## 5 Discussion
### Rubber Effects  
Once shown the results of the multi-scale approach for the bituminous mixtures containing fine CR, the rubber effects were analyzed comparing the MASTIC-CR, MORTAR-CR and SMACR with the corresponding bituminous mixtures containing only limestone filler. Once again, starting from a traditional SMA mixture without CR (SMA0), the dosages of the mastic (MASTIC-SMA) and mortar (MORTAR-SMA) components were calculated using the same normalization method showed in the previous paragraphs.  
Results in Figure 12 show that, considering the mastic and mortar scale of analysis, the combined presence of limestone filler and CR reduces the G* values if compared to the traditional SMA mastic and mortar at high frequencies (low temperatures). At the same time, G* values at low frequencies (high temperatures) are registered for the bituminous mixture with limestone filler and CR.  
Thus, it can be stated that the CR effects on the rheo-mechanical behavior can be translated to a reduction in the bitumen thermo-sensitivity. In particular, considering the mastic and mortar scales, the fine CR acts mainly at low temperatures (high frequencies) limiting the stiffness and therefore the possible thermal cracking proneness of the bituminous mastic.  
All in all, the addition of CR reduces the thermo-sensitivity of mastic, mortar and mixture but this effect is not the exactly the same for all the scale of analysis. While in the mortar, the CR effect is mainly visible at low temperatures, in the mastic scale a small variation in stiffness is registered also at high temperatures. This increase in stiffness is amplified at the mixture scale. The SMACR master curve shows a relevant increase in the stiffness at high and medium temperatures. This is a further confirmation of the influence of the aggregates' matrix size in the rubber-bitumen-aggregates interaction.  
Figure 11: LogTIsf-Temperature function.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample Length Scale** & \(\mathbf{\alpha}\) & \(\beta\) & \(\delta\) & \(\gamma\) \\ \hline SMACR & \(-2.817\) & \(1.473\) & \(10.230\) & \(-0.572\) \\ MORTAR-CR & \(-5.038\) & \(0.921\) & \(9.386\) & \(-0.410\) \\ MASTIC-CR & \(-5.731\) & \(0.532\) & \(10.240\) & \(-0.380\) \\ \hline \hline \end{tabular}
\end{table}
Table 11: Sigmoidal complex modulus model parameters.  
Considering the mixtures without rubber, the CR effects tend to be shifted from low to high temperatures when the coarser aggregates are progressively added to the bituminous mixtures. In order to validate these results in terms of mixture fatigue life, the durability of the bituminous mixtures with and without CR was assessed on mastics and mixtures. In particular, the healing of the mastics was evaluated with TS tests, while fatigue tests were carried out on SMA mixtures. The adopted test configuration for the TS tests is explained in Paragraph 3.3 and the results are given in terms of shear strain (\(\gamma\)).  
The fatigue behavior of the SMA was investigated in order to deeply investigate the effect of the rubber according to the Dry Hybrid technology within the bituminous mixtures. Results for mastics and mixtures are presented in Figures 13 and 14.  
Figure 12: Master curves comparison between mixture, mortar and mastic containing CR or not.  
Figure 13: Mastics time sweep test comparison.  
From the analysis of results, the increase in number of load applications for both SMACR mastic and mixture is clear. The presence of CR involves the improvement of mastic and mixture durability regardless the applied stress. The phenomenon is confirmed in terms of healing (TS test on mastics) and fatigue life (ITFT on mixtures).  
It is worth noting that in terms of the stiffness modulus, both mixtures show comparable values (3259 MPa for SMACR and 3188 MPa for SMA0 at 20 \({}^{\circ}\)C, calculated according to EN 12697-26 Annex C standard). In the light of the above, the adopted stress levels produced comparable horizontal deformations in the samples, validating the adopted test conditions.