Hybrid MPM–FEM with Multi-patch B-spline Basis Functions for Seepage and Piping Analysis

  • Suzuki, Yuta (Tohoku University)
  • Sugai, Riichi (Tohoku University)
  • Hidano, Soma (Tohoku University)
  • Nomura, Reika (Tohoku University)
  • Moriguchi, Shuji (Tohoku University)
  • Terada, Kenjiro (Tohoku University)

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Material point method (MPM) offers advantages in solid dynamics involving large deformations, where finite element method (FEM) would suffer from mesh distortion, and has been applied to numerical analysis of fluidized soils such as landslides. The MPM has also been extended to multi-phase problems involving pore fluid (water and air), and is now well-established as a numerical method for soil–water interaction problems. Hybrid MPM–FEM analyzes a two-phase continuous mixture consisting of a soil skeleton and a pore fluid based on Biot's mixture theory, using MPM for the solid phase and Eulerian FEM for the fluid phase. However, a trade-off remains: while B-spline basis functions mitigate the numerical instability known as cell-crossing error, they introduce difficulties in applying boundary conditions. In this study, we develop a multi-patch B-spline-based MPM that facilitates strict boundary condition imposition while maintaining higher-order continuity within patches. Although ordinary B-spline basis functions do not possess the Kronecker delta property at interior control points, the insertion of internal knots subdivides the original parametric domain into multiple patches, thereby enforcing this property at the expense of reducing inter-patch continuity to C0. By incorporating multi-patch B-spline basis functions into the hybrid MPM–FEM, analyses requiring the strict enforcement of boundary conditions on internal regions are enabled, such as those involving phenomena localized around thin slabs. Several numerical examples are presented to demonstrate the effectiveness of the proposed multiple patch strategy through hybrid MPM–FEM analyses, including seepage flow, soil heaving, and piping induced by the hydraulic head differences across a sheet pile embedded in soil.