## 3 Results and Discussion  
### Bbt  
(a) The variation of \(R_{B}\), \(\epsilon_{B}\), \(S_{B}\), and \(D_{se}\) with gradation was inconsistent (as shown in Figure 7). As shown in Figure 8, there was a positive correlation between \(\epsilon_{B}\) and \(D_{se}\), while there was a negative correlation between \(\epsilon_{B}\) and \(S_{B}\). \(\epsilon_{B}\) reflected the deformation resistance ability of the asphalt mixture, and \(D_{se}\) reflected the energy absorption ability of the material during the failure process. Both of them reflected the viscoelastic failure characteristics of the asphalt mixture, so they had a positive correlation. \(S_{B}\) was more suitable for the assessment of brittle failure, which was inconsistent with the failure mechanism of the asphalt mixture, so it had a negative correlation. In summary, \(\epsilon_{B}\) and \(D_{se}\) were recommended as indicators for evaluating the performance of asphalt mixtures.  
(b) The \(\epsilon_{B}\) and \(D_{se}\) of different gradation mixtures were different. These values indicated the deformation and energy required for the failure of the asphalt mixtures under load. As shown in Figure 9, at \(-10\)\({}^{\circ}\)C, the maximum difference in \(\epsilon_{B}\) was 2397.5 \(\mu\varepsilon\), and the maximum difference in \(D_{se}\) was 200.6 kPa. At 15 \({}^{\circ}\)C, the maximum difference in \(\epsilon_{B}\) was 2994.3 \(\mu\epsilon\), and the maximum difference in \(D_{se}\) was 15.34 kPa. The 10B-1 had the highest values of \(\epsilon_{B}\) and \(D_{se}\) at both temperatures, indicating that it had superior performance among the gradations.  
Figure 8: Correlation of evaluation indexes of BBT.  
Figure 6: Preparation of OT specimen.  
(c) There were differences in the correlation between the gradation parameters and the \(\varepsilon_{B}\) and \(D_{se}\). The R\({}^{2}\) value of the linear regression of the same gradation parameter at different temperatures was also different. As shown in Figure 10, the \(P_{4.75\text{mm}}\), \(P_{2.36\text{mm}}\), \(PCSI\), and \(D_{c}\) had strong correlations with \(\varepsilon_{B}\) and \(D_{se}\) at \(-10\)\({}^{\circ}\)C. At 15 \({}^{\circ}\)C, the \(P_{4.75\text{mm}}\) had a better correlation with \(\varepsilon_{B}\) and \(D_{se}\), while the \(P_{2.36\text{mm}}\), \(PCSI\), and \(D_{c}\) had a better correlation only with \(\varepsilon_{B}\). For a more comprehensive analysis, the \(P_{4.75\text{mm}}\), \(P_{2.36\text{mm}}\), \(PCSI\), and \(D_{c}\) were chosen to further analyze the effect of gradation.  
(d) As the \(P_{4.75\text{mm}}\), \(P_{2.36\text{mm}}\), \(PCSI\), and \(D_{c}\) increased, \(\varepsilon_{B}\) and \(D_{se}\) of the mixture improved. As shown in Figure 11, the populated data points are for the 10A-1 gradation, which was not fitted due to the differences in its relevant performance indexes from the other gradations. As the passing rate of sieves and _PCSI_ increased, the fine aggregate content in the mixture also increased, which enhanced the suspension effect of coarse aggregate in asphalt mortar. This caused a larger deformation during the bending failure process and consequently increased \(\varepsilon_{B}\). The \(D_{\text{sv}}\) of the asphalt mixture also increased with the bonding effect of asphalt mortar, which consumed more energy for the crack expansion during the bending failure. This index reflected that a more uniform gradation of asphalt mixture created a denser structure with smaller gaps between coarse aggregates. Therefore, in the gradation design, the \(D_{c}\) should be increased moderately to improve the bending resistance of the asphalt mixture. However, the \(D_{c}\) should not be excessive; otherwise, it will enhance the interference effect of finer aggregate and increase the porosity of the asphalt mixture, thus impairing its damage resistance. Based on this analysis, this paper recommends that the \(D_{c}\) should be controlled below 2.50.  
Figure 11: _Cont._