# Effect of Initial Granular Structure on the Evolution of Contact Force Chains
## 3 Results and Discussion  
### Effect of Initial Granular Assembly Conditions on the Structure of the Contact Force Chain  
Figure 6a shows the macroscopic load-displacement curves for all uniaxial loading tests under the condition in which lateral displacement was constrained. The load was measured by the load cell connected to the loading rod, and the displacement was measured by the LVDT connected to the top of the loading plate. As shown in Figure 6a, the stiffness of the uniaxial compression test increased regardless of the initial granular conditions (e.g., the behavior of typical granular materials). Although the values differed slightly for each experiment, the difference among them was insignificant. In the case of UU (uniaxial loading of a uniform structure) and UI (uniaxial loading of an imperfect structure), failure did not occur during the vertical loading up to 4000 N. Figure 6b shows selected data from the microscopic photoelastic response comparison. Each step observed is shown in Figures 7b-f and 8b-f. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Test ID** & **Loading Condition** & **Packing Condition** & **No. of Repetitions** \\ \hline UU & Uniaxial (U) & Uniform structure & 3 \\  & & w/o imperfection (U) & \\ UI & & Structure & 2 \\  & & w/ imperfections (I) & \\ SU & Shallow foundation (S) & Uniform structure & 3 \\  & & w/o imperfection (U) & \\ SI & & Structure & 3 \\  & & w/ imperfections (I) & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test loading and packing (structural) conditions. Figure 5: Typical photoelastic images during: (**a**) uniaxial loading with a uniform structure, F = 2000 N; (**b**) uniaxial loading with imperfections, F = 2000 N; (**c**) shallow foundation loading with a uniform structure, F = 400 N; (**d**) shallow foundation loading with imperfections, F = 400 N.  
Figure 6: Load–displacement curves for UU and UI subjected to uniaxial loading: (**a**) overall data; (**b**) selected data for comparison. Figure 7: Contact force chains detected by red, green, and blue (RGB) photoelastic digital image analysis during uniaxial loading of a uniform structure: (**a**) before loading; (**b**) F = 500 N; (**c**) F = 1000 N; (**d**) F = 1500 N; (**e**) F = 2000 N; (**f**) F = 2500 N; (**g**) F = 3000 N; (**h**) F = 4000 N. Primary contact force chains are marked as red circles, particles with forces <100 N are shown as black circles. Interestingly, although there was no significant difference in the macroscopic load-displacement curves of the UU and UI conditions shown in Figure 6, the distribution of the internal contact force chain structure of the granular assembly in the photoelastic images was markedly different. Figures 7 and 8 show that the chain structures measured from the photoelastic response in UU and UI changed with the load level. As shown in Figure 7, in the case of UU, where there were no initial defects, contact force chains were formed in the left and right diagonal directions according to the particle arrangement when a load was applied (Figure 7b,c). Subsequently, as the load increased, the number of linear contact force chain structures, which were developed diagonally around the upper part of the granular assembly, increased. Simultaneously, a horizontal chain structure gradually occurred  
Figure 8: Contact force chains detected by RGB photoelastic digital image analysis during uniaxial loading of an imperfection structure: (**a**) before loading; (**b**) F = 500 N; (**c**) F = 1000 N; (**d**) F = 1500 N; (**e**) F = 2000 N; (**f**) F = 2500 N; (**g**) F = 3000 N; (**h**) F = 4000 N.  
gradually near the upper plate (Figure 7d,e). When the load reached 4000 N, it can be seen that the force was distributed evenly inside of the granular assembly (Figure 7f).