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.

Rayleigh waves are crucial in earthquake engineering due to their significant contribution to structural damage. This study aims to accurately synthesize Rayleigh wave fields in both uniform elastic half-spaces and horizontally layered elastic half-spaces. To achieve this, we developed a self-programmed FORTRAN program utilizing the thin layer stiffness matrix method. The accuracy of the synthesized wave fields was validated through numerical examples, demonstrating the program's reliability for both homogeneous and layered half-space scenarios. A comprehensive analysis of Rayleigh wave propagation characteristics was conducted, including elliptical particle motion, depth-dependent decay, and energy concentration near the surface. The computational efficiency of the self-programmed FORTRAN program was also verified. This research contributes to a deeper understanding of Rayleigh wave behavior and lays the foundation for further studies on soil-structure interaction under Rayleigh wave excitation, ultimately improving the safety and resilience of structures in seismic-prone regions.

In order to investigate the differences between the dynamic response problems of quasi-saturated and saturated foundations. Based on the theory of quasi-saturated porous media, the dynamic response problem of a semi-infinite quasi-saturated soil foundation is investigated. Using the Fourier integral transform, the computational lexicon of the dynamic response of a quasi-saturated soil foundation under bar simple harmonic loading on the ground surface is established according to the Helmholtz vector decomposition principle. The effects of saturation degree and loading frequency on soil displacement, stress, and pore water pressure in the quasi-saturated foundation were analyzed. The results show that the loading frequency and the degree of saturation greatly influence the dynamic response of the quasi-saturated soil. With the increase of saturation, the surface displacement magnitude and positive stress magnitude increase, especially when Sr = 1, the surface displacement magnitude and positive stress magnitude change significantly, but the value of shear stress is not sensitive to the change of saturation. Pore water pressure increases with saturation and is most significantly affected by saturation relative to stress and displacement.