Analysis of three-dimensional unsaturated–saturated flow induced by localized recharge in unconfined aquifers

Abstract

In the process of groundwater recharge, surface water usually enters an aquifer by passing an overlying unsaturated zone. Little attention has been given to the development of analytical solutions to a coupled unsaturated–saturated flow model due to localized recharge up to now. This paper develops a mathematical model to depict three-dimensional transient unsaturated–saturated flow in an unconfined aquifer with localized recharge on the ground surface. The model contains Richards' equation for unsaturated flow, a flow equation for saturated formation, and the Gardner constitutive model describing the behavior of unsaturated soil properties. Both flow equations are coupled through the continuity conditions of the head and flux at the water table. The semi-analytical solution to the coupled flow model is derived by the methods of Laplace transform and Fourier cosine transform. A sensitivity analysis is performed to explore the head response to the change in each of the aquifer parameters. A quantitative tool is presented to assess the recharge efficiency signifying the percentage of the water from the recharge to the aquifer. We found that the effect of unsaturated flow on the saturated hydraulic head is negligible if two criteria associated with the unsaturated soil properties and initial aquifer thickness are satisfied. The head distributions predicted from the present solution match well with those from finite-difference simulations. The predictions of the present solution also agree well with the observed data from a field experiment at an artificial recharge pond in Fresno County, California.