Analytical solution of confined seepage problem through alluvial foundation and evaluation

Many analytical methods proposed for solving two-dimensional problems of groundwater 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 allows 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 Schwartz-Christoffel integrals are used to determine the uplift pressure in alluvial foundations in different depths and sizes 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 this method and the results of laboratory methods were compared to evaluate the accuracy of analytical results and to critically discuss the strengths and weaknesses. The results indicate that in some cases new analytical method underestimates uplift pressure while in some circumstances there is a good agreement between them.