A novel coupled NS‐PFEM with stable nodal integration and polynomial pressure projection for geotechnical problems

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Abstract
The node‐based smoothed particle finite element method (NS‐PFEM) offers high computational efficiency but is numerically unstable due to possible spurious low‐energy mode in direct nodal integration (NI). Moreover, the NS‐PFEM has not been applied to hydromechanical coupled analysis. This study proposes an implicit stabilised T3 element‐based NS‐PFEM (stabilised node‐based smoothed particle finite element method [SNS‐PFEM]) for solving fully hydromechanical coupled geotechnical problems that (1) adopts the stable NI based on multiple stress points over the smooth domain to resolve the NI instability of NS‐PFEM, (2) implements the polynomial pressure projection (PPP) technique in the NI framework to cure possible spurious pore pressure oscillation in the undrained or incompressible limit and (3) expresses the NI for assembling coefficient matrices and calculating internal force in SNS‐PFEM with PPP as closed analytical expressions, guaranteeing computational accuracy and efficiency. Four classical benchmark tests (1D Terzaghi's consolidation, Mandel's problem, 2D strip footing consolidation and foundation on a vertical cut) are simulated and compared with analytical solutions or results from other numerical methods to validate the correctness and efficiency of the proposed approach. Finally, penetration of strip footing into soft soil is investigated, showing the outstanding performance the proposed approach can offer for large deformation problems. All results demonstrate that the proposed SNS‐PFEM with PPP is capable of tracking hydromechanical coupled geotechnical problems under small and large deformation with different drainage capacities.

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