## 3 Gradation Design
### Gradation Synthesis  
#### 3.2.1 Gradation Design  
In the absence of mineral powder and binder, according to the step-by-step filling theory, in order to minimize the gap of the skeleton structure formed between the coarse aggregates and to avoid its expansion through the fine aggregate, the secondary skeleton dense structure should completely fill the main skeleton's gap. Therefore, the composition design of CRT should adopt the volume method, and some improvement measures should be made on the basis of the coarse aggregate void-filling (CAVF) method. The skeleton intrusion compact volume method was proposed. The calculation process is as follows:  
\[q_{c}+q_{f}+q_{p}=\ 100\%, \tag{2}\]  
\[\frac{q_{c}}{100\rho_{\rm sc}}(\rm VCA\ -\ V_{\rm VS})=\ \frac{q_{p}}{\rho_{\rm tp }}\ +\ \frac{q_{f}}{\rho_{\rm tf}}\ +\ \frac{q_{a}}{\rho_{a}}\ +\ \frac{q_{r}}{\rho_{\rm tr}}, \tag{3}\]  
\[\frac{q_{a}}{100\rho_{a}}\ =\ (\rm VMA\ -\ V_{\rm VS})\ \times\frac{q_{c}}{100\rho_{\rm sc}}, \tag{4}\]  
where \(q_{c}\), \(q_{f}\), \(q_{p}\), \(q_{r}\), and \(q_{a}\) are the mass fractions of the coarse aggregate, fine aggregate, filler, CR, and asphalt, respectively; \(\rho_{\rm sc}\), \(\rho_{\rm tp}\), \(\rho_{\rm tf}\), \(\rho_{a}\), and \(\rho_{\rm tr}\) are the apparent densities of the coarse aggregate, filler, fine aggregate, asphalt, and CR, respectively; VCA = the air void; V\({}_{\rm VS}\) = the objective void; and VMA = the void in the mineral aggregate.  
In the design, when CR is not incorporated, if V\({}_{\rm VS}\), VMA, and \(q_{p}\) are determined, other parameters can be calculated. VVS was set to 4%, VMA was set to 15%, and gradation 1 was taken as 5%. It can be seen from Table 8 that the VCA of fine aggregate gradation 1 was slightly larger than that of gradation 2. In order to better fill the coarser fine aggregate, the gradation 2 filler content was smaller than that of gradation 1. At the same time, considering that the dry process asphalt mixture in the later stage adopted a skeleton dense gradation, a gradation 2 of 4% was considered to be comprehensive.  
For the calculation, let \(X\) be the percentage of coarse aggregate, \(Y\) be the percentage of fine aggregate, \(Z\) be the asphalt-aggregate ratio, and the other parameters be as listed in Table 2, Table 6, and Table 8. The results are listed in Table 9, and the synthetic gradations are listed in Table 10. The proportion of coarse aggregates was generally between 65% and 75%, and the loose state of gradation 1 did not meet the requirement.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Gradation Types** & \begin{tabular}{c} **Particle Size** \\ **Range (mm)** \\ \end{tabular} & **Proportion (\%)** & \
\begin{tabular}{c} **Synthetic Apparent** \\ **Density (g/cm3)** \\ \end{tabular} &
\begin{tabular}{c} **Tight Density** \\ **(g/cm3)** \\ \end{tabular} & **Air Void (\%)** \\ \hline \multirow{4}{*}{Gradation 1} & 2.36–1.18 & 19.64 & & & \\  & 1.18–0.6 & 16.07 & & & \\  & 0.6–0.3 & 23.80 & 2.811 & 1.779 & 36.724 \\  & 0.3–0.15 & 25.50 & & & \\  & 0.15–0.075 & 15.00 & & & \\ \hline \multirow{4}{*}{Gradation 2} & 4.75–2.36 & 17.78 & & & \\  & 2.36–1.18 & 14.54 & & & \\  & 1.18–0.6 & 17.40 & 2.813 & 1.825 & 35.118 \\ \cline{1-1}  & 0.6–0.3 & 26.78 & & & \\  & 0.3–0.15 & 13.50 & & & \\  & 0.15–0.075 & 10.00 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 8: Fine aggregate grading compositions.