Slumping of groundwater mounds: revisiting the Polubarinova-Kochina theory

Abstract

Decay or rise of the water table from a disturbed (mound or trough) position to a quiescent flat state is studied by a linear potential theory that does not rely on the Dupuit-Forchheimer vertical averaging but is a solution to the full Laplace equation. We consider an unconfined aquifer of high (infinite) thickness disturbed by a linear or point hydrodynamic dipole and assemblies of dipoles, which generate two- and three-dimensional seepage. Hydrologically, the dipoles mimic a channel (or circular-recharge basin), which generates the mound. The dipole ascends (descends) and the corresponding free surface, on which the isobaricity and kinematic conditions hold, slumps. A solvability condition, which stipulates no singularities in the seepage domain, is explicitly presented. The mound signal is defined as the time peak of the water table at any piezometer located away from the original recharge area. The flow net and isotachs prove the Bouwer caveat that the Dupuit-Forchheimer theory is specious if applied to high-thickness aquifers accommodating mounds originating from short infiltration events. The analytical value of the water table peak and the time of its arrival are compared with piezometric observations in recharge experiments conducted in a coastal aquifer of the United Arab Emirates, where the hydraulic conductivity is assessed from hydrographs. The inversely determined hydraulic conductivity fits well with those found from infiltration double-ring experiments and MODFLOW simulation.