Modeling of Horizontal Water Redistribution in an Unsaturated Soil

When two soil samples with the same hydraulic properties but different initial water saturations are brought into contact, water will redistribute horizontally between the samples until some equilibrium is reached. The part with a higher initial saturation undergoes drainage while imbibition occurs in the other part. Hysteresis will not allow water to redistribute evenly between the two parts. In this study we used two different modeling approaches to analyze a recent experiment related to the water redistribution process. In one approach, we assumed applicability of the standard Richards equation with a hysteretic capillary pressure-saturation relationship (including scanning curves). This approach assumes continuity in the water pressure and flux across the contact surface between the two sides. In the second approach, we used an extended two-phase flow formulation based on rational thermodynamics principles and involving the air-water specific interfacial area. For this approach, we used continuity in the Gibbs free energy for air-water interfaces and the interfacial area flux as additional conditions at the contact surface. We employed two different initial conditions: uniform initial saturation for each side and slightly nonuniform initial saturation distributions consistent with the measured water contents. We compared results of both models with measurements. The Richards equation with full hysteresis could not reproduce the measured saturation distribution unless an unrealistic value of the imbibition retention curve was assigned. The interfacial area model compared well with the experimental data after optimization of some of the model parameters.