Investigation of Two‐Phase Hybrid Seepage Flux Finite Element Method for Seepage Analysis

ABSTRACT This study presents a new Hybrid Seepage flux Finite Element Method (HS‐FEM) for steady‐state seepage field problems, specifically focused on unconfined seepage through porous media. While conventional numerical methods (e.g., standard FEM, finite difference method) can accurately solve steady‐state seepage, they face challenges in handling free‐surface boundary conditions, such as mesh distortion or free surface traversing elements. The presented HS‐FEM requires only a single element for dam structures composed of homogeneous material, eliminating the need for extensive mesh refinement at interfaces as required by conventional FEM. The HS‐FEM assumes independent higher‐order seepage flux variables within element domains while prescribing hydraulic head on element boundaries. As the seepage flux field satisfies the governing equations, this approach establishes a two‐field HS‐FEM formulation using the seepage flux and boundary head as primary variables. The presented method constructs a higher‐order seepage flux field within element domains and employs an iterative discretization strategy for solving the free surface boundary. Through the combination of these two approaches, it achieves computational accuracy comparable to conventional dense‐mesh FEM while using significantly sparser discretization. Comparative analyses of five numerical examples with existing research results and MARC software demonstrate:(1) accurate determination of free surface positions, (2) excellent agreement in seepage flux distributions with MARC results, (3) enhanced sensitivity in capturing seepage flux discontinuities at material interfaces, and (4) optimizable hydraulic head distribution within element domains through either nodal refinement or higher‐order interpolation. These comprehensive validations confirm the effectiveness of the presented methodology.