Three dimensional seepage analysis using a polyhedral scaled boundary finite element method

Abstract

This work presents a polyhedral scaled boundary finite element method (PSBFEM) for three dimensional seepage analysis. We first derive the scaled boundary formulation for 3D seepage problems, and subsequently incorporate Wachspress shape functions to construct shape functions over arbitrary polygonal elements, thereby establishing the foundation of the proposed polyhedral SBFEM. The method combines the semi-analytical nature of the SBFEM with the geometric flexibility of polyhedral and octree meshes, making it well-suited for complex seepage simulations. The PSBFEM is implemented within the ABAQUS UEL framework to facilitate steady-state, transient, and free-surface seepage analyses. A series of numerical examples are conducted to verify the accuracy, efficiency, and convergence properties of the proposed approach, including benchmark tests and applications with intricate geometries. The results demonstrate that the PSBFEM achieves higher accuracy and faster convergence than conventional FEM, particularly when using hybrid octree meshes with local refinement. This framework provides a robust and efficient computational tool for three-dimensional seepage analysis in geotechnical and hydraulic engineering applications.