Application assessment of hybrid smoothed finite element method for geotechnical deformation and stability analysis

Abstract

In the node-based smoothed finite element method (NS-FEM), the unknowns including displacement, stress and strain are all stored at element nodes, contributing to good numerical accuracy and implementation convenience of the method. For the geotechnical deformation analyses, however, NS-FEM may cause the non-physically oscillated deformation. In this work, the cause of the non-physical geotechnical deformation behavior associated with NS-FEM is investigated, and it is found that the non-physical geotechnical deformation is attributed to unevenness of the assembled stiffness in NS-FEM. To obviate the non-physical geotechnical deformation problem, the hybrid smoothed finite element method (HS-FEM), as a combination of finite element method (FEM) and NS-FEM, is applied. Based on a flexible strip footing resting on the ground of weightless soil, a linear elastic medium with a circular cavity and a two-layered soil slope, the applicability of HS-FEM(α) with adequate parameter α to geotechnical deformation and stability analysis is validated.

Keywords

uneven stiffness / strip footing / slope stability / node-based smoothed finite element method / hybrid smoothed finite element method / strain energy

References

[1] SloanS W. Geotechnical stability analysis [J]. Géotechnique, 2013, 63(7): 531-571

[2] LiuG R, DaiK Y, NguyenT T. A smoothed finite element method for mechanics problems [J]. Computational Mechanics, 2007, 39(6): 859-877

[3] LiuG R, ChenL, Nguyen-ThoiT, et al. . A novel singular node-based smoothed finite element method (NS-FEM) for upper bound solutions of fracture problems [J]. International Journal for Numerical Methods in Engineering, 2010, 83(11): 1466-1497

[4] Nguyen-ThoiT, Vu-DoH C, RabczukT, et al. . A node-based smoothed finite element method (NS-FEM) for upper bound solution to visco-elastoplastic analyses of solids using triangular and tetrahedral meshes [J]. Computer Methods in Applied Mechanics and Engineering, 2010, 199(45–48): 3005-3027

[5] Nguyen-ThoiT, LiuG R, Nguyen-XuanH, et al. . Adaptive analysis using the node-based smoothed finite element method (NS-FEM) [J]. International Journal for Numerical Methods in Biomedical Engineering, 2011, 27(2): 198-218

[6] YuanW-h, WangB, ZhangW, et al. . Development of an explicit smoothed particle finite element method for geotechnical applications [J]. Computers and Geotechnics, 2019, 106: 42-51

[7] JinY-f, YinZ-y, ZhouX-w, et al. . A stable node-based smoothed PFEM for solving geotechnical large deformation 2D problems [J]. Computer Methods in Applied Mechanics and Engineering, 2021, 387: 114179

[8] MengJ-j, ZhangX, HuangJ-s, et al. . A smoothed finite element method using second-order cone programming [J]. Computers and Geotechnics, 2020, 123103547

[9] ChaiY-b, LiW, GongZ-x, et al. . Hybrid smoothed finite element method for two-dimensional underwater acoustic scattering problems [J]. Ocean Engineering, 2016, 116129-141

[10] PianT H H, WuC-chunHybrid and incompatible finite element methods [M], 2006, Boca Raton, Chapman & Hall/CRC

[11] FengH, CuiX Y, LiG Y. A stable nodal integration method with strain gradient for static and dynamic analysis of solid mechanics [J]. Engineering Analysis with Boundary Elements, 2016, 62: 78-92

[12] TimoshenkoS, GoodierJ NTheory of elasticity [M], 19703rd edition.New York, McGraw-Hill

[13] NaeiniS A, RabeB K, MahmoodiE. Bearing capacity and settlement of strip footing on geosynthetic reinforced clayey slopes [J]. Journal of Central South University, 2012, 19(4): 1116-1124

[14] WangL, ZhengG, OuR-nan. Finite element analysis of effect of soil displacement on bearing capacity of single friction pile [J]. Journal of Central South University, 2014, 21(5): 2051-2058

[15] WangD-y, ChenX, YuY-z, et al. . Stability and deformation analysis for geotechnical problems with nonassociated plasticity based on second-order cone programming [J]. International Journal of Geomechanics, 2019, 19(2): 1-13

[16] ChenX, WangD-y, YuY-z, et al. . A modified Davis approach for geotechnical stability analysis involving non-associated soil plasticity [J]. Géotechnique, 2020, 70(12): 1109-1119

[17] ChengY M, LansivaaraT, WeiW B. Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods [J]. Computers and Geotechnics, 2007, 34(3): 137-150

[18] ZienkiewiczO C, HumphesonC, LewisR W. Discussion: Associated and non-associated visco-plasticity and plasticity in soil mechanics [J]. Géotechnique, 1977, 27(1): 101-102

[19] ChenX, WuY-k, YuY-z, et al. . A two-grid search scheme for large-scale 3-D finite element analyses of slope stability [J]. Computers and Geotechnics, 2014, 62: 203-215

[20] WangD-y, ChenX, QiJ-l, et al. . Assessment on strength reduction schemes for geotechnical stability analysis involving the Drucker-Prager criterion [J]. Journal of Central South University, 2021, 28(10): 3238-3245