# Parametric Analysis for 3D Modeling of Consolidation-Induced Solute Transport Using OpenFOAM
## 4 Results and Discussion
### Effects of the Shear Modulus on Solute Transport  
Changes in concentration in the center over time depend on the shear modulus \(G\) (Figure 15a). Lower \(G\) leads to higher concentrations, especially near the top, as increased soil deformation improves consolidation and pushes the solute into the upper layers. In contrast, a higher \(G\) slows concentration changes and reduces peaks because of less deformation. At the edge (Figure 15b), although the concentration at the edges is lower than that at the center, the low \(G\) still leads to a higher concentration distribution. For example, the concentration at the top edge is approximately 50% higher under low \(G\) conditions compared to high \(G\) conditions. This phenomenon indicates that the deformation effect plays a significant role in the migration of the solute even in the edge regions, although its influence is smaller due to constraints of the boundary conditions. The deformation in the boundary regions is less pronounced than in center regions, resulting in a more limited variation in concentration. The depth profiles (Figure 15c,d) reveal that concentrations decrease with depth, with lower \(G\) causing higher concentrations. For instance, at a depth of 2.5 m, the concentration under low \(G\) conditions is approximately 15% higher than that under high \(G\) conditions. This suggests that the solutes are more likely to migrate to deeper layers under low \(G\) conditions. Higher \(G\) slows the solute migration, resulting in lower concentrations overall. This pattern is present at the edge, although the concentrations there remain lower due to reduced deformation. The horizontal variation of the solute concentration (Figure 16) shows that in the early years (1 to 3), the low \(G\) leads to a rapid increase in concentration, especially at the bottom center, where the peak concentration rises by approximately 190%. During the stabilisation period (5 to 20 years), the concentration curves gradually converge, but the influence of low \(G\) remains significant, particularly in the middle and lower regions. Compared to high \(G\), low \(G\) consistently results in higher concentration distributions throughout the entire simulation period, indicating the sustained impact of the consolidation process on solute migration. This trend is further evident in the tenth-year horizontal distribution (Figure 17). For example, **Case 4** (low shear modulus \(G\)) exhibits significantly higher center concentrations compared to **Case 1** (moderate \(G\)) and **Case 5** (high \(G\)), as indicated by the darker color. This suggests that softer soil more effectively restricts pore water movement induced by consolidation, resulting in a stronger accumulation effect near the source area. In contrast, **Case 1** and **Case 5** show lower center concentrations and more similar distribution patterns. This may be attributed to the increased stiffness of soil with higher \(G\), which reduces the influence of seepage flow on concentration distribution. In conclusion, the shear modulus strongly influences the solute transport. The shear modulus \(G\) influences the intensity and pathways of seepage flow by regulating the degree of soil deformation and the dissipation rate of pore water pressure. These changes ultimately govern the rate of solute migration and the concentration distribution. A lower \(G\) results in greater soil deformation, faster seepage flow and higher concentrations, whereas a higher \(G\) reduces soil deformation, slows down the migration rate, and leads to lower and more uniform concentration distributions. Figure 15: _Cont._Figure 16: 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 shear modulus. Solid lines represent **Case 1**; squares represent **Case 4**; triangles represent **Case 5**.