Analytical Assessment of Solute Distribution for Evaluation of Diffusion and Membrane Behavior Properties of Saturated and Unsaturated Soils

ABSTRACT Diffusion and membrane behavior of clays and clay‐soil mixtures are important properties for predicting long‐term performance of engineered containment barriers. Concurrent measurement of effective diffusion coefficients ( D * ) and membrane efficiencies (ω) of unsaturated soil typically is performed with a modified through‐diffusion test apparatus where relatively thick high air entry (HAE) disks are required at the specimen boundaries to maintain a constant degree of saturation. The presence of the HAE disks between the circulated solutions and the specimen inhibits direct monitoring of the concentration gradient that develops across the specimen, which is critical to accurate calculation of D * and ω. In this study, an analytical model (TDM‐U) is proposed to depict solute distribution within a multilayer system composed of soil, HAE disks, and porous stones, and support evaluation of diffusive and membrane behavior properties of both saturated and unsaturated specimens. Based on the comparison with numerical simulation and other two existing models, the proposed model yielded a relatively high accuracy of less than 5% relative error in calculated D * over a wide range of flow rates spanning from 5 × 10 −11 m 3 /s to 7.5 × 10 −9 m 3 /s, with different inflow/outflow port locations, and for both saturated and unsaturated soil conditions. Ultimately, the proposed TDM‐U model exhibited a strong correlation with experimental data under different degrees of saturation and pore water concentration, and can potentially support more reliable predictions of contaminant transport processes in engineered barriers.