An accurate inverse model for the detection of leaks in sealed landfills

Leaks from landfills to underlying soil layers are one of the main problems that endanger the sustainability of waste disposal in landfills. Indeed, the possible failing of in-situ equipment can give rise to serious pollution consequences or costly inspection work in the landfill body. In this paper, we develop the time dependent mathematical relationship between the concentration of water at the surface of the landfill and the flux at the bottom of the landfill. This makes it possible to detect a leak using non-expensive measurements made at the surface of the landfill. The resulting model is obtained by analytically solving Richard's equation with a piecewise linear boundary condition at the bottom. The unknown coefficients of the piecewise linear functions, which can be estimated using the measurements at the surface, provide the necessary information for detecting leaks. The algorithm has been numerically tested using simulated data of rain precipitation. The method proposed could be conveniently used to complement the usual monitoring techniques due to the limited costs of its implementation.