# Parametric Analysis for 3D Modeling of Consolidation-Induced Solute Transport Using OpenFOAM
## 4 Results and Discussion  
### Effects of Hydraulic Conductivity on Consolidation  
During consolidation, pore water pressure (\(p\)) and vertical displacement (\(u_{z}\)) exhibit a notable spatio-temporal evolution. Initially, loading rapidly increases the pore pressure, peaking in two years and then gradually decreasing as consolidation progresses. These changes are more pronounced at the center, with greater pressure and displacement, while the edges experience weaker effects.  
In the center (Figures 4a and 5a), hydraulic conductivity (\(\mathbf{K}\)), a measure of the soil's ability to transmit water, plays a critical role in these changes. High \(\mathbf{K}\) allows water to move through the soil more easily, accelerating pressure dissipation and leading to greater vertical displacement as pore water is expelled. Conversely, low \(\mathbf{K}\) restricts water flow, slowing the reduction in pore pressure and resulting in smaller displacements. At the edges (Figures 4b and 5b), poor drainage near the boundaries causes a localized buildup of pore water pressure, leading to a relative increase in pressure at the center when compared to the top boundary. This limited drainage also restricts vertical displacement near the edges. Furthermore, Figures 4c,d and 5c,d further illustrate the depth-dependent variation in pressure and vertical displacement. As depth increases, the lower \(\mathbf{K}\) impedes drainage, causing more pronounced pressure changes, while vertical displacement tends to stabilize in deeper layers.  
Under the applied load, the pore-water pressure and horizontal displacement show distinct spatial patterns. Pore pressure peaks within the loading area and gradually decreases over time, particularly after 20 years, as the water is expelled during consolidation. Horizontal displacement reflects outward stretching within the loading area, with less tension outside. Since the model has identical dimensions in the \(x\) and \(y\) directions, \(u_{x}\) and \(u_{y}\) are numerically equivalent and are, therefore, both represented as \(u_{xy}\). Over time, both the pore pressure and the displacement stabilize as the consolidation effects weaken and the soil reaches equilibrium.  
Figure 4: Distributions of pore pressures 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**) \(p\) vs. \(t\) at the center; (**b**) \(p\) vs. \(t\) on the edge; (**c**) \(p\) vs. \(z\) at the center for 1, 2, and 3 years; (**d**) \(p\) vs. \(z\) at the edge for 1, 2, and 3 years; (**e**) \(p\) vs. \(z\) at the center for 5, 10, and 20 years; (**f**) \(p\) vs. \(z\) on the edge for 5, 10, and 20 years.  
Figure 5: Distributions of vertical displacement 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**) \(u_{z}\) vs. \(t\) at the center; (**b**) \(u_{z}\) vs. \(t\) on the edge; (**c**) \(u_{z}\) vs. \(z\) at the center for 1, 2, and 3 years; (**d**) \(u_{z}\) vs. \(z\) at the edge for 1, 2, and 3 years; (**e**) \(u_{z}\) vs. \(z\) at the center for 5, 10, and 20 years; (**f**) \(u_{z}\) vs. \(z\) on the edge for 5, 10, and 20 years.  
Figure 6: Distributions of pressure along (**a**,**b**) the top horizontal cut line at \(z=3\) m; (**c**,**d**) the middle horizontal cut line at \(z=1.5\) m for varying hydraulic conductivity. Solid lines represent **Case 1**; squares represent **Case 2**; triangles represent **Case 3**.  
Figure 7: Horizontal displacement along horizontal cut line at \(z=1.5\) m over time for varying hydraulic conductivity. Blue lines represent **Case 1**; black lines represent **Case 2**; red lines represent **Case 3**.