Response of an Unconfined Sloping Aquife

This paper presents an analytical solution of the one-dimensional linearized Boussinesq equation characterizing unsteady groundwater flow in an unconfined aquifer, overlying an impervious downward sloping bed. The study explores the scenario where one end of the aquifer is in contact with a constant water level, while the other end experiences an exponentially rising water level due to an adjoining stream. Additionally, the aquifer receives either a constant recharge or a cycle of time-varying vertical recharge. By employing the Laplace transform to solve the seepage model, analytical expressions for hydraulic head and flow rate in the aquifer are derived. These expressions elucidate phenomena like the sudden rise or gradual increase in the stream water associated with sloping or horizontal beds, represented under asymptotic conditions. The paper illustrates the response of both short and long aquifers to variations in bed slope, recharge rate, and stream water rise through numerical examples. Furthermore, it analyzes the sensitivity of flow rate in relation to various parameters influencing the aquifer system.