A Novel Solution for Seepage Problems Implemented in the Abaqus UEL Based on the Polygonal Scaled Boundary Finite Element Method

Abstract

The scaled boundary finite element method (SBFEM) is a semianalytical computational scheme based on the characteristics of the finite element method (FEM) and boundary element method that combines their respective advantages. In this paper, the SBFEM and polygonal mesh technique are integrated into a new approach to solve steady-state and transient seepage problems. The proposed method is implemented in Abaqus employing a user-defined element (UEL). A detailed implementation of the procedure is presented in which the UEL element is defined, the internal variables RHS and AMATRX are updated, and the stiffness/mass matrix is solved using eigenvalue decomposition. Several benchmark problems are solved to verify the proposed implementation. The results show that the polygonal element of the polygonal SBFEM (PSBFEM) is more accurate than the standard FEM element of the same element size. For transient problems, the results for the PSBFEM and FEM are in excellent agreement. Hence, the proposed method is robust and accurate for solving steady-state and transient seepage problems. The developed UEL source code and the associated input files can be downloaded from GitHub.

A PSBFEM Approach for Solving Seepage Problems Based on the Pixel Quadtree Mesh

“…In this study, we explore a seepage problem in a twodimensional domain, allowing us to derive the governing equations in the following manner [17,40]:…”

“…However, it should be emphasized that mesh generation would require a substantial increase in preprocessing time and the level of human intervention, particularly in instances where the stratigraphy comprises a complex array of intersecting material layers [15]. In seepage analyses, it is commonly assumed that soil layers exhibit homogeneity [16,17]. However, implementing such a method would require a substantial increase in both the preprocessing time and the level of human intervention, particularly in instances where the stratigraphy comprises a complex array of intersecting material layers.…”

“…The scaled boundary FEM (SBFEM) is a classical approach to handling the presence of hanging nodes on quadtree meshes [17,19]. The SBFEM integrates the beneficial aspects and properties of both the FEM and BEM, resulting in a unique semianalytical approach.…”

“…Therefore, the PSBFEM could use the quadtree mesh to solve the engineering problem of complex geometry efficiently. Few researchers have recently begun using the SBFEM to solve seepage problems [17,[37][38][39]. These works demonstrate that the SBFEM exhibits better accuracy and efficiency than the conventional FEM in solving seepage problems.…”

A novel solution for seepage problems using physics-informed neural networks

“…The BEM, in particular, relies on discretizing only the domain's boundaries, making it suitable for problems with infinite domains or those primarily influenced by boundary conditions. Yang et al (Yang et al 2021(Yang et al , 2022 solved the heat conduction problem and seepage problem through a new method that combines SBFEM with polygonal mesh technology. Lei et al (Lei et al 2022) proposed a new method that combines the smoothing finite element method (S-FEM) and gradient smoothing technology (GST) to solve the seepage free surface problem of earth-rock dams.…”