## 4 Results
### Tortuosity Relating to Water Channel Flow  
Figure 6 shows a histogram of tortuosity. Tortuosity is one of the parameters to characterize mass transport in porous media. Although mass transport is not discussed in this study, the evaluation method and results are described as a useful parameter for explaining this numerical experiment.  
Tortuosity is the ratio of flow paths traveled by the tracer to the straight-line distance. Two arbitrary points in a porous medium are selected as the start and end points. The  
Figure 5: Streamlines indicating simulated rainwater infiltration paths in the pore structure, derived from DEM-FEM coupled analysis under steady-state conditions: (**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). Preferential flow paths are observed in Case 3 due to the inclusion of non-spherical particles, suggesting the formation of water channels.  
Figure 6: Histogram of tortuosity values calculated from each streamline trajectory. Tortuosity represents the ratio of the actual tracer path length to the straight-line distance and reflects the complexity of the pore geometry. A broader distribution in Case 3 indicates more irregular flow paths due to structural heterogeneity.  
distance traveled by the tracer can be calculated using the streamlines described above. The straight-line distance can be calculated by projecting the flow lines onto the line connecting the start and end points. This makes it possible to determine the tortuosity.  
The results show that the most frequent value of tortuosity in the virtual ground with uniform spherical size (Case 1) was 1.258. In Cases 2 and 3, the most frequent value was closer to 1, although the shape of a histogram was more widely spread than Case 1. In Case 2, despite the heterogeneity of particle size, the flow remained mainly uniform. The median value in Case 2 was 1.218, which was almost the same as that in Case 1.  
In contrast, Case 3 (containing thin plate and rod-shaped particles) exhibited a broader and more skewed distribution, with a noticeable increase in the number of tracers following low-tortuosity paths (e.g., median values near 1.051). This suggests that water flow was selectively channeled through preferential pathways, while other regions exhibited minimal flow. The shift in tortuosity toward lower values, accompanied by increased variance, provides quantitative evidence of water channel formation.  
Therefore, tortuosity analysis complements streamline visualization and provides a statistical means to detect and compare the presence and extent of water channel flow across different porous structures. This highlights the potential of the proposed framework, not only for qualitative reproduction but also for the quantitative characterization of water channels in heterogeneous landfill-like media. The calculation of the tortuosity based on the streamlines shown here is conducted only in the flow direction. As a note of caution, the obtained tortuosity is thought to be a parameter close to the longitudinal dispersion length, not a parameter that is multiplied by the molecular diffusion coefficient.