Analytical Solution for Coupled Solute Transport and Consolidation Under Semi‐Infinite Conditions and Its Application to Clay Liner Thickness Design

ABSTRACT Clay liners are widely used in waste containment systems to prevent groundwater contamination. This study presents transient analytical solutions for solute transport coupled with consolidation in a semi‐infinite domain. No closed‐form solution exists for this configuration despite its common use in theoretical analyses. The solution is derived using the Laplace transform and validated against existing models and experimental data. It provides explicit expressions for solute concentration and pore water pressure, capturing the combined effects of deformation, seepage, and diffusion. Based on this framework, new formulas for clay liner thickness are proposed for two breakthrough criteria (I and II). These formulas enable mechanical load to be incorporated into the design. Results show that the coupled effects of solute transport and consolidation significantly accelerate solute migration, as consolidation‐induced pore water flow enhances advective transport. Compared with finite boundary conditions, a semi‐infinite boundary slows solute migration. The required liner thickness increases with mechanical loading, with Criterion I exhibiting a substantially higher growth than Criterion II, although the growth rate decreases with increasing load for both criteria. Under a mechanical loading of 400 kPa, the thickness predicted by Criterion I is 25.7% greater than that predicted by Criterion II. In the landfill case study, the proposed methodology confirms the adequacy of the existing liner and demonstrates potential cost savings of 27.0% and 49.5% under Criteria I and II, respectively. This work provides an efficient tool for evaluating solute transport coupled with consolidation and offers practical guidance for clay liner design optimization in engineering applications.