Analytical solution for one-dimensional contaminant diffusion through unsaturated soils beneath geomembrane

Diffusion is the dominating process in the migration of contaminants through landfill liners, below which the soils are generally unsaturated. Analytical method is often considered as a preferred approach over numerical method to solve diffusion problems. In this study, a one-dimensional diffusion model of contaminants is firstly developed to account for unsaturated properties of the soils beneath landfill barriers. Based on an assumption of linear water pressure distribution, the nonlinear governing equation in the diffusion model is transformed into a linear equation using an exponential expression of soil water retention curve and a linear model of unsaturated diffusion coefficient. Subsequently, the corresponding analytical solution is obtained and the solution is then applied to investigate the effects of soil type, water pressure condition and groundwater depth on the diffusion of contaminants. The analytical results show that groundwater depth has the most influential effect on the steady flux rate of contaminants. Furthermore, the obtained steady flux rates in soil layers with high desaturation rate are negligible when the groundwater depth exceeds 3 m and 2 m. The results also indicate that a thicker soil layer with high desaturation rate is recommended to be an effective diffusion barrier to mitigate the pollution of the underlying soils and groundwater.