## 3 Gradation Design
### Coarse and Fine Aggregate Design
#### 3.1.3 Fine Aggregate Design  
In order to form an embedded structure between the grading particles and ensure that the gap ratio was small enough to improve the overall stability of the mixture, the grading filling theory was used to design the fine aggregate ratios of coarse aggregate gradations 1 and 2. The method of finding the best ratio for the lowest porosity was refined.  
Here, take the class I filling in gradation 1 as an example. The aggregate of 2.36-1.18 mm and 1.18-0.6 mm was given a total weight of 5 kg in accordance with the proportions in Table 7, and the aggregate was evenly mixed as the test material. The test results are shown in Table 7. Figure 3 is a graph of the variation in the air void proportional to the different compositions of the aggregate (wt %).  
From the peak fitting analysis in Figure 3, we can get an arrangement ratio between 2.36-1.18 mm and 1.18-0.6 mm of 55:45. The skeletal structure formed by the aggregates of two particle sizes under this gradation was the densest, and the air void was 46.016%. Then, the class II filling was carried out with the results of the class I filling, and the subsequent fillings were carried out by superposition.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multirow{2}{*}{**Particle Size**} & \multirow{2}{*}{**Proportion**} & \multicolumn{3}{c}{**Density (kg/m\({}^{3}\))**} & \multicolumn{3}{c}{**Air Void (\%)**} \\ \cline{3-10}  & & **Range (mm)** & & **Type** & **Size** & **Size** & **Size** & **Size** & **Size** & **Size** \\ \hline \multirow{4}{*}{Gradation 1} & 16–13.2 & 10.7 & & & & & & & \\  & 13–2.9 & 28.4 & & & & & & & \\  & 9.5–475 & 48.1 & 1.683 & 1.573 & 1.527 & 39.858 & 43.809 & 45.444 \\  & 4.74–2.36 & 12.8 & & & & & & & \\ \hline \multirow{4}{*}{Gradation 2} & 16–13.2 & 16.5 & & & & & & & \\  & 13–2.9 & 38.8 & 1.696 & 1.604 & 1.557 & 39.675 & 42.941 & 44.601 \\ \cline{1-1}  & 9.5–475 & 44.8 & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 6: Calculation results of the sieve pass rate of the coarse aggregate.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Projects**} & \multirow{2}{*}{**Units**} & \multicolumn{6}{c}{**Different Composition Ratios of 2.36–1.18-mm and 1.18–0.6-mm Aggregates**} \\ \cline{3-10}  & & **10.0** & **9.1** & **8.2** & **7.3** & **6.53.5** & **6.4** & **5.54.5** & **5.5** & **4.6** \\ \hline Aggregate quality & g & 1520 & 1540.5 & 1562 & 1572 & 1575.5 & 1576.5 & 1576.6 & 1569.5 & 1541.5 \\ Tight density & g/cm\({}^{3}\) & 1.462 & 1.481 & 1.502 & 1.512 & 1.515 & 1.516 & 1.516 & 1.509 & 1.482 \\ Apparent density & g/cm\({}^{3}\) & 2.822 & 2.819 & 2.816 & 2.813 & 2.811 & 2.810 & 2.808 & 2.806 & 2.803 \\ Air void & \% & 48.209 & 47.452 & 46.660 & 46.259 & 46.109 & 46.045 & 46.016 & 46.226 & 47.127 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Class I filling test results.  
Figure 3: Air void at different ratios of 2.36–1.18 mm and 1.18–0.6 mm.  
Therefore, the class I-IV fillings and class I-V fillings were performed on gradation 1 and gradation 2, respectively, according to the division boundaries of the coarse and fine aggregates. The results of the two-stage grading and filling are shown in Figure 4. According to the relationship between the void ratio and the proportion of the filling for each class, the optimum ratio value under the filling of the level was obtained by peak fitting. The grading compositions are listed in Table 8.  
Figure 4: Air void variations with secondary particle size fractions: (**a**) gradation 1; (**b**) gradation 2.