# Effect of Initial Granular Structure on the Evolution of Contact Force Chains
## 3 Results and Discussion
### Effect of Initial Granular Assembly Conditions on the Bearing Capacities of Shallow Foundations
Afterward, the most obvious contact force transmission structure was observed (Figure 12d). It can be seen that the number of particles corresponding to the main force chain gradually decreased with decreasing load. Additionally, after the step shown in Figure 12e, the particle arrangement shifted to the left side of the foundation surface, which caused the void between particles to increase and dilatancy to occur. Meanwhile, on the right side, a distinct contact force chain was observed. In the final stage of loading (Figure 12h), all contact force chains disappeared, and wedge-shaped failure surfaces were observed at the bottom. Figure 12: Contact force chains detected by RGB photoelastic digital image analysis during shallow foundation loading: (**a**) before loading; (**b**) F = 200 N, d = 5.08 mm; (**c**) F = 400 N, d = 6.3 mm; (**d**) F = 600 N, d = 7.21 mm; (**e**) F = 450 N, d = 7.52 mm; (**f**) F = 200 N, d = 7.78 mm; (**g**) F = 3500 N, d = 8.98 mm; (**h**) F = 20 N, d = 9.81 mm. With shallow foundation loading, the wedge-shaped final failure geometry was similar to the results obtained using the basic limit equilibrium that is used conventionally. Nevertheless, in the case of SI, wherein local imperfections existed in the lower part of the granular assembly (Figure 13), the main contact force transmission structure formed in the vertical direction, as in the case of uniaxial loading. Thereafter, as loading progressed, the number of particles corresponding to the main force chain increased and formed in a direction perpendicular to the loading surface, as in uniaxial loading. Additionally, it was confirmed that the region where the main force chain occurred was the size of the width of the foundation and failed. As in the case of SU, dilatancy was observed near the end of the foundation width in the final loading step shown in Figure 13f. However, micromechanical studies of the same type of material were performed in the same direction. Figure 13: Contact force chains detected by RGB photoelastic digital image analysis during shallow foundation loading with imperfections: (**a**) before loading; (**b**) F = 100 N, d = 2.57 mm; (**c**) F = 200 N, d = 3.22 mm; (**d**) F = 300 N, d = 4.00 mm; (**e**) F = 400 N, d = 4.96 mm; (**f**) F = 450 N, d = 5.29 mm; (**g**) F = 370 N, d = 5.83 mm; (**h**) F = 170 N, d = 7.81 mm. have shown that the instability of a loaded granular assembly is due to the buckling of contact force chain structures formed with the assembly [16; 38]. [PERSON] and [PERSON] [38] applied loads to an initial connection state of an ideal particle and a state wherein instability was applied to the contact force chain structure by arbitrarily generating a 2\({}^{\circ}\) buckling angle. Furthermore, the force generated during the elastic-plastic buckling behavior was confirmed by the equation and results of their DEM. This result, combined with those of a more recent study by [PERSON] et al. [37], suggest that particle rotation can cause the buckling of contact force chain and incipient failure of the entire load-displacement curve, thus affecting the final bearing capacity. Table 2 summarizes the quantitative results of the particle force detection in photoelastic images of SU and SI using digital RGB photoelastic analysis. In the case of SU, the maximum support load measured by the load cell was 649.6 N. As a result of image analysis, it was found that the average particle force in the entire granular assembly also increased up to 40 N. In the case of SI, the maximum support load measured by the load cell was 441.0 N. It was found that the average particle force in the entire granular assembly was also the maximum (34 N). Additionally, the tendency of the total force calculated from each particle exhibited the maximum values in images (d) and (f) in the cases of SU and SI, respectively, and this tendency agreed well with the results of load cell measurements.