Steady two-dimensional seepage flow analysis analytical and numerical methods

Abstract

The primary aim of the present work is to study the influence of sloping boundaries with discontinuities in slopes and the effect of surfaces of seepage on seepage characteristics in case of confined and unconfined flows of homogeneous as well as heterogeneous liquids; the flow being assumed steady, two-dimensional and Darcian. The effects of anisotropy and stratifications in the flow medium have also been considered along with the above-mentioned factors, for one problem. Both exact analytical and numerical methods are employed for solving the problems. Experimental method of electrical analog technique is used in one case to check the results. While the problems with discontinuities in slopes have been handled by analytical method like Schwarz-Christoffel transformation, the problems involving seepage surface and stratification are solved by numerical approach using the method of finite differences. Chapter-wise, the contents of the thesis are as follows: Chapter 1 gives the scope and nature of the work undertaken, and Chapter 2 presents a review of literature in the pertinent field of study. In Chapter 3, the flow underneath an impermeable structure founded on a sloping soil with discontinuities in slopes is solved by rigorous analytical method of Schwarz-Christoffel transformation. The analytical solution is verified by numerical and electrical analog methods. Results are presented for various slopes of soil and for different base widths of the impervious structure. The solution is extended to a general anisotropic medium. The same problem mentioned in Chapter 3, but with a surface of seepage on the downstream side is studied in Chapter 4, using the finite difference method. The results of seepage surface are compared with those of equipotential surface for various parametric conditions. Chapter 5 deals with the above-mentioned problem but with a layered soil. The finite difference technique is used for solution. The outflow surface is treated as an equipotential surface as well as a seepage surface and comparison with homogeneous flow medium is also presented. The influence of relative permeabilities on seepage characteristics is studied. In Chapter 6, a semi-confined flow through an aquifer is analysed. The aquifer comprises two homogeneous isotropic media separated by an inclined interface sloping across the thickness of the aquifer. There is a sharp increase in the permeability across the interface which causes a phreatic line to occur. Conformal mapping with the help of Schwarz-Christoffel transformation and inversion of hodograph is used for obtaining configurations of phreatic line and quantity of seepage. A two-phase flow problem is investigated in Chapter 7. A confined coastal aquifer with inclined outflow face acting as a surface of seepage is considered. Method of finite differences is used for solution. An iterative process which uses constrained least square fit is employed for fixing the interface. Chapter 8 consists of important conclusions of the study.