# Parametric Analysis for 3D Modeling of Consolidation-Induced Solute Transport Using OpenFOAM
## 4 Results and Discussion
### Effects of the Shear Modulus on Consolidation  
Figure 10(a),b illustrates the temporal evolution of pore pressure (\(p\)) under different shear modulus conditions. At the center, lower shear modulus results in a peak pressure of 200 Pa at year 2, which is 230% higher than the high shear modulus condition. Pressure decreases gradually over time, reaching 40 Pa after 20 years. At the edge, the pressure is consistently lower, peaking at 48 Pa under low shear modulus and reducing by 80% by year 20 (Figure 10(b)). In terms of vertical displacement (\(u_{z}\)) (as shown in Figure 12), a lower shear modulus leads to greater compression, with a peak displacement of 0.58 m in the center after 20 years, which is 600% higher than the high shear modulus condition. This effect is most pronounced in the shallow and middle layers, while a higher shear modulus limits deformation and reduces displacement. Figure 11: _Cont._  
Figure 10: Concentration contour plots in the \(x\)-\(y\) plane at \(z=1.5\) m under varying hydraulic conductivity over 10 years. Figure 11: Distribution of 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 shear modulus. Solid lines represent **Case 1**, squares represent **Case 4**, and triangles represent **Case 5**: (**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 12(a),b shows pressure distribution at the top. In the short term (1 to 3 years, Figure 12(a)), the pressure is higher in the loading area. Higher shear modulus reduces pressure due to increased soil stiffness, while lower shear modulus results in greater deformation and higher pressure. In the long term (5-20 years, Figure 12(b)), pressure stabilizes, with the lower shear modulus maintaining higher pressure and the higher shear modulus reducing it. Similarly, Figure 12(c),d shows pressure distribution in the middle, with a lower shear modulus causing higher pressure in the short term and stabilizing at a higher level over time compared to a higher shear modulus. The horizontal displacement (\(u_{xy}\)) shows symmetric outward movement from the center, with alternating positive and negative displacements outside the loading area due to the expansion of the soil under load. At 2 years (Figure 13(b)), the horizontal displacement at the edges peaks, with a lower shear modulus leading to a larger displacement due to softer soil. From 2 to 20 years (Figure 13(b)-e), horizontal displacement decreases but remains larger under lower shear modulus, while higher shear modulus consistently limits deformation. In conclusion, the shear modulus significantly impacts soil deformation and pore pressure distribution. The lower shear modulus leads to softer soil, higher pore pressure, and greater vertical and horizontal displacements, while the higher shear modulus increases stiffness, reducing both pressure and deformation. The center experiences higher pressure and deformation than the edges, but both are strongly influenced by shear modulus. These results align with the expected physical behavior of soil stiffness, where higher shear modulus reduces deformation by increasing resistance to shear stresses. Figure 12: Distribution of vertical displacements 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 shear modulus.