## 8 Conclusions  
In this paper, the packing characteristics of aggregate blend with single-size and two-size particles and the effects of particle shape, particle size, and size ratio on the packing characteristics were studied by the indoor packing test. The following conclusions can be drawn.  
1. The comparison between the SSP test and sphere packing models shows that the results of packing analysis using ideal spheres cannot be simply used to describe the packing characteristics of real aggregate mixtures. The morphology of aggregate particles is different from each other. Even the particles in the aggregate with single size do not have exactly equal size. The packing behavior of aggregate particles is more complex than that of ideal spheres.
2. Particle morphology has a significant effect on the \(V_{a}\) of packed aggregate. Whether in the SSP or TSP test, the \(V_{a}\) of crushed stone blend is significantly higher than that of gravel blend. In the SSP test, the biggest difference is for 4.75 mm particles in the loose packing test, where the \(V_{a}\) of crushed stone blend is 16.64% higher than that of gravel blend. The smallest is for 1.18 mm particles in the loose packing test, where the \(V_{a}\) of crushed stone blend is 5.27% higher than that of gravel.
3. The \(I_{pf}\) can be used to quantitatively distinguish the skeleton building and air void filling functions of smaller size particles in the TSP test. The \(I_{pf}\) is between 0 and 1, where 1 indicates that smaller size particles plays the same skeleton role as larger size particles in the blend, and 0 indicates that smaller size particles only fills air voids in the blend.
4. The function of particles cannot be simply divided into skeleton building and air void filling. Particles in a mixture have the above two functions in varying degrees. Even in the combination of 16 VS 1.18 (size ratio is only 0.074), the \(I_{pf}\) of smaller particle size is not zero.
5. The function of particles changes with respect to different particle size compositions. In the same combination, \(I_{pf}\) of smaller particles increases with the increasing of its proportion. The larger the particle size ratio in the mixture, the larger the increase of \(I_{pf}\) with the addition of smaller particles. The change of \(I_{pf}\) with the proportion of smaller size particles indicates that the function of particles is closely related to the specific composition of different size particles, and cannot be simply distinguished according to the relationship between particle sizes.  
Figure 10: The differences of \(V_{a}\) between 4.75 VS 2.36, 2.36 VS 1.18 and 16 VS 4.75: (**a**) Crushed stone; (**b**) gravel.  
Particle size has a significant impact on the packing characteristics of aggregates. For the SSP test, there is a significant difference in \(V_{a}\) between packed aggregates with different sizes. For the TSP test, under the same particle size ratio and the same volume ratio, there are significant differences in \(V_{a}\) and \(l_{p\!f}\) of smaller size particles among the combinations with different maximum particle size, where the change trend is complex and still needs further study.  
Conceptualization, Y.M., J.L., J.W. and X.L.; methodology, Y.H., Y.M., J.L., and J.W.; software, N/A; validation, X.L., Y.H., and Y.M.; formal Analysis, N/A; Investigation, Y.M., J.L., J.W., Y.H., and L.W.; resources, N/A; data curation, Y.H. and Y.M.; writing--original draft preparation, X.L., J.L., and J.W., writing--review and editing, Y.H., L.W., and Y.M.; visualization, X.L., J.L., and J.W.; supervision, Y.M.; project administration, Y.M.; funding acquisition, Y.M.  
The research reported in this paper is funded by the National Natural Science Foundation of China (No. 51178013).  
The authors would like to express thanks for the financial support from the National Natural Science Foundation of China.  
The authors declare no conflict of interest.