THREE DIMENSIONAL SEEPAGE BELOW HYDRAULIC STRUCTURES LAID ON PERVIOUS FOUNDATIONS

Abstract

The present day methods of computation of uplift pressures below hydraulic structures laid on pervious forma tions, are based on the assumption of two-dimensional seepage,. This assumption may lead to appreciable errors in case of rela tively narrow structures. Recently, some of these narrow structures designed on the assumption of two dimensional seepage have been tested for uplift pressures using three-dimensional electrical analogy. The effect of the existence of the watertable has also been taken into account in these studies. The resulting pressures obtained have been used as the basis of design of such structures. An Important problem in the repre sentation of these models in the electrical analogy tray is the correct simulation of the water-table. In this investigation, three-dimensional seepage below narrow hydraulic structures has been studied9 both ana lytically and experimentally, in order to provide an improved basis for the computation of uplift pressures. The analytical solution of the problem involves the solution of three-dimensional Laplace's equation with the actual boundary conditions considering the geometry of the free surface behind the abutment from the canal to the water-table. A suitable analytical method for handling such problems even with approximations is not available, A new method of solution of such problems has ^oeen developed in this investigation as a half space problem neglecting the seepage region above the level of the floor and the existence of the water-table. Seepage from the upstream portion of the canal to the downstream portion to predict pressure distribution below the floor, has been considered under the above assumptions. The build-up of the free surface behind the abutment, from canal ta water-table, due to the existence of water table for a canal floor of negligible width and finite length has been computed neglecting the vertical component of velocity of seepage from and to the canal using Dupuit -Forchhiemer theory. Free surface con tours have been determined for different distances of the water table from the canal under different water table elevations„ The effect of the thickness of the pervious formation on the build-up of the free surface has also been computed. The effect of this build up of free surface on the pressures below the canal floor has been evaluated by means of a series of experiments, in which floors of various length-width ratios and with different length-depth ratios were used in a threedimensional electrical analogy tray. The effect of free surface on the potential distribution below the floor has been taken into account by fixing wires at the bottom of the tray along water table contours, in the space between the plates representing the canal and the water table. As a result of this investigation, means have been pro vided to determine the pressures below depressed floors without cut.-offs for different elevations of the water table. It is hoped that this study will lead to a better under- standing of the problem of three-dimensional seepage below hydraulic structures.