## 4 Results  
### Results of Virtual Ground Creation  
Figure 3 shows the virtual ground in which samples with different particle sizes and shapes were filled by freefall. Figure 4 is a mesh diagram of an analysis space. This is a result of judging the inside and outside of the selected position (\(x\), \(y\), \(z\)) in Equation (6), identifying the pore structure and creating a mesh that can be applied to fluid analysis. For a wider distribution and finer particle size, more detailed area determination is necessary when extracting the pore structure. As a result, the number of cross-sectional images must be increased. The three-dimensional pore structure, which is constructed by overlaying these images, significantly increases the number of elements when the mesh is processed. In Case 1, which has a uniform particle size, the pore structure could be divided into approximately 550,000 elements. In Case 2, which has a wide range of particle sizes, it was necessary to adjust the mesh width to accommodate the smaller particles, and the number of elements increased to approximately 29.78 million elements.  
Fluid analysis was performed by applying the Navier-Stokes equations to the analysis space containing the constructed mesh. As Navier-Stokes equations include four unknowns, the system of linear equations became huge scale. The scale of the linear system is determined by the product of the total number of nodes and the number of unknowns. For this reason, the scale of the linear system is large in Case 2, over approximately 100 million. Specifically, the scale of the linear system in Case 1 was 8,861,728, in Case 2 was 137,821,040, and in Case 3 was 6,805,632.  
A large number of cross-sectional images and a fine mesh are required to precisely extract the pore structure from a virtual ground, which contains a range of particle sizes and distributions, like the example of Case 2. As a result, the scale of the linear system to be solved increases significantly. Therefore, from the point of computational load, the effectiveness of this method is remarkable: when the range of particle size distributions is narrow, or presence of relatively fine particles does not affect global water flow, this feature is particularly useful for the analysis of waste landfill sites and gravel drainage layers. However, the size of analysis space used in this study is insufficient for a detailed analysis of water flow dynamics in waste landfill sites and gravel drainage layers. Considering the impact of scale effects on water flow, it is necessary to revise the evaluation to a larger scale. When the particle size distribution is limited and the effects of fine particles can be ignored, analysis of the flow in the pore structure with this method is considered to be advantageous in terms of reducing effort and cost.  
Figure 3: Virtual ground models generated via DEM-based freefall simulations for three cases: (**a**) uniform spherical particles (Case 1); (**b**) mixed spherical particles with different diameters (Case 2); and (**c**) mixed spherical, thin plate, and rod-shaped particles (Case 3). These configurations represent idealized ground, particle-size-distributed ground, and heterogeneous waste-like landfill, respectively.