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Seepage analysis using a polygonal cell-based smoothed finite element method

Yang Yang, Mingjiao Yan, Zongliang Zhang, Yinpeng Yin, Qiang Liu, You-liang Li

TL;DR

The paper develops a polygonal CSFEM for seepage in saturated porous media by integrating Wachspress polygonal interpolation with cell-based gradient smoothing, enabling boundary-integral assembly and improved mesh flexibility. A fixed-mesh, solution-driven adaptive framework with hybrid quadtree–polygonal discretizations efficiently captures sharp gradients and moving wet–dry interfaces, while maintaining robustness on distorted meshes. Validation across patch tests, steady-state, transient, and free-surface seepage problems shows accuracy comparable to conventional FEM with substantially fewer degrees of freedom and reduced CPU time, especially when adaptivity is employed. The approach offers a practical, robust tool for geotechnical applications involving complex geometries and evolving seepage fronts.

Abstract

This work develops a polygonal cell-based smoothed finite element method for steady-state, transient, and free-surface seepage in saturated porous media. Wachspress interpolation on convex polygonal elements is combined with cell-based gradient smoothing, so that element matrices are assembled using boundary integrals without in-element derivatives. Polygonal, quadtree, and hybrid quadtree--polygonal meshes are employed to accommodate local refinement and hanging nodes, and a solution-driven adaptive strategy further concentrates resolution near steep gradients and wet--dry transitions. Free-surface seepage is solved using a fixed-mesh iterative scheme that updates the wetted region, permeability field, and boundary conditions. Benchmark tests demonstrate accurate hydraulic-head and free-surface predictions, and show that adaptivity attains similar accuracy with substantially fewer degrees of freedom and CPU time.

Seepage analysis using a polygonal cell-based smoothed finite element method

TL;DR

The paper develops a polygonal CSFEM for seepage in saturated porous media by integrating Wachspress polygonal interpolation with cell-based gradient smoothing, enabling boundary-integral assembly and improved mesh flexibility. A fixed-mesh, solution-driven adaptive framework with hybrid quadtree–polygonal discretizations efficiently captures sharp gradients and moving wet–dry interfaces, while maintaining robustness on distorted meshes. Validation across patch tests, steady-state, transient, and free-surface seepage problems shows accuracy comparable to conventional FEM with substantially fewer degrees of freedom and reduced CPU time, especially when adaptivity is employed. The approach offers a practical, robust tool for geotechnical applications involving complex geometries and evolving seepage fronts.

Abstract

This work develops a polygonal cell-based smoothed finite element method for steady-state, transient, and free-surface seepage in saturated porous media. Wachspress interpolation on convex polygonal elements is combined with cell-based gradient smoothing, so that element matrices are assembled using boundary integrals without in-element derivatives. Polygonal, quadtree, and hybrid quadtree--polygonal meshes are employed to accommodate local refinement and hanging nodes, and a solution-driven adaptive strategy further concentrates resolution near steep gradients and wet--dry transitions. Free-surface seepage is solved using a fixed-mesh iterative scheme that updates the wetted region, permeability field, and boundary conditions. Benchmark tests demonstrate accurate hydraulic-head and free-surface predictions, and show that adaptivity attains similar accuracy with substantially fewer degrees of freedom and CPU time.
Paper Structure (19 sections, 36 equations, 24 figures, 6 tables, 1 algorithm)

This paper contains 19 sections, 36 equations, 24 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Theoretical formulation of the polygonal CSFEM for seepage problems
  3. Smoothed gradient in a polygonal element
  4. Element stiffness and capacity matrices
  5. Polygonal interpolation using Wachspress basis functions
  6. Free-surface solutions
  7. Numerical examples
  8. Patch test
  9. Steady-state seepage analysis
  10. Foundation of a concrete dam
  11. Permeable media
  12. Transient seepage analysis
  13. Dam foundation with irregular geometry
  14. Transient seepage analysis for complex geometry
  15. Free-surface seepage problems
  16. ...and 4 more sections

Figures (24)

  • Figure 1: Geometry and boundary conditions for the cubic seepage model.
  • Figure 2: Geometry and mesh models of the patch test: (a) geometry and boundary conditions; (b) polygonal mesh; (c) quadtree mesh.
  • Figure 3: Hydraulic head distribution for the patch test: (a) polygonal mesh; (b) quadtree mesh; (c) exact solution.
  • Figure 4: Geometry and boundary conditions of the concrete dam.
  • Figure 5: Mesh models of the dam foundation: (a) FEM mesh; (b) CSFEM mesh.
  • ...and 19 more figures