## 7 Size Effect  
For ideal sphere packing with two particle sizes, packing characteristics are related to particle size ratio, but not to particle size [8]. However, the packing characteristics of aggregates are different from those of ideal spheres due to the influences of particle morphology and frictional resistance between particles. From Figures 5 and 6, for combinations of 4.75 VS 2.36 and 2.36 VS 1.18, the variations of \(I_{pf}\) and \(V_{a}\) are obvious with the change of \(P_{bv}\)\({}^{s}\), indicating that packing characteristics are not only related to particle size ratio, but also related to the particle size.  
In order to analyze the effect of particle size on the packing behavior of blends with two-size particles, the combinations of 16 VS 4.75, 4.75 VS 2.36 and 2.36 VS 1.18 with equal particle size ratio are selected for comparisons. Figure 9 presents the differences in \(I_{pf}\) between 4.75 VS 2.36, 2.36 VS 1.18, and 16 VS 4.75 for different \(P_{bv}\)\({}^{s}\). Figure 10 depicts the difference of \(V_{a}\) between 4.75 VS 2.36, 2.36 VS 1.18, and 16 VS 4.75 for different \(P_{bv}\)\({}^{s}\).  
From Figure 9, it can be found that the \(I_{pf}\) of smaller particles is significantly different in the combinations with different maximum particle sizes. In the crushed stone dry-roadded test, compared with the 16 VS 4.75 combination, all \(I_{pf}\) values of smaller size particles in 4.75 VS 2.36 combination are 0.1 larger, and it is even 0.39 lager when \(P_{bv}\)\({}^{s}\) is 5%. Even for the combinations of 4.75 VS 2.36 and 2.36 VS 1.18, for which the size ratio is exactly same, there is a significant difference between the values of \(I_{pf}\) of smaller size particles. Comparing Figure 7(a) with Figure 7(b), the packing behavior difference between crushed stone and gravel mixture can be understood. For the 4.75 VS 2.36 combination, whether the loose or dry-roadded packing test, the \(I_{pf}\) difference of smaller size particles to 16 VS 4.75 combination for the crushed stone blend is more significant than that of gravel, while that of 2.36 VS 1.18 combination is just the opposite. In addition, with the increase of the proportion of smaller size particles in the blend, the effect of size on packing function decreases gradually.  
Figure 9: _Cont._  
Figure 10 shows that the \(V_{a}\) values of 4.75 VS 2.36 and 2.36 VS 1.18 combinations are higher than those of 16 VS 4.75 combination in almost all test cases, and there are significant differences between the combinations of 4.75 VS 2.36 and 2.36 VS 1.18. Among crushed stone dry-roadded test, the difference between 4.75 VS 2.36 and 16 VS 4.75 is the most prominent. Except for the difference of 2.66% when the \(P_{bv}\)\({}^{s}\) is 5%, the differences at other \(P_{bv}\)\({}^{s}\) are more than 3%, and most of them are more than 4%, where the maximum is 4.93%. Compared Figure 10a with Figure 10b, it can be found that the differences of \(V_{a}\) for gravel mixtures are smaller than those for crushed stone mixtures except for the combination of 2.36 VS 1.18.  
By comparing the packing test data mentioned above, the effect of size on the packing characteristics of the aggregate blend can be clearly observed. However, the experimental data do not show a significant trend, and the changes are relatively complex, which still needs further study.  
Figure 10: \(Cont\).  
Figure 9: The differences of \(I_{ff}\) between 4.75 vs 2.36, 2.36 VS 1.18 and 16 VS 4.75: (**a**) Crushed stone; (**b**) gravel.