## 4 Analysis on Test Results
### Three-Point Bending Test Results  
Three point bending tests based on JHR 3-7-5 [14] were performed to evaluate the mechanical properties of the asphalt concretes in terms of resistance to cracking. The specimens, which were 50 \(\times\) 50 \(\times\) 300 mm rectangular beams, were tested to determine the bending strength at \(-\)10 \({}^{\circ}\)C and 20 \({}^{\circ}\)C with a loading rate of 50 and 100 mm/min. The results of bending strength, strain and stiffness of asphalt mixtures are presented in Table 8.  
It can be found in Table 8 that the stiffness decreased and strain increased with the reduction of NMAS for SMA mixtures. As for bending stress, it was proportional to the change of NMAS; especially for the results at 20 \({}^{\circ}\)C. Bending strain is a significant material property, which is often utilized as an indicator of ductility and cracking potential for the asphalt mixture. Asphalt mixtures with higher strain at failure are more resistant to cracking than those with lower values under similar loading and environmental conditions. The rank of bending strain for different SMA mixtures is as follows. It can be concluded that a decrease of NMAS helped to improve the cracking resistance of SMA mixtures.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Test Condition** & **Properties** & **SMA5** & **SMA13** & **SMA20** & **SMA30** \\ \hline \multirow{8}{*}{\(-\)10 \({}^{\circ}\)C} & \multirow{2}{*}{50 mm/min} & Bending Stress, MPa & Average & 8.8 & 10.9 & 11.3 & 10.4 \\  & & CV, \% & 10.2 & 9.07 & 11.5 & 12.3 \\ \cline{2-7}  & \multirow{2}{*}{Strain,} & Average & 8.3 \(\times\) 10\({}^{-3}\) & 7.7 \(\times\) 10\({}^{-3}\) & 7.4 \(\times\) 10\({}^{-3}\) & 7.1 \(\times\) 10\({}^{-3}\) \\  & & CV, \% & 15.6 & 17.8 & 16.7 & 19.2 \\ \cline{2-7}  & \multirow{2}{*}{Stiffness, MPa} & Average & 1060.2 & 1415.6 & 1527.0 & 1464.8 \\  & & CV, \% & 14.3 & 16.7 & 18.2 & 20.1 \\ \cline{2-7}  & \multirow{2}{*}{100 mm/min} & Bending Stress, MPa & Average & 9.0 & 9.8 & 9.9 & 9.8 \\  & & CV, \% & 12.4 & 14.1 & 10.4 & 11.1 \\ \cline{2-7}  & \multirow{2}{*}{Strain,} & Average & 4.8 \(\times\) 10\({}^{-3}\) & 4.0 \(\times\) 10\({}^{-3}\) & 3.6 \(\times\) 10\({}^{-3}\) & 3.0 \(\times\) 10\({}^{-3}\) \\  & & CV, \% & 15.3 & 18.6 & 13.1 & 19.5 \\ \cline{2-7}  & \multirow{2}{*}{Stiffness, MPa} & Average & 1875 & 2450 & 2750 & 3266.7 \\  & & CV, \% & 17.1 & 13.1 & 18.9 & 17.5 \\ \hline \multirow{8}{*}{\(20\ {}^{\circ}\)C} & \multirow{2}{*}{50 mm/min} & Bending Stress, MPa & Average & 2.5 & 2.9 & 3.8 & 3.8 \\  & & CV, \% & 8.9 & 10.3 & 12.2 & 11.9 \\ \cline{1-1} \cline{2-7}  & \multirow{2}{*}{Strain,} & Average & 3.0 \(\times\) 10\({}^{-2}\) & 2.4 \(\times\) 10\({}^{-2}\) & 2.2 \(\times\) 10\({}^{-2}\) & 2.0 \(\times\) 10\({}^{-2}\) \\  & & CV, \% & 12.6 & 10.4 & 17.9 & 18.1 \\ \cline{1-1} \cline{2-7}  & \multirow{2}{*}{Stiffness, MPa} & Average & 83.3 & 120.8 & 172.7 & 190 \\  & & CV, \% & 9.5 & 11.2 & 16.3 & 14.5 \\ \cline{1-1} \cline{2-7}  & \multirow{2}{*}{100/mm/min} & Average & 3.9 & 4.1 & 4.8 & 5 \\  & & CV, \% & 10.4 & 13.9 & 12.4 & 9.7 \\ \cline{1-1} \cline{2-7}  & \multirow{2}{*}{Strain} & Average & 2.4 \(\times\) 10\({}^{-2}\) & 2.0 \(\times\) 10\({}^{-2}\) & 1.3 \(\times\) 10\({}^{-2}\) & 1.2 \(\times\) 10\({}^{-2}\) \\  & & CV, \% & 10.2 & 9.6 & 13.8 & 17.3 \\ \cline{1-1} \cline{2-7}  & \multirow{2}{*}{Stiffness, MPa} & Average & 162.5 & 205 & 369.2 & 416.7 \\  & & CV, \% & 8.6 & 11.1 & 16.2 & 13.5 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Results of three-point bending test.