# Parametric Analysis for 3D Modeling of Consolidation-Induced Solute Transport Using OpenFOAM
## 4 Results and Discussion
### Effects of Hydraulic Conductivity on Solute Transport  
Figure 8 illustrates the changes in solute concentration at various depths at both the center and the edge positions, showing the breakthrough times. After one year, contaminants have migrated significantly to the top and, by five years, spread across the entire depth, with the highest concentrations near the surface. Although excess pore pressure dissipates mostly in the twentieth year, solute diffusion continues, indicating ongoing contaminant transport. At the edge, it takes 20 years for the concentration at the bottom to reach 5%, reflecting slower transport compared to the center.  
Horizontally, the solute concentrations are primarily concentrated within the loading area and increase over time (Figure 9). However, solute outside the loading area also rises, particularly after 20 years, indicating a gradual spread of contaminants beyond the initial zone. Over time, the solute diffuses throughout the site, leading to broader contamination.  
Hydraulic conductivity (**K**) significantly influences the distribution of the solute. Under low **K**, the solute accumulates in the upper layers as restricted water flow prevents downward migration. In contrast, high **K** accelerates water infiltration, facilitating rapid solute transport and accumulation in the lower layers. This process is amplified by increased pore water pressure and soil deformation, which further enhance solute migration.  
Figure 10 demonstrates the horizontal concentration distribution in the center region of the model during the tenth year under varying hydraulic conductivity conditions. It can be observed that, despite differences in **K**, the overall horizontal concentration distribution exhibits minimal variation in shape, with all cases showing approximately symmetrical diffusion patterns. This aligns with the results in Figure 9, which indicate that within the studied spatial and temporal scales, variations in **K** have limited effects on horizontal distribution but may significantly influence vertical migration behavior.  
In the early stages of consolidation, solute concentration changes significantly. For example, in the third year, under high **K** conditions, concentration increases by approximately 10% in the middle of the model and by around 35% at the bottom. In contrast, under low **K** conditions, slower drainage impedes solute migration, resulting in a slight decrease in concentration of about 5% in the middle and roughly 25% at the bottom. As the consolidation process progresses, water flow gradually stabilizes, solute distribution becomes more uniform, and concentration changes diminish, eventually reaching a new equilibrium.  
In summary, hydraulic conductivity plays a crucial role in solute migration. Low **K** leads to solute accumulation in the upper layers, while high **K** promotes downward diffusion, especially in deeper regions. Solute transport continues over the long term, with slower diffusion at the edges. Spatio-temporal changes in solute concentration are closely related to hydraulic conductivity, and these changes stabilize over time during consolidation.  
Figure 8: Cont.  
Figure 8: Distributions of concentration over time and depth at the center (\(x=y=20\) m, \(z=1.5\) m/3 m) and on the edge (\(x=y=30\) m, \(z=1.5\) m/3 m) for varying hydraulic conductivity. Solid lines represent **Case 1**, squares represent **Case 2**, and triangles represent **Case 3**: (**a**) \(c_{f}\) vs. \(t\) at the center; (**b**) \(c_{f}\) vs. \(t\) on the edge; (**c**) \(c_{f}\) vs. \(z\) at the center for different years; (**d**) \(c_{f}\) vs. \(z\) at the edge for different years.  
Figure 9: Distributions of concentration along (**a**,**b**) the top horizontal cut line at \(z=3\) m; (**c**,**d**) the middle horizontal cut line at \(z=1.5\) m; (**e**,**f**) the bottom horizontal cut line at \(z=0\) m for varying hydraulic conductivity. Solid lines represent **Case 1**; squares represent **Case 2**; triangles represent **Case 3**.