Predicting steady-state seepage flow in complex half-space using a modified scaled boundary finite element method

Abstract

Seepage problems in half-space domains are crucial in hydrology, environmental, and civil engineering, involving groundwater flow, pollutant transport, and structural stability. Typical examples include seepage through dam foundations, coastal aquifers, and levees under seepage forces, requiring accurate numerical modeling. However, existing methods face challenges in handling complex geometries, heterogeneous media, and anisotropic properties, particularly in multi-domain half-spaces. This study addresses these challenges by extending the modified scaled boundary finite element method (SBFEM) and using this method to explore steady seepage problems in complex half-space domain. In the modified SBFEM framework, segmented straight lines or curves, parallel to the far-field infinite boundary, are introduced as scaling lines, with a one-dimensional discretization applied to them, thereby reducing computational costs.Then the weighted residual method is applied to obtain the modified SBFEM governing equations and boundary conditions of steady-state seepage problem according to the Laplace diffusion equation and Darcy’s law. Furthermore, the steady seepage matrix at infinity is obtained by solving the eigenvalue problem of Schur decomposition and then the 4th-order Runge-Kutta algorithm is used to iteratively solve until the seepage matrix at the boundary lines is reached. Comparisons between the present numerical results and solutions available in the published work have been conducted to demonstrate the efficiency and accuracy of this method. At the same time, the influences of the geometric parameters and complex half-space domain on the seepage flow characteristics in complex half-space domain are investigated in detail.