## 3 Results and Discussions
### Bending Beam Test  
Table 10 shows the bending beam test results of six different types of asphalt mixtures at different temperatures.  
Figure 5 shows that the NMS has an obvious influence on the bending failure strain of hybrid-modified SMA when the test temperature and CRM content are constant. In addition, the bending failure strain decreased generally as the test temperature increased and the dose of CRM also decreased.  
Taking the case of the modified binder of 5% SBS + 20% CRM as an example, the bending fracture strains of SMA-5, SMA-10 and SMA-13 at 0 \({}^{\circ}\)C were 4669 \(\mu\)\(\epsilon\), 4177 \(\mu\)\(\epsilon\) and 3813 \(\mu\)\(\epsilon\), respectively. The bending fracture strain decreased by 10.2% and 18.0% for SMA-10 and SMA-15, compared with the value of SMA-5. For the case of the modified binder of 5% SBS + 10% CRM, when the CRM content was reduced, the bending fracture strain of SMA-5 is 11.3% and 21.9% higher than those of SMA-13 and SMA-10. The trend was in general true for the other test temperatures and doses of CRM.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Gradation** & **Asphalt Mixture** & **Test** & **Bending Tensile** & **Maximum Bending** & **Bending** \\
**Types** & **Types (5\% SBS)** & **Temperatures/\({}^{\circ}\)C** & **Strength/MPa** & **Tensile Strains/\(\mu\)\(\epsilon\)** & **Stiffness/MPa** \\ \hline \multirow{6}{*}{SMA-5} & \multirow{6}{*}{+10\%CRM} & \(-\)10 & 9.9 & 3028 & 3263 \\  & & \(-\)5 & 9.7 & 3463 & 2910 \\  & & 0 & 10.2 & 3991 & 2613 \\  & & \(-\)10 & 11.5 & 3203 & 3632 \\  & +20\%CRM & \(-\)5 & 10.3 & 3822 & 2702 \\  & & 0 & 10.2 & 4649 & 2228 \\  & & \(-\)10 & 9.2 & 2765 & 3348 \\  & +10\%CRM & \(-\)5 & 9.1 & 3016 & 3004 \\  & & 0 & 10.1 & 3631 & 2898 \\  & & \(-\)10 & 9.7 & 2918 & 3388 \\  & +20\%CRM & \(-\)5 & 10.2 & 3398 & 2993 \\  & & 0 & 10.3 & 4177 & 2544 \\  & & \(-\)10 & 7.3 & 2660 & 2766 \\  & +10\%CRM & \(-\)5 & 7.9 & 3070 & 2567 \\  & & 0 & 8.2 & 3683 & 2229 \\ SMA-13 & & \(-\)10 & 7.9 & 2664 & 2966 \\  & +20\%CRM & \(-\)5 & 7.4 & 3027 & 2471 \\  & & 0 & 8.9 & 3813 & 2337 \\ \hline \end{tabular}
\end{table}
Table 10: Bending beam test results of asphalt mixtures.  
Figure 5: Bending failure tensile strains affected by NMS.  
Figure 6 showed the effect of NMS on the stiffness modulus of the hybrid-modified SMA. The stiffness increased generally as the test temperature increased and also the dose of CRM. At the same temperature, the stiffness of SMA-10 was greater than that of the other two NMS. The trend was true for both doses of CRM. It must be noted that the tread of the stiffness changed with the NMS in a different way from that of the freezing fracture strain.  
The relationship between bending stiffness of the SMA and test temperature was studied. Taking the case of the SMA-13 with hybrid-modified 5%SBS + 20%CRM as an example, when the test temperature increased from \(-10\)\({}^{\circ}\)C to \(-5\)\({}^{\circ}\)C and \(0\)\({}^{\circ}\)C, the bending stiffness decreased from 2966 MPa, 2471 MPa to 2337 MPa. A decreasing rate of 16.7% and 21.2% was observed for temperatures of \(-5\)\({}^{\circ}\)C and \(0\)\({}^{\circ}\)C, respectively, as compared with that of \(-10\)\({}^{\circ}\)C. The higher the temperature, the smaller the stiffness and the better the crack resistance at low temperature. These trends are basically similar to the existing findings of asphalt mixtures.