## 4 Results and Discussion
### Design Criteria of Mesoscopic Evaluation Indices for the Main Skeleton
#### 4.3.2 Design Criteria of Mesoscopic Evaluation Indices for the Main Skeleton  
According to the specifications [30], in the hot summer zone of China, the dynamic stability (DS) of the asphalt mixture nutting test must be 1000, 2800, and 3000 times/mm for non-modified asphalt mixture, modified asphalt mixture, and modified SMA mixture, respectively. In order to ensure the nutting resistance of the asphalt mixture, it is assumed that the DS standard of the designed asphalt mixture should be more than 2000 and 5000 times/mm for the non-modified asphalt mixture and modified asphalt mixture, respectively. According to the calculation of DS given by Equation (4), the deformations between 45 and 60 min during the nutting test are 0.315 and 0.126 mm, respectively:  
\[DS=\frac{(t_{2}-t_{1})\times N}{d_{2}-d_{1}}\times C_{1}\times C_{2} \tag{4}\]  
where t\({}_{1}\) is 45 min; t\({}_{2}\) is 60 min; d\({}_{1}\) is the deformation at time t\({}_{1}\); d\({}_{2}\) is the deformation corresponding to time t\({}_{2}\); C\({}_{1}\) is the type coefficient of the nutting test machine (generally, its value is 1.0); C\({}_{2}\) is the test coefficient when the 300-mm wide specimen is prepared in the laboratory (its value is 1.0); N is the rolling speed of the test wheel (usually 42 times/min).  
There are several internal factors that affect the nutting resistance of asphalt mixture; these include coarse aggregate performance, asphalt performance, and gradation and admixture performance. According to the test results and reports in literature, it is typically assumed that the compaction deformation of the initial nutting tests for 0-45 min is 2.0 mm [31]. Therefore, during the standard nutting test of asphalt mixture, when the deformation of non-modified asphalt mixture reaches 2.315 mm and that of modified asphalt mixture reaches 2.126 mm, the main skeleton reaches the critical value of the external load. Based on the data in Figure 11 and Table 11, to ensure that the DS of the non-modified asphalt mixture should be more than 2000 times/mm and that of modified asphalt mixture should be more than 5000 times/mm, the corresponding main skeleton mesoscopic evaluation indices of asphalt mixtures should be at least \(\overline{n}_{c}\) = 1.5 and C = 15%. Accordingly, this paper proposes that the design criteria of mesoscopic evaluation indices for the main skeleton be \(\overline{n}_{c}\)\(\geq\) 1.5 and C \(\leq\) 15% in the preparation of asphalt mixture specimens using the wheel rolling method. The foregoing can be used  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Type of Mixture**} & \multicolumn{2}{c}{**Mesoscopic Indices**} & \multicolumn{4}{c}{**Macroscopic Indices**} \\ \cline{2-7}  & **Coordination** & **\#\({}_{c}\)** & **C (\%)** & **DS** & **RD at Loading** & **RD at Loading** \\  & **Number Peak Value** & **\#\({}_{c}\)** & **C (\%)** & **(times-mm\({}^{-1}\))** & **Time of 1 h (mm)** & **Time of 3 h (mm)** \\ \hline
70\# asphalt AC-13C & 1.78 & 1.88 & 7.48 & 2136 & 5.88 & 10.26 \\ Rock asphalt AC-13C & 1.69 & 1.82 & 7.29 & 3980 & 2.50 & 5.25 \\ SMA-13 & 2.02 & 2.15 & 4.89 & 4222 & 1.46 & 3.64 \\ Average value & 1.83 & 1.95 & 6.55 & 3446 & 3.28 & 6.38 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Corresponding mesoscopic and macroscopic indices when main skeleton reaches critical value.  
as basis for the design of DSAM with a nominal maximum particle size of 13.2 mm; this will ensure that the coarse aggregates interlock, form a steady main skeleton, and improve the rutting resistance of the asphalt mixture.