## 4 Results and Discussion
### Specimen Force Chain Variation  
Bulk particles are primarily arranged in dense rows; contact between adjacent particles forms many paths for transferring external loads, which usually take the form of a quasi-linear chain structure, called a force chain. Several force chains intersect to form a network throughout granular material in a granular system; the contact force between particles is an important factor affecting the mechanical performance of granular materials [35; 36]. Inter-particle links occur under external loading, which form linear and more stable force chains. These force chains form a network, which support gravitational and external loads throughout the granular medium. Contact forces between particles are complex, with different magnitudes and directions. The external load share is different when local particles in the contact network are subjected to different forces. There are strong and weak contacts between particles. Paths that transfer larger shares of loads constitute strong force chains, and paths that transfer smaller shares  
Figure 6: Changes in porosity during vibration molding. (**a**) is the specimen model used for vibration molding in this paper; (**b**) is the axial section of the specimen model; (**c**) is the axial section of the specimen before vibration; (**d**) is the axial section of the specimen after vibrating for 10 s; (**e**) is the axial section of the specimen after vibrating for 20 s; (**f**) is the axial section of the specimen after vibrating for 30 s; (**g**) is the axial section of the specimen after vibrating for 40 s; (**h**) is the axial section of the specimen after vibration is completed. In the figure, E is abbreviation for exponent, for example, the number 1.2973E0 stands for 1.2973.  
of loads form weak force chains. Strong and weak force chains are the paths of external load transfer, and these paths constitute the entire contact network [37; 38]. In Figure 7, the contact force between large particles is coarse and dense, which shows that the force in the CSM was primarily transferred between skeletal particles. As a result of the skeleton effect of coarse aggregates, the strength of the mixture after molding largely depended on the skeleton formed by coarse aggregates embedded with each other, rather than on the strength of the cement paste. Figure 8 shows the force chain evolution process of the compaction molding specimen, illustrating the change process as the force gradually radiated from the surface of the entire specimen. Each line segment in Figure 8 represents a contact between particles, and the thickness of the line represents the magnitude of the contact force. From the beginning to the end of the loading process, the load was gradually transferred from the top of the mixture to the bottom. During the first ten compactions, the specimen's force chain density rapidly increased, while the specimen's height and porosity significantly decreased. After ten compactions, the decreasing trend of the specimen's height and porosity slowed and stabilized. This is because the cement-stabilized macadam was in a loose state with large internal voids and relatively few contact points between skeletal particles before loading started. As the number of compactions increased, CSM specimens were gradually compacted, skeletal particles embedded with each other, and the contact force of the skeletal particles in the specimens increased. These force chains constituted a force chain network, which supported the gravity and external load of the entire particle medium. Particles produced relatively little movement and displacement under the action of an external compaction force; force transmission was relatively fast. The force chain structure evolution process during vibration molding is distinct from the force chain structure evolution process during compaction molding. Figure 9 illustrates the force chains of vibration molding specimens before vibration, after vibration for 10 s, 20 s, 30 s, and 60 s, and post vibration.