Accurate Empirical Calculation System for Predicting the Seepage Discharge and Free Surface Location of Earth Dam over Horizontal Impervious Foundation

Abstract

In the numerical analysis of the Laplace equation, which is the governing equation of the seepage phenomena of homogeneous, isotropic earth dams, it has been confirmed that numerical analysis with high accuracy is possible by using the interpolation finite difference method (IFDM). In a previous paper, based on this numerical analysis method, the equivalent Kozeny (KZ) flow method was proposed as a new empirical method to calculate the seepage discharges and free surface locations of earth dams. Although this method is generally a highly accurate method compared with the empirical method of A. Casagrande, owing to calculating the seepage problems within a few percentages of discharge relative errors, several additional studies are necessary. By integrating the finding of this study to the previous literature, an empirical seepage calculation system with high accuracy, the equivalent KZ flow method, is created. Owing to the finally proposed empirical method, called “interpolation-equivalent KZ flow method”, the discharge and free surface location can be predicted with high accuracy in a wide range.

A comprehensive high-accuracy numerical calculation system for the 2D Poisson equation by the interpolation finite difference method

“…(57), there are two terms 𝑢 2𝑥2𝑦 and 𝑢 4𝑥4𝑦 that do not result in 𝑓 𝑘𝑥𝑙𝑥 . In the definition of 𝑜 𝑖𝑗 (12), an additional 𝑢 6𝑥6𝑦 term is generated.…”

“…The author of the present study has also proposed and reported the interpolation FDM (IFDM) as a numerical calculation system with the above three characteristics. In this paper, which is based on published papers [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], I especially focus on the second of the above three features. In the area of computational fluid dynamics (CFD) using the finite difference method, many other valuable research results have been published in the treatment of irregular domains.…”