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.

Open pit mines are large geotechnical structures. Their stability is an important consideration in the mining industry. The deformations of geotechnical structures often involve the coupled interaction between the pore fluid pressure and the nonlinear deformation of soil, characterised by poro-elasto-plastic behaviour. This paper develops the scaled boundary finite element method (SBFEM) to address poro-elasto-plastic in slope stability problems. It builds upon a previously developed elasto-plastic formulation to consider the effect of pore fluid pressure and its interaction with the nonlinear deformation within the soil. The pore pressure field introduces an additional variable in the governing equations that is similarly discretised using SBFEM shape functions. The SBFEM is implemented together with a pixel-based quadtree mesh generation technique, enabling automatic meshing directly from digital images. This leads to efficient automation when modelling problems with iterative changes in the geometry such as in optimisation of construction processes during the rehabilitation of slopes. The formulation is validated first using a standard numerical benchmark. Application of the developed technique in construction applications in slopes where the stability and effect of pore water pressure is considered e.g., tailings dam construction and optimisation of backfilling process is demonstrated in three examples to demonstrate feasibility.