Appropriate Boundary Condition for Dupuit-Boussinesq Theory on the Steady Groundwater Flow in an Unconfined Sloping Aquifer With Uniform Recharge

The application of Dupuit-Boussinesq theory on the two-dimensional steady groundwater flow in an unconfined sloping aquifer with uniform recharge is theoretically investigated. The examination of conditions at the downstream and upstream is performed. The method of phase plane is used to geometrically interpret the characteristics of the nonlinear theory by various initial conditions. For phase portrait analysis, three configurations for aquifers are considered. In each type of aquifer three conditions of recharges as well as downstream groundwater tables are also considered for comprehensive analysis. Based on the phase portrait analysis, one explicit formula in terms of known parameters and downstream boundary condition is derived to easily and straightforwardly determine an appropriate upstream boundary condition. The derived explicit formula can facilitate correct modeling using Boussinesq theory.