# Effect of Initial Granular Structure on the Evolution of Contact Force Chains
## 1 Introduction  
When assessing the bearing capacity of geotechnical foundations, traditional approaches are based on the limit-state equilibrium. This view first assumes a fully plastic state, and then roughly assumes a plastic failure surface. The stress equilibrium is subsequently found on the failure surface and the ultimate strength in a given situation is obtained. Lastly, the pre-failure state is evaluated by considering the factor of safety. However, a controversial question has arisen: does the bearing capacity of soils composed of granular assemblies coincide with the traditional view? Various studies have reported that the bearing capacity behavior of such granular assemblies differs from the traditional view [1; 2; 3; 4; 5; 6].  
Since the introduction of granular physics in the 1990s, which can accommodate the distribution of contact forces for a large number of particles that occur inside a granular assembly, studies have been conducted on contact force networks. Through recent studies on the processes underlying changes in the distribution of contact forces inside granular assemblies, it has been found that chain structures or networks have specific orientations with respect to the external load within the granular assembly. In particular, the contact force is distributed in the direction of the major principal stress [7; 8; 9; 10]. It has also been reported that local buckling in granular assemblies ultimately contributes to the formationof macroscopic shear bands [11; 12; 13; 14; 15; 16; 17]. Furthermore, many studies on the effects of contact force chain factors (e.g., the interparticle friction coefficient, loading regime, packing density, contact model, boundary condition, grain shape, etc.) have been conducted [18; 19; 20].  
Although various studies on the behavior of granular materials at the microscale have been conducted, most have been based on discrete element method (DEM) simulations; to date, experimental studies and quantitative evaluations of the effect of the initial structure of granular assemblies on the supportive structure and force chain formation remain insufficient. When the same load is applied, the behavior of a granular assembly, including the arrangement of discrete elements and the inherent structural instability, can be completely different from the behavior of a granular assembly with regular structures, which do not include initial structural instabilities.  
In this study, when a granular assembly stacked with model particles was subjected to uniaxial compression loading or shallow foundation loading, the effect of the initial granular structure on the macroscopic load transmission was studied using a photoelastic model. Two initial granular structures were reproduced by laminating model particles that were made by attaching thin photoelastic sheets to cylindrical model particles. Two-dimensional (2-D) reflective photoelasticity tests were performed under a granular condition with a uniform structure and without initial defects, as well as under a condition with initial local imperfections in the lower part of the granular assembly. Digital photographic images were taken continuously during the experiment. The obtained images were analyzed using the red, green, and blue (RGB) photoelasticity image analysis protocol developed by [PERSON] and [PERSON] [21], and the particle forces transmitted through the main contact force chain were analyzed quantitatively. While the load-displacement relationship was analyzed macroscopically, the force distribution inside the granular assembly was observed microscopically. Additionally, a particle image velocimetry (PIV) technique was employed to confirm the movement of particles and the expansion of the initial local defects in the granular assembly.