Analytical solution based on stream-aquifer interactions in partially penetrating streams

An analytical solution of drawdown caused by pumping was developed for an aquifer partially penetrated by two streams. The proposed analytical solution modifies Hunt＇s analytical solution and considers the effects of stream width and the interaction of two streams on drawdown. Advantages of the solution include its simple structure, consisting of the Theis well function and parameters of aquifer and streambed semipervious material. The calculated results show that the proposed analytical solution agrees with a previously developed acceptable solution and the errors between the two solutions are equal to zero without consideration of the effect of stream width. Also, deviations between the two analytical solutions increase with stream width. Four cases were studied to examine the effect of two streams on drawdown, assuming that some parameters were changeable, and other parameters were constant, such as the stream width, the distance between the stream and the pumping well, the stream recharge rate, and the leakage coefficient of streambed semipervious material.

Approximation of surface-groundwater interaction mediated by vertical streambank in sloping terrains

New analytical solutions are derived to estimate the interaction of surface and groundwater in a stream-aquifer system.The analytical model consists of an unconfined sloping aquifer of semi-infinite extant,interacting with a stream of varying water level in the presence of a thin vertical sedimentary layer of lesser hydraulic conductivity.Flow of subsurface seepage is characterized by a nonlinear Boussinesq equation subjected to mixed boundary conditions,including a nonlinear Cauchy boundary condition to approximate the flow through the sedimentary layer.Closed form analytical expressions for water head,discharge rate and volumetric exchange are derived by solving the linearized Boussinesq equation using Laplace transform technique.Asymptotic cases such as zero slope,absence of vertical clogging layer and abrupt change in stream-stage can be derived from the main results by taming one or more parameters.Analytical solutions of the linearized Boussinesq equation are compared with numerical solution of corresponding nonlinear equation to assess the validity of the linearization.Advantages of using a nonlinear Robin boundary condition,and combined effects of aquifer parameters on the bank storage characteristic of the aquifer are illustrated with a numerical example.