## 3 Packing Characteristics of Packed Single-Size Particles  
Table 3 lists the values of \(V_{a}\) corresponding to the SSP tests of the gravel and crushed stone particles by the loose and dry-roadded packing tests. The corresponding values of \(RD_{V_{a}}^{L-R}\) and \(RD_{V_{a}}^{CS-G}\) are also listed in Table 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Size (mm)**} & \multirow{2}{*}{**Type**} & \multicolumn{3}{c}{\(V_{a}\) (\%)} & \multicolumn{2}{c}{\(RD_{V_{a}}^{L-R}\) (\%)} & \multicolumn{2}{c}{\(RD_{V_{a}}^{CS-G}\) (\%)} \\ \cline{3-8}  & & **Loose** & **Dry-Rodded** & **Loose** & **Dry-Rodded** \\ \hline \multirow{2}{*}{16} & CS & 45.47 & 40.41 & 11.13 & \multirow{2}{*}{11.55} & \multirow{2}{*}{11.00} \\ \cline{2-8}  & G & 40.22 & 35.97 & 10.58 & & \\ \hline \multirow{2}{*}{13.2} & CS & 44.18 & 40.18 & 9.05 & \multirow{2}{*}{8.30} & \multirow{2}{*}{13.04} \\ \cline{2-8}  & G & 40.51 & 34.94 & 13.75 & & \\ \hline \multirow{2}{*}{9.5} & CS & 47.21 & 42.93 & 9.06 & \multirow{2}{*}{14.89} & \multirow{2}{*}{15.17} \\ \cline{2-8}  & G & 40.18 & 36.42 & 9.36 & & \\ \hline \multirow{2}{*}{4.75} & CS & 46.52 & 41.91 & 9.90 & \multirow{2}{*}{16.64} & \multirow{2}{*}{15.37} \\ \cline{2-8}  & G & 38.78 & 35.47 & 8.53 & & \\ \hline \multirow{2}{*}{2.36} & CS & 47.47 & 42.52 & 10.44 & \multirow{2}{*}{12.22} & \multirow{2}{*}{10.83} \\ \cline{2-8}  & G & 41.67 & 37.91 & 9.03 & & \\ \hline \multirow{2}{*}{1.18} & CS & 47.92 & 44.11 & 7.95 & \multirow{2}{*}{5.27} & \multirow{2}{*}{7.25} \\ \cline{2-8}  & G & 45.40 & 40.91 & 9.89 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of single-size packing (SSP) tests. Figure 3: Schematic of defined indicators for describing the two-size packing. The sphere packing models are usually employed to characterize the packed aggregate particles. The \(V_{a}\) of the cubic lattice packing of equal spheres is 47.64% [45], which is commonly considered as a very loose regular packing type. The \(V_{a}\) of the close random packing is about 36% [45], which is supported by test and theoretical analysis. A very loose random packing with about 44% voids and a loose random packing with about 40% voids are usually obtained in tests [45]. As can be seen from Table 3, the loose gravel is similar to the loose random packing of equal spheres in \(V_{a}\) for all the tested sizes except 1.18 mm, for which the loose gravel is similar to the very loose random packing. The loose crushed stone is similar to the cubic lattice packing (for 9.5 mm or smaller) or the very loose random packing (for 13.2 mm or bigger). For the gravel with a size of 1.18 mm, the dry-roadded is similar to the loose random packing. For the gravel with other test sizes, the dry-roadded is similar to the close random packing. For the crushed stone, the dry-roadded is similar to the loose or very loose random packing. It is shown that the packing characteristics of aggregate particles with single size are more complex than those of the packed equal spheres, which may be attributed to 1) the effects of particle morphology and 2) particles that are not really in equal size. \(RD_{V_{a}}^{L-R}\) is helpful to quantitatively understand the effects of packing test methods on the packing characteristics of aggregates particles. As expected, the loosing packing test can result in smaller \(V_{a}\) than the dry-roadded packing test. As shown in Table 3, the maximum \(RD_{V_{a}}^{L-R}\) is 13.75%, which belongs to the gravel with a size of 13.2 mm. The minimum \(RD_{V_{a}}^{L-R}\) is 7.95%, which corresponds to the crushed stone with a size of 1.18 mm. All the other values of \(RD_{V_{a}}^{L-R}\) are around 10%. \(RD_{V_{a}}^{CS-G}\) provides a quantitative way to investigate the effects of particle morphology on the packing characteristics of aggregates particles. As shown in Table 3, the maximum \(RD_{V_{a}}^{CS-G}\) for loose packing reaches 16.64%. The minimum \(RD_{V_{a}}^{CS-G}\) for loose packing also arrives at 5.27%.