ANALYSIS OF SEEPAGE UNDER A DEPRESSED STEPPED WEIR WITH A SHEET PILE

Abstract

The movement of ground water is a basic part of soil mechanics. Its influence can be found in almost every area of civil engineering, including irrigation and reclamation. In addition, the elegance and logical structure of its theory renders it of interest to engineering scientists. It plays a vital role in Irrigation engineering for an irrigation engineer. Since, ancient times in irrigation engineering, weirs remain as the most extensively used control structures for the diversion of flow and for measurement of flow. Though the type and shape of weirs differ from place to place, depending on the available materials for construction, sub-soil condition and hydrology of the river, they are provided with one or more sheet piles when constructed in alluvial soils. Weirs are designed to satisfy the surface and sub-surface flow considerations. Where as the surface flow considerations decide the crest level, down stream floor length and minimum depths of upstream and downstream sheet-pile/cut-off, the sub-surface flow considerations at the maximum ponding condition requires more attention to protect the structure against heaving, roofing, piping and uplift. The parameters i.e. sheet-pile depth and floor length influence the uplift pressure at different points under the floor. The uplift pressures are counteracted by the weight of the floor. The weir generally consists of either a horizontal or sloping floor with sheet pile. Khosla et.al. have analysed the flow under a stepped weir considering it to be resting on the surface of a porous medium of infinite depth. They have presented design charts, which are extensively used by the field engineers. Khosla's concept of barrage or weir design for subsurface flow (Khosla et.al.1936) is based on the assumption that the thickness of floor is negligible and it is resting on the surface, the values of uplift pressure thus obtained refer to the bottom level of the floor, where in practical, structures are somewhat depressed into, acting as foundation. To remove the error in pressure distribution for neglecting floor thickness, a correction is being applied to the uplift pressure obtained according to Khosla's theory. This factor is being computed by interpolation assuming that there occurs a linear variation in the pressure along the depth of sheet-pile and the variation is equal to the variation in pressure distribution along the depth of depression. In fact, in order to achieve a tractable analytical solution, the depression of the hydraulic structure has been neglected. With such assumptions, the number of vertices taking part in the conformal transformation is reduced. Hence, the present study was undertaken to analyse the flow under a depressed-stepped weir using the conformal mapping technique to compare the solution with that of Khosla et.al and to develop an analytical solution using numerical methods for computation of pressure distribution which can be directly used as the equation for anticipated uplift pressure and there will be no need of applying a correction factor.