An Analytical Solution for Confined Seepage Problem Beneath Hydraulic Structures

Abstract

A number of analytical methods have been proposed for solving two-dimensional problems of groundwater flow, which are concerned with functions which transform the problem from a geometric status where solution must be found to another status in which the solutions are known. Conformal mapping and its appropriate techniques allow us to change complex flow problems into regular geometric shapes. In this paper, an analytical solution is provided for calculating uplift pressure in alluvial foundations below dams. In the present study, velocity hodograph and Schwarz–Christoffel integrals are used to determine the uplift pressure in alluvial foundations for different depths and lengths of sheet pile and upstream blanket. An important point in this study is the asymmetric insertion of blanket relative to sheet pile along the longitudinal path. Finally, the results obtained from the employed analytical method and the results of laboratory studies are compared to evaluate the accuracy of analytical solution. The results of the studies indicate that in some cases, the present analytical method underestimates uplift pressure, while in some circumstances there is a good agreement between theoretical and laboratory methods.