# 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
The frequency of the particles that were classified as the main force chain and the sum of the forces of the particles also agreed well with the variation in load. Under shallow foundation loading, when imperfections existed, the peak load reduction rate measured by the load cell was \(\sim\)75% (compared to the uniform structure), and the peak load reduction rate obtained from the image analysis was estimated to \(\sim\)82% (in terms of the total force). Interestingly, this result was very similar to the calculations theoretically described by [PERSON] and [PERSON] [38], who found that the load transmission of a granular assembly was reduced by \(\sim\)18% when there was an instability, as compared with no instability. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Test ID: SU**} & \multicolumn{8}{c}{**Images**} \\ \cline{2-10}  & **(a)** & **(b)** & **(c)** & **(d)** & **(e)** & **(f)** & **(g)** & **(h)** \\ \hline Axial load (N) & 0 & 200 & 400 & 600 & 450 & 200 & 350 & 20 \\ Displacement (mm) & 0 & 5.08 & 6.3 & 7.21 & 7.52 & 7.78 & 8.98 & 9.81 \\ Average particle force & & 33 & 33 & 36 & 40 & 37 & 33 & 35 & 33 \\ in overall assembly (N) & 2,910 & 2,883 & 2,868 & 2,881 & 2,830 & 2,869 & 2,883 & 2,934 \\ In overall assembly & & 96,030 & 95,139 & 103,248 & 115,240 & 104,710 & 94,677 & 100,905 & 96,822 \\ In overall assembly & & & & & & & & \\ Average particle force in the main & & & & & & & & \\ force chain & - & 136 & 127 & 127 & 130 & 130 & 133 & 146 \\ (N) & & & & & & & & \\ Particle frequency & - & 44 & 109 & 186 & 139 & 55 & 77 & 38 \\ in the main force chain & - & 5,984 & 13,843 & 23,622 & 18,070 & 7,150 & 10,241 & 5,548 \\ \hline Test ID: SI & (a) & (b) & (c) & (d) & (e) & (f) & (g) & (h) \\ \hline Axial load (N) & 0 & 100 & 200 & 300 & 400 & 450 & 370 & 170 \\ Displacement (mm) & 0 & 2.57 & 3.22 & 4 & 4.96 & 5.29 & 5.83 & 7.81 \\ Average particle force & 32 & 32 & 31 & 30 & 33 & 34 & 32 & 32 \\ in overall assembly (N) & & & & & & & & \\ Particle frequency in & 2887 & 2878 & 2813 & 2720 & 2752 & 2771 & 2765 & 2828 \\ overall assembly & & & & & & & & \\ Total force & 92,384 & 92,096 & 87,203 & 81,600 & 90,816 & 94,214 & 88,480 & 90,496 \\ in overall assembly & & & & & & & & \\ Average particle force & - & 123 & 124 & 130 & 129 & 130 & 129 & 132 \\ in the main force chain & & & & & & & & \\ Total force & - & 34 & 58 & 75 & 114 & 141 & 102 & 55 \\ in the main force chain & - & 4182 & 7192 & 9750 & 14,706 & 18,330 & 13,158 & 7260 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of quantitative detection of granular assemblies under shallow foundations. Unlike uniaxial loading, shallow foundation loading allows the rearrangement (particularly rotation) of particles to occur more freely because the upper part of the assembly is not completely constrained. If local imperfections exist rather than homogeneous granular conditions, the granular assembly becomes unstable, and this can cause the particles to rotate actively, even under small loads. It is believed that the rotation of particles may have caused buckling of the contact force chain structure and more active dilatancy of the granular material in this study. As a result, it seems that the initial conditions of the granular assembly (compared to uniaxial compressive loading) have a greater effect on the bearing capacity of shallow foundation loading.