Total Head Evaluation using Exact and Finite Element Solutions of Laplace Equation for Seepage of Water under Sheet Pile

Abstract

In this study, the strong and weak forms of Darcy flow equation has been derived. The final obtained equation is Laplace partial differential equation. For total head evaluation, Laplace equation is solved using exact solution depending on Fourier series and numerical solution depending on finite element method. A computer program has been developed in MATLAB program to solve the Laplace equation using both exact and finite element solutions and the seepage of water under sheet pile is taken as a case study. Different number of points and nodes has been selected for the two methods. It is shown that both exact and finite element solutions have a good match in distribution for the study area especially when the Fourier points are increased.

Keywords

• Laplace equation
• Fourier series
• FEM
• total head
• seepage