Well pumping in unconfined aquifers: The influence of the unsaturated zone

An approximate analytical solution describing transient flow toward a partially penetrating well pumped at a constant discharge in a rigid, homogeneous, anisotropic, unconfined aquifer of infinite radial extension and finite depth, considering flow in the unsaturated zone above the free surface, is presented. The proposed solution generalizes Dagan's (1967) one, which is based on saturated flow theory solely. The characteristic hydraulic properties of the unsaturated zone, namely, the retention and hydraulic conductivity curves, are described by analytical expressions that depend on the parameter 1/a', which roughly represents the effective thickness of the unsaturated zone. The problem is solved analytically by replacing the pumping well screen by a line sink distribution of uniform strength, by linearizing the unsaturated flow equation and boundary conditions at the moving free surface, and by transferring the upper boundary to infinity. In order to check the validity of the approximate analytical solution, the problem, free of such approximations, was solved numerically by a finite element scheme for a representative particular case. Comparison between analytical and numerical solutions showed excellent agreement. The influence of the unsaturated zone was found to be negligible for most common cases encountered in application. In the marginal cases of very shallow rigid aquifers and of soils with particularly large unsaturated effective thickness 1/a', the influence of the unsaturated zone upon drawdown was found to be significant at relatively short times, close to the pumping well and close to the free surface.