DESIGN OF WEIRS ON PERMEABLE ANISOTROPIC POROUS MEDIUM

Abstract

Field and laboratory tests indicate that most natural and man-made porous media exhibit directional variation in'permeability. However, in general practice, hydraulic structures are designed based on the analysis of flow through isotropic porous media. The analyses have shown that the anisotropy may have considerable influence on the pressure and exit gradient distributions. This dissertation is therefore primarily concerned with the development of the charts, as design aids, for pressure at key points and exit gradient distributions for a flat bottomed weir with a vertical sheet pile on anisotropic porous medium. The analysis is done by transforming the anisotropic flow region into a fictitious isotropic domain and applying Schwarz-Christoffel transformation to the transfornied region. The results obtained in transformed region are retransformed to the actual anisotropic flow domain and the charts are developed. In general, as a thumb rule, a filter blanket is provided in downstream of a weir for a length of D to 2D, where D is the anticipated depth of scour measured from the downstream bed of the river. A method to find the length of filter blanket is not yet available. An analytical method for obtaining the length of filter blanket is suggested in the dissertation. The scope and nature of work undertaken is presented in Chapter 1. This is followed by a review of literature in chapter 2, which embraces the pertinent theory of seepage in anisotropic porous media and the provision of filter blanket downstream the weir. Chapter 3 deals with the analysis for flat bottomed weir with a vertical sheet pile on anisotropic porous medium of infinite depth. Numerical results are presented for uplift pressure at key points and exit gradient distribution for various position of sheet pile and different degree of anisotropy. The results are compared with those of Khosla et al, for the particular case in which maximum and minimum coefficient of permeability ratio is one. The inclination of the direction of coefficient of permeability and the ratio of maximum and minimum coefficient of permeability have considerable influence on the pressure and exit gradient distribution. Chapter 4 deals with the problems in a weir on anisotropic flow domain where maximum exit gradient becomes infinite when downstream sheet pile is vertical. The analyses are made for the provision of exit gradient controlling device (a concrete block ix with certain shape) and the numerical results for obtaining the size and shape of such device are given. Chapter 5 deals with the design of a filter blanket for a weir on isotropic porous media of infinite depth. The analysis is carried out applying Schwarz-Christoffel transformation. The exit gradient distribution corresponding to straight line scour of the downstream reservoir boundary is analysed. Numerical results for the length of the filter blanket are given for various ratio of weir width and length of sheet pile. The ratio of width of weir and the length of downstream vertical sheet pile has considerable influence on the length of filter blanket. Finally, in Chapter 6, the results presented in earlier chapters are discussed and the important conclusions of the study are summerised.