Analytical Solutions for a Coupled Hydro‐Mechanical‐Chemical Model Under Exponentially Decaying Concentration Boundary Conditions

ABSTRACT In active landfills, contaminant concentrations in leachate are time‐dependent. They vary with waste degradation and leaching processes rather than remaining constant throughout the landfill service life. However, most analytical solutions for fully coupled hydro‐mechanical‐chemical (HMC) models commonly assume a constant upper boundary concentration. This assumption limits their ability to describe the temporal attenuation of contaminant source strength. This study derives analytical solutions for a fully coupled HMC model of contaminant transport in clay liners under exponentially decaying concentration boundary conditions. The derivation combines boundary homogenization, eigenfunction expansion in a finite domain, Laplace transformation, and matrix exponential solution of the modal equations. The solutions evaluate the effects of the source decay coefficient λ , initial upper boundary concentration c 0 , hydraulic conductivity k h , chemico‐osmotic efficiency coefficient ω , and boundary formulation on coupled transport behavior. Results show that the exponentially decaying boundary reduces long‐term overestimation of contaminant transport potential compared with the constant concentration boundary. Increasing λ from 0.025 to 0.05 year −1 delays breakthrough by 3.17 years. The initial upper boundary concentration mainly controls concentration level and migration depth, with limited influence on relative concentration at the liner base. Increasing k h promotes downward contaminant migration and shortens breakthrough time. Increasing ω increases the magnitude of negative pore water pressure and settlement while slowing contaminant migration and delaying breakthrough. The single‐exponential decay boundary reaches the breakthrough criterion at 42.21 years, whereas the double‐exponential decay boundary does not reach breakthrough within 50 years. Neglecting source attenuation may underestimate the actual barrier performance of clay liners.