# 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  
Figure 10 shows the load-displacement curves obtained by applying a shallow foundation load to the two granular assemblies. Unlike the uniaxial compressive load condition shown in Figure 8, a very irregular load-displacement relationship was observed when a shallow foundation load was applied. Figure 10c shows selected data for comparing photoelastic responses. In the initial part of the load-displacement curve, there was a pattern of increasing stiffness under all granular conditions with or without initial defects, but then the load rapidly decreased as the first peak occurred. Afterward, the second peak was observed; a new peak occurred at a lower load than the first peak value, and the load decreased rapidly. The maximum peak load was 649.6 N for SU and 441.0 N for SI, which indicates that the value for SI was \(\sim\)68% of that for SU. In particular, in the case of the SI (Figure 10c), the load tends to increase after relatively brief decrease at a stage marked by (d) in Figure 10c. This phenomenon can be explained by incipient failure, which has previously been noted by [PERSON] et al. [37]. According to [PERSON] et al. [37], the final bearing capacity is determined by the incipient failure. In particular, it has been confirmed that incipient failure is caused by local buckling of the contact force chain structure inside the granular assembly. Figure 11 shows the change in work, which was obtained by integrating the load-displacement curve shown in Figure 10c. In the case of SU, more work was involved than for SI and more energy was accumulated. As with the load-displacement curve, the work increased rapidly at the beginning of loading, but the rate of work decreased significantly after the first peak occurred. This may be because the accumulation of elastic energy due to the buckling of the contact force chain at the time of the first peak was different from the accumulation before the peak occurred. The final work of the SU and SI conditions were 2000 N \(\cdot\)mm and 1700 N \(\cdot\)mm, respectively, which indicates that SI can only store \(\sim\)80% of the energy as SU. This disparity may be due to the differences in the load transmission processes that occur in SU and SI. Each step observed during photoelastic analyses is shown in Figures 10c and 11. Figure 9: Changes in particle forces during load tests: (**a**) average particle force in the overall assembly; (**b**) sum of the particle force in the overall assembly; (**c**) average particle force in the main contact force chains; (**d**) frequency of the particles in the main contact force chains; (**e**) sum of the particle force in the main contact force chains. In addition to the aforementioned macroscopic observations, image analysis was also performed for shallow foundation loading to compare the load support patterns and supportive loads according to the presence of imperfections. Figures 12 and 13 show the results obtained by analyzing the images recorded during the loading tests for SU and SI. In the case of shallow foundation loading, as well as uniaxial loading, it can be seen that the load transmission structure of the granular assembly varied significantly depending upon the presence of imperfections. The formation and collapse of the contact force chain structures shown in Figures 12 and 13 tend to follow the load-displacement curves shown in Figure 10c. Figure 11: Changes in work during loading. Figure 10: Load–displacement curves for SU and SI under shallow foundation loading: (**a**) uniform structure; (**b**) structure with imperfections; (**c**) selected data for comparison. In the case of SU (shown in Figure 12), wherein there was no initial defect, when loading began, contact force chains began to be formed diagonally at both ends of the foundation plate, showing good agreement with [PERSON] [23]. In particular, the similarity is that the force chains generated at an angle of 60 degrees depending on the stacked tetrahedral structure.