Analytical Solution of Linearized Boussinesq Equation for Unsteady Seepage Flow in Ditch-Drain Sloping Aquifer

Analytical Solution of Linearized Boussinesq Equation for Unsteady Seepage Flow in Ditch-Drain Sloping Aquifer

This paper presents a generalized solution of linearized Boussinesq equation to predict unsteady flow of subsurface seepage induced by localized recharge over sloping ditch-drain aquifer. The mathematical model is based on Boussinesq equation with Dupuit-Forchheimer assumption in which the spatial location of the recharge basin is treated as an additional parameter. Analytical expressions for water head distribution in the aquifer and discharge rate into the ditches are obtained by solving the governing flow equation with eigenvalue-eigenfunction method. Upward and zero sloping cases are deduced from the main results by appropriately adjusting the slope parameter. A numerical example illustrates the combined influence of bed slope, recharge rate and spatial coordinate of the recharge basin on the dynamic profiles of phreatic surface.