Analytical solutions for a fully coupled hydraulic‐mechanical‐chemical model with non‐zero initial concentration of contaminant

Abstract

Analytical solutions for coupled problems are very significant for both understanding the physical mechanism and verifying the numerical methods. However, existing solutions usually focus on advection‐dispersion models without considering the coupling effect of contaminant transport or partial‐coupled models with the zero initial concentration (ZIC) condition, which are impractical in many engineering applications. This paper proposes novel analytical solutions to solve the non‐zero initial concentration (NZIC) problem for a fully‐coupled hydraulic‐mechanical‐chemical (HMC) model by Fourier transform. The proposed analytical solutions are highly competent and efficient compared with existing solutions from the literature. The solutions are applied to investigate the long‐term contaminant transport behavior and consequent deformation of clay liner under NZIC conditions. Results show that the presence of NZIC greatly promotes contaminant ions migration and shorten breakthrough time. The higher the initial concentration, the shorter the breakthrough time. When the initial concentration is increased by 3 and 5 times, the corresponding breakthrough time is reduced by 23.9 and 27.1 years, respectively. In practical engineering, neglecting the NZIC of contaminant can lead to an overestimation of performance efficiency of clay liners.