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

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.

A novel stabilized nodal integration formulation using particle finite element method for incompressible flow analysis

“…A similar conclusion has emerged from dynamic analysis for elastic or elastoplastic materials (i.e., soft soil), where the smoother stress, pressure, and equivalent plastic strain fields have been obtained by the SNS-PFEM. 19,33 Such a spatial instability did not influence the calculation of the static problem by the implicit NS-PFEM but affected the dynamic analysis by the explicit NS-PFEM. 23 Figure 15 suggests that the conclusions from the solid mechanics are applicable in the incompressible flow analysis as well.…”

“…[28][29][30][31][32] The SNS-PFEM was then proposed by introducing the stabilized nodal integration into the framework of NS-PFEM for simulating geotechnical problems with large deformation. 19,33,34 Nevertheless, this algorithm has not been applied in fluid analysis.…”

Multiscale multiphysics modeling in geotechnical engineering

“…For geotechnical engineering, numerous applications involve multiscale and multiphysics processes, such as internal erosion, hydraulic fracturing, energy piles, municipal waste disposal, production from unconventional oil and gas reservoirs, heat stimulation and depressurization of natural gas hydrate formation, pavement subjected to heating-cooling cycles, contaminant transport, and CO 2 sequestration (Sun et al, 2018;Li et al, 2020;Shao et al, 2020;Yang et al, 2020Yang et al, , 2022Liu et al, 2021;Qian et al, 2021;Jin and Yin, 2022;Wang et al, 2022b). In the literature, the terminology "multiphysics" always implies two or more physical fields in the so-called thermo-hydro-mechanicalchemical-bio-electrical coupling.…”

Circumventing volumetric locking in stabilized smoothed particle finite element method and its application to dynamic large deformation problems

“…In comparison to PFEM, the main advantages of SPFEM include: (1) field variable mapping in PFEM is completely avoided; (2) free of volumetric locking; (3) higher computational efficiency due to low-order elements and fewer integration points; (4) more adaptive to mesh distortion. The SPFEM has so far been applied to the quasi-static problems in solid mechanics, 14 dynamic problems in geomechanics, 15,17 fluid dynamic problems, 18 fluid-solid interaction problems, 19,20 saturated porous media problems, [21][22][23] and multiscale coupled SPFEM/DEM modeling. 24 These studies have shown that SPFEM can provide promising results in solving large deformation problems.…”