS elastomer used may justify the very good fatigue cracking resistance of this new mixture. The asphalt mixture with bio-oil and ground rubber from the previous study [6] presented a  
Figure 3: Variation in the number of loading cycles (N\({}_{I}\)) before fatigue failure with the tensile micro strain (\(\mu\epsilon\)) applied in the fatigue test for the studied mixtures. lower fatigue resistance, probably due to the higher stiffness of the bio-binder or the lower amount of ground rubber used. One of the main models used to predict the fatigue life of an asphalt mixture in road pavements was that proposed by Shell [35]. The fatigue laws obtained for both modified asphalt mixtures (with waste motor oil and SBS or with bio-binder and GTR) indicate a fatigue life higher than that computed by the Shell model for an asphalt mixture with 4000 MPa and an asphalt volume content of 12%, which confirms the suitable fatigue performance of those mixtures. Moreover, the experimental fatigue coefficients K\({}_{1}\) and K\({}_{2}\) mentioned by other authors [36] were determined to be 5 \(\times\) 10\({}^{-14}\) and 5.171 for the conventional asphalt mixture with B35/50 bitumen. The new mixture with 10% motor oil and 5% SBS presented fatigue coefficients of K\({}_{1}\) = 1 \(\times\) 10\({}^{-14}\) and K\({}_{2}\) = 5.508, while the mixture with bio-binder and GTR presented fatigue coefficients of K\({}_{1}\) = 1 \(\times\) 10\({}^{-11}\) and K\({}_{2}\) = 4.368. In conclusion, both mixtures with modified binders (B35/50 & MotorOil & SBS and PG64-22 & cryoMBO) showed an adequate fatigue performance, at least similar to that that of the conventional asphalt mixture. The stiffness modulus of asphalt mixtures is a very important parameter for road pavement design, and it also influences the mixture fatigue performance. Figure 4 shows the master curves of the dynamic stiffness modulus of the several asphalt mixtures studied in this work for a reference temperature of 21 \({}^{\circ}\)C. In order to obtain these master curves, the conventional mixture with B35/50 bitumen and the asphalt mixture with waste motor oil and SBS were tested at 0, 10, 20 and 30 \({}^{\circ}\)C, according to the current practice [3], while the asphalt mixture with bio-oil and ground rubber was tested at 4, 21 and 37 \({}^{\circ}\)C, following another procedure [37].