Simplified and rigorous approaches to model the transport of inorganic contaminants through composite liners with defective geomembranes

Composite liners consisting of a geomembrane, placed over a low-permeability clay layer, are used throughout the world for the lining of waste disposal facilities, with the aim to prevent the groundwater quality from being compromised, and an unacceptable risk for the human health and the environment from occurring. Despite the importance of developing a rational approach to calculate the contaminant transport rate through composite liners, for both the design of new landfills and for the risk assessment of the existing ones, limited attention has been paid so far to this issue and, particularly, to the derivation of analytical solutions, which can help designers make a preliminary assessment of the containment performance of lining systems and verify that more complex numerical models are fundamentally correct. After an overview of the simplified calculation approaches that are currently adopted for the performance-based design of composite liners, a novel theoretical framework is presented in this paper, which allows the advective-diffusive transport of inorganic contaminants to be modelled considering imperfect contact conditions between the geomembrane and the underlying clay layer. Closed-form analytical solutions to the contaminant mass flow rate have been derived for the cases of pure advection and pure diffusion, with a view to quantifying the error that is made when the mass conservation condition for the solute phase is disregarded, as is the case of the aforementioned simplified approaches.