Mathematical Modeling of Subsurface Seepage Flow over Sloping Terrain due to Vertical Recharge and Seepage from Stream Stage Variations

Abstract

 This paper develops a mathematical model simulating time varying groundwater flow in an unconfined aquifer overlying a sloping impervious bed. The aquifer is contacted with two streams, one of which has a constant water level and the other stream is rising form an initial level to a final level by a known exponentially function of time. The aquifer is also receiving vertical recharge at a constant rate. The flow is simulated by a nonlinear Boussinesq equation and its approximate analytical solution is obtained using Laplace transform method. Closed form analytical expressions are derived for hydraulic head distribution in the aquifer and flow rate at the stream-aquifer interface. The results derived in the study are illustrated with a numerical example.