Water table fluctuation in aquifers overlying a semi-impervious layer due to transient recharge from a circular basin

An analytical solution of a linearised form of Boussinesq equation is presented in this paper to describe the water table fluctuation in unconfined aquifers overlying a semi-impervious layer in response to transient recharge. This solution does not require the common assumption of an impervious formation underlain the unconfined aquifer. On the contrary, it shows that even when the hydraulic conductivity of the semi-impervious layer is several orders of magnitude less than the aquifer hydraulic conductivity, downward leakage can be important and can lead to large overestimations of water table heights if it is ignored. The rate of recharge is considered to decrease exponentially with time during a single cycle of recharge while two cycles of time varying recharge are approximated by continuous elements described by Nth degree polynomials. Numerical solution of the non-linear Boussinesq equation was implemented to validate the applied linearisation.