## 4 Results and Discussion
### Variation in Average Coordination Number  
As a mesoscopic parameter, the average coordination number reveals detailed structural information regarding the inside of granular material and affects the macroscopic properties of granular material more directly than the packing density. The average coordination number is defined as the ratio of the sum of the number of contacts in the measurement circle to the number of particles in the measurement circle.  
The measurement circle is user-specified (volume in three dimensions; area in two dimensions), within which a number of quantities in a PFC model are measured. The quantities measured include coordination number, porosity, sliding fraction, stress, and strain rate [30].  
\[C_{N}=\frac{\sum_{N_{b}}n_{C}^{(b)}}{N_{b}} \tag{4}\]  
Figure 9: Skeleton particle force chain diagrams. (**a**) Force chain before vibration; (**b**) force chain after 10 s vibration; (**c**) force chain after 20 s vibration; (**d**) force chain after 30 s vibration; (**e**) force chain after 60 s vibration; and (**f**) force chain post vibration. In the figure, E is abbreviation for exponent, for example, the number 4.5E7 stands for \(4.5\times 10^{7}\).  
where \(N_{b}\) is the number of particles in the measurement circle and \(n_{C}^{(b)}\) is the actual number of contacts (normal contact force greater than zero) for a single particle within the measurement circle.  
In this study, two particles were considered to be in contact with each other when the normal contact force was non-zero. The coordination number can be interpreted as the average number of particles in contact with each particle in the specimen, which reflects the state of the specimen to some extent, such as degree of denseness. The larger the coordination number, the denser the particles; the smaller the deformation, the greater the strength. Conversely, the smaller the coordination number, the looser the particles; the greater the deformation, the smaller the strength.  
In the simulated specimens, the measurement circle was arranged to obtain the change process of the average coordination number of particles in each specimen, as shown in Figure 10.  
In both forming methods used in this study, the early increase in the CSM's average coordination number was very fast. The trend of the average coordination number tended to slow after a certain point. After molding, the average coordination number of the vibration molding specimen was approximately 2.3% higher than that of the compaction molding specimen. This is because the cement-stabilized macadam mixture received vibration and impact in the forming process. CSM segregation surrounded the outer layer of material particles with a water film, which lubricated particle movement, reducing the friction and bonding force between materials. Particles easily moved to a dense state, and embedded with each other to achieve high bearing capacity and stability.  
In the compaction molding method, because the specimen was subjected to a single force, the hammer forced particles in the mixture to approach each other when the material was in a loose state until they moved to a stable position. However, compared with the vibration forming method, particles in the heavy compaction forming specimen were less mobile and the degree of inter-particle nesting was low. The average coordination number of particles in the compaction molding specimen was slightly lower than that of the vibration molding specimen.  
Figure 10: Variation in coordination numbers.