A Finite Element Model for the Unsteady Groundwater Flow over Sloping Beds

A numerical solution of the nonlinear two-dimensional unsteady groundwater flow over sloping beds, using the Galerkin finite element method, is presented. The applied differential equation is based on the assumption that the streamlines are parallel to the sloping bed while the conventional differential equation is based on the Dupuit–Forchheimer assumption of horizontal flow. Furthermore, the gradient of the piezometric head is evaluated as a function of the unknown slope of the groundwater free surface and not simply as the absolute slope of the water table. Water table profiles and seepage rates obtained from the model are compared with those obtained by analytical solutions and experimental results for steady one-dimensional flow and for different values of bed slope. Results of the present model compares reasonably well with experimental results and with the results of Childs' analytical solution. The unsteady-state solution for different values of bed slope are compared to the results of a model based on the assumption that the water table slope is equal to the bed slope. The differences in the predicted water table by these two models are insignificant for small slopes but increase with increasing slope.