An improved node-based smoothed point interpolation method for coupled hydro-mechanical problems in geomechanics

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.

Section: Verification Of the Numerical Approachsupporting

confidence: 83%

Section: Hydro‐mechanical Coupled Sns‐pfemmentioning

confidence: 88%

Section: Verification Of the Numerical Approachmentioning

confidence: 97%

Section: Verification Of the Numerical Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Wang

Jin

Yin

et al. 2022

Augmenting low‐order finite element method with partial nodal strain smoothing for flow‐deformation analysis of geomechanical problems

Shafee

Khoshghalb

2022

Self Cite

In this study, the application of a numerical technique referred to as partial node-based smoothed finite element method (PNS-FEM) in flow-deformation analysis of problems in geomechanics is presented. The PNS-FEM is developed by augmenting the computation of the stiffness and permeability matrices of the domain in the linear finite element method (FEM) with partial nodal strain smoothing. The PNS-FEM takes advantage of contradicting errors of the solutions of the linear FEM and the node-based smooth point interpolation method (NSPIM) to yield close-to-exact solutions. The formulation of the PNS-FEM and the steps required to develop a PNS-FEM code from an FEM code are thoroughly presented. The performance of the PNS-FEM is then examined through five numerical examples concerning linear and nonlinear porous materials undergoing various types of loading. The results show that partial nodal smoothing is a very simple, yet effective, technique to considerably improve the performance of the linear FEM in coupled problems of geomechanics.

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

Liu,

Huang,

Gou

et al. 2023

The smoothed particle finite element method (SPFEM) is an effective framework for large deformation analysis. The original SPFEM possesses the rank deficiency issue due to the direct nodal integration technique, which can be overcome by incorporating the strain gradient stabilization method. However, an extra volumetric locking due to the strain gradient stabilization term has been found. In this study, we propose a simple and efficient approach, the B‐dev approach, which only considers the deviatoric part of the smoothed strain gradient for stabilization to overcome the volumetric locking issue. First, the correctness of the stabilized SPFEM method is verified by an elastic cantilever beam vibration problem without considering incompressibility. Then, through the example of the strip footing penetration problem, the volumetric locking in the stabilized SPFEM is demonstrated and the capability of the proposed B‐dev approach in terms of overcoming the volumetric locking is verified. Furthermore, the stabilized SPFEM with B‐dev approach is applied to two types of elastoplastic problems in geotechnical engineering. All numerical results illustrate that the proposed approach can improve the performance of the stabilized SPFEM in dealing with incompressible and large deformation problems in geomechanics.