Abstract
New generalized solutions of linearized Boussinesq equation are derived to approximate the dynamic behavior of subsurface seepage flow induced by multiple localized time-varying recharges over sloping ditch–drain aquifer system. The mathematical model is based on extended Dupuit–Forchheimer assumption and treats the spatial location of recharge basins as additional parameter. Closed form analytic expressions for spatio-temporal variations in water head distribution and discharge rate into the drains are obtained by solving the governing flow equation using eigenvalue–eigenfunction method. Downward and zero-sloping aquifers are treated as special cases of main results. A numerical example is used for illustration of combined effects of various parameters such as spatial coordinates of the recharge basin, aquifer’s bed slope, and recharge rate on the dynamic profiles of phreatic surface.
Highlights
Managing sustainability of limited water resources is a challenging task in the face of ever-increasing demand for water and the geotechnical problems associated with overuse of available water
New analytic solutions are developed and tested for estimation of spatio-temporal variations in unconfined water table over sloping ditch–drain aquifer system due to localized transient recharge from multiple basins
The mathematical model presented in this study is based on Dupuit–Forchheimer assumptions in which spatial coordinates of recharge basins are treated as additional parameters
Summary
Managing sustainability of limited water resources is a challenging task in the face of ever-increasing demand for water and the geotechnical problems associated with overuse of available water. Rai et al (2006) and Rai and Manglik (2012) applied this scheme to predict the water head distribution in unconfined aquifers for multi-recharge and pumping operations These studies provide useful insight into the groundwater flow system; the upland watershed hydrology concerning subsurface drainage over hillslope cannot be satisfactorily explained with these results. Closed form analytic expressions for water head distribution in the aquifer and discharge rate into the ditches are obtained by solving the linearized Boussinesq equation with eigenvalue–eigenfunction method. Some special cases such as no slope and uniform localized recharge are derived as limiting cases of the analytic results. Following the procedure described in preceding section, the solution of seepage flow is obtained as
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