## 3 Results and Analysis  
### Maximum Dry Density and Optimized Water Content  
Figure 5 illustrates the obtained results from the repeated compaction tests. It is observed that the dry density of graded crushed stone increases first then starts to drop as water content keeps increasing. It was found that the compaction curves have convex distributions. The dry density of graded crushed stone had a similar variation law after repeated compaction, and the compaction curve continued to shift upwards as the repeated compaction time increased. Water content is an important factor affecting the dry density of graded crushed stone. When the water content reaches a certain suitable value, the dry density of graded crushed stone can reach the maximum value. With the increase in the repeated compaction time, graded crushed stone will have better compaction effect. After fitting, the water content and dry density corresponding to the peak point of the compaction curve are defined as the optimal water content and optimal dry density. The maximum dry density and optimized water content corresponding to different repeated compaction times were obtained and the results are summarized in Table 4. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Repeated Compaction Times**} & \multicolumn{2}{c}{**Maximum Dry**} & \multirow{2}{*}{**Optimized Water Content\%**} \\  & **Density/(g-cm\({}^{-3}\))** & \\ \hline
1 st & 2.272 & 5.25 \\
2 nd & 2.293 & 5.35 \\
3 rd & 2.321 & 5.40 \\
4 th & 2.343 & 5.57 \\
5 th & 2.368 & 5.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Test results of repeated compaction. Figure 4: Graded crushed stone samples after repeated compaction and screening. Figure 5: Test curves of repeated compaction. Table 4 indicates that as the repeated compaction time increases, the corresponding maximum dry density and optimized water content of the graded crushed stone increases. Figure 6 shows the correlation between the maximum dry density of the graded crushed stone and repeated compaction times. It is observed that within the studied range of repeated compaction times, there is a linear correlation between the maximum dry density of the graded crushed stone and repeated compaction times. This correlation can be mathematically expressed as follows:  
\[\rho_{dm}=2.247+0.024n\ (n=1,\ 2,\ 3,\ \ldots) \tag{5}\]  
where \(\rho_{dm}\) is the maximum dry density of the graded crushed stone at \(n\)th repeated compaction. When the stone is broken, there must be voids between the formed particles. In general, the voids will not completely disappear after the graded crushed stone is compacted again. This shows that although the maximum dry density of graded crushed stone had a linear correlation with repeated compaction times, this linear law will not apply when the repeated compaction time is greater. Therefore, there is an upper limit for the maximum dry density, which will not increase infinitely with the increase in repeated compaction times. The measured apparent density of the graded crushed stone was 2.70 g-cm\({}^{-3}\), and in general, the upper limit of the maximum dry density will not exceed this value. Figure 7 shows the distribution of the graded crushed stone's optimized water content against the repeated compaction times. Figure 6: Distribution of the maximum dry density against the repeated compaction times. Figure 7: Distribution of optimized water content against the repeated compaction times. It is observed that as the repeated compaction times increases, the corresponding optimized water content of the graded crushed stone increases linearly, which can be expressed in the following form:  
\[\omega_{0}=5.062+0.14n\ (n=1,\ 2,\ 3,\ \ldots) \tag{6}\]  
where \(\omega_{0}\) is the optimized water content of graded crushed stone at \(n\)th repeated compaction. According to the change rules mentioned above, the optimal water content of graded crushed stone will encounter the same problem as the maximum dry density.