# Effect of Initial Granular Structure on the Evolution of Contact Force Chains
## 2 Materials and Methods
### Photoelastic Model Particles and Test Program
#### 2.2.2 Experimental Setup and Test Program  
Figure 3 shows the test apparatus, which included a loading frame and an LF/_Z_-2 reflective polariscope (Vishay Intertechnology, Inc.). Model particles with diameters of 10 mm and 20 mm were stacked in a hexagonal rhombohedral structure inside of a steel frame with a width of 770 mm (Figure 3a). Approximately 3,000 particles were stacked to a height of 380 mm. As shown in Figure 3b, white light that passed through the polarized plate was reflected by the photoelastic sheet on the surface of the particle and an image was obtained using a camera for digital RGB analysis. A detailed description of the reflective polariscopes was provided by [PERSON] and [PERSON] [33]. Photoelastic images were obtained using a Canon EOS-650D camera equipped with an EF-S 55-250 mm/4-5.6 IS II lens (Canon, Inc., Japan). The focal length was 55 mm, and the resolution of the image was 300 pixels per inch (PPI), which is high enough to capture a photoelastic response. The purpose of this study was to investigate the effect of initial granular structure on the load transmission structure. To this end, two granular assemblies, the first with a uniform structure and no initial defects and the second with local and structural imperfections in the lower part of the assembly were prepared. Figure 4a shows the uniform structure condition in which particles with 10-mm diameters were stacked. The granular assembly, which consisted only of the aforementioned particles stacked on a smooth bottom, formed a typical cubic tetrahedral packing with a coordination number of 8. As shown in Figure 4b, particles with 20-mm diameters were first layered on the bottom of the frame, onto which particles with 10-mm diameters were stacked. The 10-mm diameter particle layer, which was bounded by the 20-mm diameter particle layer, was in a relatively unstable state during initial stacking. Therefore, this granular assembly could be regarded as a two-layer structure with local defects. Figure 2: Detection of changes in fringe order patterns of a single particle according to particle force (N). Two initial particle assembly cases were tested under two loading conditions: uniaxial compression and shallow foundation loading. As shown in Figure 4, the axial displacement of the loading device could be controlled using gears. The load, which was applied through a loading plate, and the axial displacement of the loading plate could be precisely measured by installing a Linear Variable Differential Transformer (LVDT) on the load cell at the loading bar and on the upper part of the loading plate. Load cell and LVDT data were obtained through a data logger at 0.1-second intervals. During the loading test, the rate of axial displacement of the loading plate was controlled to 0.07 mm/sec. In order to simulate shallow foundation loading, a 10-cm-wide model foundation plate, which was connected to the loading device, was installed at the top of the granular assembly during shallow foundation experiments. To simulate overburden pressure, which may affect the bearing capacity of a shallow foundation, metal plates with certain weights were manufactured and placed on the right and left sides of the model foundation plate, as shown in Figure 4b. The pressure applied by the pair of metal plates to the upper surface of the granular assembly was approximately 10 kN/m\({}^{2}\); the pairs of plates was used during experimentation. The experimental conditions are summarized in Table 1. Test ID in Table 1 is expressed as a combination of two letters representing the loading condition (uniaxial (U) or shallow (S)) and the packing condition (uniform structure without imperfections (U) or a structure with imperfections (I)). The experiment was repeated 2-3 times for each case. During the experiment, digital images were captured through the front acrylic walls, and subsequently used for digital RGB photoelastic analysis.