## 2 Aggregates and Test Design
### Test Design  
There are many factors affecting the packing behavior of aggregate blends. In this study, the analysis of the packing behavior of blends with single-size and two-size particles was conducted to understand the influence of particle composition, particle size, particle shape, and other factors, which is helpful for future studies on packing behavior of aggregate blends with multi-size particles. The test was designed with consideration of the following aims:  
1. The characteristics of single-size packing and the size effect;
2. The characteristics of two-size packing and the effects of size and size ratio;
3. The effect of particle morphology on the packing characteristics of single-size and two-size packing. Aggregates with different particle sizes and morphology were selected to perform single-size packing (SSP) tests using the loose and dry-roadded packing tests. The packing state of SSP is unitary for the particles that have the same packing function (for skeleton building). The air void content, \(V_{a}\), is employed to quantify the SSP characteristics. The relative difference of \(V_{a}\) between loose and dry-roadded tests is defined in Equation (4) for quantifying the effects of packing method. The relative difference of \(V_{a}\) between crushed stone and gravel is also defined (Equation (5)) to understand the effects of particle morphology. \[RD_{V_{a}}^{L-R}=\frac{V_{a}^{L}-V_{a}^{R}}{V_{a}^{L}} \tag{4}\]  
where \(V_{a}^{L}\) is the \(V_{a}\) derived from the loose packing test, and \(V_{a}^{R}\) is the \(V_{a}\) derived from the dry-roadded packing test. \[RD_{V_{a}}^{CS-G}=\frac{V_{a}^{CS}-V_{a}^{G}}{V_{a}^{CS}} \tag{5}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline Size (mm) & 16 & 13.2 & 9.5 & 4.75 & 2.36 & 1.18 \\ \hline Crushed stone & 2.799 & 2.802 & 2.796 & 2.79 & 2.737 & 2.68 \\ \hline Gravel & 2.546 & 2.538 & 2.581 & 2.565 & 2.501 & 2.594 \\ \hline \end{tabular}
\end{table} 
Table 1: Aggregate bulk density (g/cm\({}^{3}\)). Figure 2: \(S_{Cm}^{2}\) for aggregates with size above 2.36 mm. where \(V_{a}^{CS}\) is the \(V_{a}\) of packed crushed stone particles, and \(V_{a}^{G}\) is the \(V_{a}\) of packed gravel particles. Two-size packing (TSP) tests were performed with consideration of different size ratios, maximum particle sizes, and particle morphologies using the loose and dry-roadded packing tests. In each TSP test, the mass ratio of the smaller to the bigger was gradually changed from 0 to 1 for investigating the packing function of each size particle. Table 2 lists all the combinations of the TSP test. The packing state of each size particle in the TSP test is complex. Some indicators are defined for further understanding the packing characteristics. Denote \(A_{b}\) to represent the bigger size particles packing the volume \(V\) alone. Denote \(A_{s}\) as the smaller size particles packing \(V\) alone under the same packing method. Take a two-size combination with a given mass ratio to pack \(V\) under the same packing method, and record the bigger particles and the smaller particles in \(V\) as \(a_{b}\) and \(a_{s}\), respectively. Denote the packing volume of \(a_{b}\) and \(a_{s}\) under the same packing method as \(V_{p}{}^{b}\) and \(V_{p}{}^{s}\), respectively. Figure 3 could be helpful to understand the meanings of the above mentioned symbols. The percentage of the packing volume of \(a_{b}\) in \(V\) for the packed two-size combination can be defined as  
\[P_{pv}^{b}=\frac{V_{p}^{b}}{V} \tag{6}\]  
Denote the bulk volume of \(a_{b}\) and \(a_{s}\) as \(V_{b}{}^{b}\) and \(V_{b}{}^{s}\) respectively. The bulk volume percentage of the bigger particles in the two-size combination can then be defined as  
\[P_{bv}^{b}=\frac{V_{b}^{b}}{V_{b}^{b}+V_{b}^{s}} \tag{7}\]  
And that of the smaller size particles can be defined as  
\[P_{bv}^{s}=\frac{V_{b}^{s}}{V_{b}^{b}+V_{b}^{s}} \tag{8}\]  
The packing volume increases from \(V_{p}{}^{b}\), \(a_{b}\) packed alone, to \(V\) by adding \(a_{s}\) to the blend in the TSP tests.