Similitude Criteria for Flow from Unconfined Aquifers

Seepage in a two-dimensional unconfined aquifer of rectangular cross-section is analyzed to determine the rate of outflow into an adjoining water body which fully penetrates the aquifer. The analysis is made by using capillary flow theory as well as saturated Darcy flow theory with and without the Dupuit assumptions. In addition to the usual criteria of similarity of geometry, initial and boundary conditions, also the relative capillary conductivity and the dimensionless water content suction relationship must be similar. From the latter criterion a convenient parameter was formulated which expresses the effect of capillarity in relation to the depth of the aquifer. It was found that this parameter is useful to determine whether or not the capillary flow above the water table is important. An analysis was made which shows the errors that may arise in the prediction of the outflow rate by neglecting capillarity and using the Dupuit assumptions.