# Effect of Initial Granular Structure on the Evolution of Contact Force Chains
## 3 Results and Discussion
### Evolution of Structural Imperfections under Shallow Foundation Loading  
In order to observe the evolution of local imperfections in the lower part of granular assemblies during testing for SI, a general digital image was recorded with an additional camera without a photoelastic filter. Figure 14 shows an image of the lower part of the granular assembly captured by the additional camera. As can be seen in the image, even during the initial state of loading, the arrangement of particles was uneven in the lower part of the assembly, and the number of contact points of some particles decreased with a large void. Although it is difficult to observe large changes in the void until the step shown in Figure 14b, the particle arrangement suddenly collapsed in the step shown Figure 14c after the first peak of the load-displacement curve, which caused the void to gradually expand into the center of the assembly. Finally, in Figure 14d, it can be seen that the void expanded into a zigzag pattern to form a final failure surface.  
In order to confirm particle movement and the expansion of imperfections, PIV was used [39; 40]. The PIV analysis was performed for the same load and displacement stages as shown in Figure 13, and Figure 15 shows the four incremental displacement vectors as a result of PIV analysis together with contact force chains. However, the value was removed for the area affected by the reflection of light. The size of the vector shown in Figure 15 was enlarged to aid in the visual identification of the amount and direction of particle movement. The magnitude of the reference vector in Figure 15a-c shows that the particles actually moved by only two pixels. In the case of Figure 15d, the particle movement is much larger, and thus the size of the vectors was expressed at 1/2 the size of those in Figure 15a-c.  
Figure 14: Evolution of structural imperfections under shallow foundation loading: (**a**) 0 mm (Figure 13a); (**b**) 3.22 mm (Figure 13c); (**c**) 4.96 mm (Figure 13e); (**d**) 5.83 mm (Figure 13g).  
Figure 15: Evolution of imperfections with displacement vectors resulting from particle image velocimetry (PIV) for structures with imperfections under shallow foundation loading: (**a**) 0–2.57 mm (Figure 13a,b), (**b**) 3.22–4.00 mm (Figure 13c,d), (**c**) 4.96–5.29 mm (Figure 13e,f), (**d**) 5.83–7.81 mm (Figure 13g,h).  
As shown in Figure 15a, movement of particles in the upper part of the granular assembly was active during the early stage of loading. This is the process by which external loads on the foundation are transmitted to the particle assembly. Figure 15b,c show that as the load increased, particle movement propagated throughout the interior of the assembly. Interestingly, the movement of particles first occurred in the counterclockwise direction on the right side of the initial defects, and then proceeded in a clockwise direction on the left side of the initial defects. Through this process, the initial defects existing in the lower part of the granular assembly were expanded throughout the entire assembly. As seen in Figure 15d, the active movement of particles occurred around the zigzag-shaped failure plane observed in Figure 14d. Therefore, it was confirmed that the local substructural defects inside the assembly expanded throughout the granular assembly during loading and the contact chains of the particles buckled which resorts to failure.