# Parametric Analysis for 3D Modeling of Consolidation-Induced Solute Transport Using OpenFOAM
## 2 Theoretical Model
### Parameter Selection  
To perform a parameter sensitivity analysis, parameters are divided into three categories: consolidation parameters, solute transport parameters, and parameters influencing both consolidation and solute migration. Consolidation parameters include the shear modulus \(G\) and Poisson ratio \(\
u\). While fluid flow is the direct driving force for solute migration, \(G\) and \(\
u\) indirectly but significantly influence solute migration in the consolidation context. These parameters control soil deformation and compression, altering pore structure and flow paths, which directly impact solute migration patterns. They also affect the soil's compression rate and volumetric strain, leading to changes in pore water pressure. This volume change modifies the hydraulic gradient, affecting the rate and direction of solute migration. Therefore, the model includes the indirect effects of \(G\) and \(\
u\) to better simulate solute migration under consolidation. Solute transport parameters include the partitioning coefficient \(K_{d}\), which governs the partitioning of solute between solid and liquid phases, making it critical for migration rate and extent. A higher \(K_{d}\) indicates stronger adsorption to the solid phase, reducing solute mobility in the liquid phase and slowing migration. Conversely, a lower \(K_{d}\) keeps the solute more in the liquid phase, promoting faster transport. This factor directly influences solute distribution and concentration changes across media. Furthermore, solute transport is primarily driven by consolidation and diffusion, with these effects being most significant in the vertical \(z\)-direction under the given conditions. The longitudinal dispersion coefficient \(\alpha_{L}\) characterizes dispersion along the primary flow direction, which, in this case, aligns with the \(z\)-axis. Conversely, the transverse dispersion coefficients \(\alpha_{TH}\) and \(\alpha_{TV}\) describe dispersion perpendicular to the primary flow, corresponding to the \(x\)- and \(y\)-axes, respectively. In porous media, heterogeneity along the dominant flow direction increases variations in solute migration, thereby amplifying longitudinal dispersion. Previous studies have demonstrated that \(\alpha_{L}\) is typically 5 to 10 times larger than \(\alpha_{TH}\)[14]. Parameters affecting both consolidation and solute migration include hydraulic conductivity \(\mathbf{K}\) and saturation \(S_{r}\). Hydraulic conductivity \(\mathbf{K}\), encompassing lateral (\(K_{x}\) and \(K_{y}\)) and vertical (\(K_{z}\)) components, is often characterized by its anisotropy ratio. \(\mathbf{K}\) governs the rate of water discharge, affecting pore water pressure dissipation during consolidation and flow rate during solute migration. Similarly, \(S_{r}\) impacts initial pore water pressure and alters the stress state of the soil. These changes in stress and flow paths influence solute transport dynamics. To systematically evaluate the effects of these parameters on solute migration, three experimental scenarios were designed: a baseline case (**Case 1**) and two control groups. **Case 1** serves as the reference, representing solute migration under steady conditions. **Control Group 1** modifies **Case 1** by reducing a key parameter to simulate low-parameter conditions, while **Control Group 2** increases the same parameter to explore its effects under high-parameter conditions. This comparative framework enables a systematic identification of each parameter's influence on solute migration behavior. The parameter values were selected with reference to multiple studies [7; 12; 19; 23] to ensure the rationality and comparability of the results, as detailed in Tables 2 and 3.