Semi-analytical model for axisymmetric transport of contaminant through flawed geomembrane

Geomembrane (GM) is a kind of cost-efficient material for pollutant barriers in landfills, while defects can occur during the installation or service periods, resulting in a mixed-type boundary condition (MTBC) at the top surface of the underlying soil layer (SL). In this study, a novel boundary transform method is employed to handle the MTBC problem of axisymmetric transport of organic contaminant through defected GM, and a semi-analytical solution is derived to evaluate the concentration profiles in the spatiotemporal domain. The proposed solution is in the cylindrical coordinates that can incorporate the diffusion and dispersion processes, as well as the concentration condition in the GM defect. The discretization method, integral transforms and corresponding inverse transforms are applied to obtain the semi-analytical solution, which is demonstrated to be effective compared to the numerical results. The model is applied to predict the migration characteristics of organic contaminant in several cases, followed by discussions to evaluate the influencing roles of defect rate, anisotropic coefficient, and segment number. Results indicate that the existence of defects substantially reduces the barrier capacity of the GM layer, and the contaminant migration time varies in several orders of magnitude for different MTBCs.