A stable node-based smoothed finite element method for stability analysis of two circular tunnels at different depths in cohesive-frictional soils

Vo-Minh, T.; Nguyen-Son, L.

doi:10.1016/j.compgeo.2020.103865

Cited by 26 publications

(14 citation statements)

References 31 publications

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“…As Figure 4A shows, their effect is limited, indicating that pure NI modification cannot totally stabilise the pore pressure. Figure 4B, C presents that in case 2, the results are reasonable with both 𝜀 𝑓 = 0 and 𝜀 𝑓 in Equation (48). PPP is unnecessary in the drained condition, because the permeability and drainage period are large enough to avoid triggering the numerical instability.…”

Section: D Terzaghi's Consolidationmentioning

confidence: 53%

“…It can be concluded that PPP solves the problem of spurious pressure oscillations effectively, although NI stabilisation could also help somewhat. This conclusion can also be supported by a related study, 39 in which the newly developed I‐NSPIM and I‐NSRPIM based on only the NI stabilisation strategy 46–49 are adopted. As Figure 4A shows, their effect is limited, indicating that pure NI modification cannot totally stabilise the pore pressure.…”

Section: Verification Of the Numerical Approachmentioning

confidence: 56%

“…39 For case 2 shown Figure 4B, another setting of t = 15 s, Δt = 0.02 s and k = 10 -4 m/s is adopted which is corresponding to the drained conditions. The value of PPP parameter 𝜀 𝑓 is determined by the Equation (48).…”

Section: D Terzaghi's Consolidationmentioning

confidence: 99%

“…Direct NI in NS-PFEM tends to incur the numerical instability due to spurious zero-energy mode, which comes from the violation of integration constraint conditions. 18,19,30,45 Recently, a stabilisation scheme based on a locally linear strain assumption was proposed and applied in several mechanical problems, [46][47][48][49] for which circle domains and quadrature points must be identified to allow gradient evaluation. Meanwhile, a similar approach of adding more stress points in the subdomains 30,45,50 is seemingly worth consideration when constructing a stabilised node-based smoothed particle finite element method (SNS-PFEM) method, because no extra evaluations of subdomain gradient is required in the 3-node triangulation interpolation (T3) scheme.…”

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

Num Anal Meth Geomechanics

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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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Section: D Terzaghi's Consolidationmentioning

confidence: 53%

Section: Verification Of the Numerical Approachmentioning

confidence: 56%

Section: D Terzaghi's Consolidationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 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

Num Anal Meth Geomechanics

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show abstract

“…At the same time, he proposed a series of smoothed FEMs [17]. It includes the point‐smoothed FEM node smoothed (NS‐FEM) [18], the edge‐smoothed FEM (ES‐FEM) [19] and the surface‐smoothed FEM (FS‐FEM) [20], which are formed by smooth operation of the constructed node smooth domain, edge‐smooth domain and surface‐smooth domain by gradient smoothing technique. Each of the three methods has advantages and disadvantages.…”

Section: Introductionmentioning

confidence: 99%

Calculation of 3D transient Eddy current by the face‐smoothed finite element–boundary element coupling method

Wang

Jiang

2020

High Voltage

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To calculate the distribution of the magnetic field and eddy current density on the surface of an aluminium plate, a method that couples the face‐smoothed finite element method (FS‐FEM) to the boundary element method (BEM) is proposed in this study. This method combines the advantages of the FS‐FEM and BEM, which can rapidly and accurately calculate the distributions of vertical magnetic field and eddy current field on the surface of an aluminium plate. The structural parameters and material properties of the coil and aluminium plate are considered. An accurate three‐dimensional calculation model is established. Then, the vertical magnetic field and eddy current field distributions are calculated in this study. In the case of the same grid density, compared with the finite element–boundary element coupling algorithm, the simulation results show that the FS‐FEM and the boundary element coupling method have obvious advantage in improving the calculation accuracy. The maximum relative error between the calculated results and measured results is only 4%. The proposed method in this study is available for reference to the transient open‐domain eddy current field analysis.

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

Liu,

Huang,

Gou

et al. 2023

Num Anal Meth Geomechanics

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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.

show abstract

A stable node-based smoothed finite element method for stability analysis of two circular tunnels at different depths in cohesive-frictional soils

Cited by 26 publications

References 31 publications

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

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

Calculation of 3D transient Eddy current by the face‐smoothed finite element–boundary element coupling method

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

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