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Stabilized smoothed particle finite element method for coupled large deformation problems in geotechnics

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Abstract

Smoothed particle finite element method has been gaining recognition as an appropriate approach for large deformation problems in geotechnics. This paper presents formulations for coupled large deformation problems in geotechnics within the framework of SPFEM. Emphasis is put on the incompressibility associated with the undrained limit. To stabilize the pore water pressure field, the polynomial pressure projection (PPP) formulations for SPFEM are derived. The accuracy and effectiveness of the present formulations are verified against several benchmark consolidation problems. Results show that spurious oscillations associated with the utilization of equal-order interpolants for both the solid displacement and the fluid pressure can be effectively avoided. The coupled SPFEM with PPP provides a stable and efficient numerical tool in solving coupled large deformation problems in geotechnics.

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References

  1. Arnold DN (1990) Mixed finite element methods for elliptic problems. Comput Methods Appl Mech Engrg 82:281–300

    MathSciNet  MATH  Google Scholar 

  2. Belytschko T, Organ D, Krongauz Y (1995) A coupled finite element-element-free Galerkin method. Comput Mech 17(3):186–195

    MathSciNet  MATH  Google Scholar 

  3. Bochev PB, Dohrmann CR, Gunzburger MD (2006) Stabilization of low-order mixed finite elements for the stokes equations. SIAM J Numer Anal 44(1):82–101

    MathSciNet  MATH  Google Scholar 

  4. Biot MA (1956) Theory of propagation of elastic waves in a fluid-saturated porous solid: I. Low-frequency range. J Acoust Soc Am 28(2):168–178

    MathSciNet  Google Scholar 

  5. Brezzi F, Bathe KJ (1990) A discourse on the stability conditions for mixed finite element formulations. Comput Methods Appl Mech Engrg 82(1):27–57

    MathSciNet  MATH  Google Scholar 

  6. Carbonell JM, Onate E, Suarez B (2010) Modeling of ground excavation with the particle finite element method. J Eng Mech-Asce 136(4):455–463

    Google Scholar 

  7. Carbonell JM, Onate E, Suarez B (2013) Modelling of tunnelling processes and rock cutting tool wear with the particle finite element method. Comput Mech 52(3):607–629

    MATH  Google Scholar 

  8. Chen JS, Wu CT, Yoon S et al (2001) A stabilized conforming nodal integration for Galerkin mesh-free methods. Int J Numer Methods Eng 50(2):435–466

    MATH  Google Scholar 

  9. Choo J, Borja RI (2015) Stabilized mixed finite elements for deformable porous media with double porosity. Comput Methods Appl Mech Engrg 293:131–154

    MathSciNet  MATH  Google Scholar 

  10. Choo J (2019) Stabilized mixed continuous/enriched Galerkin formulations for locally mass conservative poromechanics. Comput Methods Appl Mech Engrg 357:112568

    MathSciNet  MATH  Google Scholar 

  11. de-Pouplana I, O\(\check{n}\)ate E (2017) A FIC-based stabilized mixed finite element method with equal order interpolation for solid-pore fluid interaction problems. Int J Numer Anal Methods Geomech 41(1):110–134

  12. Della VG, Cremonesi M, Pisano F (2019) On the rheological characterisation of liquefied sands through the dam-breaking test. Int J Numer Methods Eng 43(7):1410–1425

    Google Scholar 

  13. Diebels S, Ehlers W (1996) Dynamic analysis of a fully saturated porous medium accounting for geometrical and material non-linearities. Int J Numer Methods Eng 39:81–97

    MATH  Google Scholar 

  14. Dohrmann CR, Bochev PB (2004) A stabilized finite element method for the Stokes problem based on polynomial pressure projections. Int J Numer Methods Fluids 46(2):183–201

    MathSciNet  MATH  Google Scholar 

  15. Dong YK, Cui L, Zhang X (2022) Multiple-GPU for three dimensional MPM based on single-root complex. Int J Numer Methods Eng 123:1481–1504

    Google Scholar 

  16. Fan N, Jiang JX, Dong YK et al (2022) Approach for evaluating instantaneous impact forces during submarine slide-pipeline interaction considering the inertial action. Ocean Eng 245:110466

    Article  Google Scholar 

  17. Franco B, Michel F (1991) Mixed and Hybrid Finite Element Methods. Springer series in computational mathematics, Springer, New York

    MATH  Google Scholar 

  18. Franci A, Cremonesi M, Perego U et al (2020) A lagrangian nodal integration method for free-surface fluid flows. Comput Methods Appl Mech Engrg 361:112816

    MathSciNet  MATH  Google Scholar 

  19. Franci A (2021) Lagrangian finite element method with nodal integration for fluid-solid interaction. Comput Part Mech 8(2):389–405

    Google Scholar 

  20. Gibson RE, England GL, Hussey MJL (1967) The theory of one-dimensional consolidation of saturated clays: 1. finite non-linear consildation of thin homogeneous layers. Géotechnique 17:261–273

    Google Scholar 

  21. Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Month Notices Royal Astron Soc 181(3):375–389

    MATH  Google Scholar 

  22. Guo N, Yang Z, Yuan WH et al (2021) A coupled SPFEM/DEM approach for multiscale modeling of large-deformation geomechanical problems. Int J for Numer Anal Met 45(5):648–667

    Google Scholar 

  23. Idelsohn SR, Onate E, Del Pin F et al (2003) A Lagrangian meshless finite element method applied to fluid-structure interaction problems. Comput Struct 81(8–11):655–671

    Google Scholar 

  24. Li B, Habbal F, Ortiz M (2010) Optimal transportation meshfree approximation schemes for fluid and plastic flows. Int J Numer Methods Eng 83(12):1541–1579

    MathSciNet  MATH  Google Scholar 

  25. Li B, Stalzer M, Ortiz M (2014) A massively parallel implementation of the optimal transportation meshfree method for explicit solid dynamics. Int J Numer Methods Eng 100(1):40–61

    MATH  Google Scholar 

  26. Liu GR, Dai KY, Nguyen TT (2007) A smoothed finite element method for mechanics problems. Comput Mech 39(6):859–877

    MATH  Google Scholar 

  27. Liu GR, Nguyen TT, Nguyen XH et al (2009) A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems. Comput Struct 87(2):14–26

    Google Scholar 

  28. Manoharan N, Dasgupta SP (1995) Consolidation analysis of elastoplastic soil. Comput Struct 54:1005–1021

    MATH  Google Scholar 

  29. Meng J, Zhang X, Utili S et al (2021) A nodal-integration based particle finite element method (N-PFEM) to model cliff recession. Geomorphology 381:107666

    Google Scholar 

  30. Monaghan JJ (1994) Simulating free surface flows with SPH. J Comput Phys 110(2):399–406

    MATH  Google Scholar 

  31. Monforte L, Carbonell JM, Arroyo M et al (2017) Performance of mixed formulations for the particle finite element method in soil mechanics problems. Comput Part Mech 4(3):269–284

    Google Scholar 

  32. Monforte L, Arroyo M, Carbonell JM et al (2017) Numerical simulation of undrained insertion problems in geotechnical engineering with the Particle Finite Element Method (PFEM). Comput Geotech 82:144–156

    Google Scholar 

  33. Monforte L, Arroyo M, Carbonell JM et al (2018) Coupled effective stress analysis of insertion problems in geotechnics with the Particle Finite Element Method. Comput Geotech 101:114–129

    Google Scholar 

  34. Monforte L, Navas P, Carbonell JM et al (2019) Low-order stabilized finite element for the full Biot formulation in soil mechanics at finite strain. Int J Numer Anal Methods Geomech 43:1–28

    Google Scholar 

  35. Monforte L, Arroyo M, Carbonell JM et al (2021) Large-strain analysis of undrained smooth tube sampling. Geotechnique 1-17

  36. Nazem M, Sheng D, Carter JP et al (2008) Arbitrary Lagrangian-Eulerian method for large-strain consolidation problems. Int J Numer Anal Methods Geomech 32:1023–1050

    MATH  Google Scholar 

  37. Navas P, Rena CY, López-Querol S et al (2016) Dynamic consolidation problems in saturated soils solved through u-w formulation in a LME meshfree framework. Comput Geotech 79:55–72

    Google Scholar 

  38. Navas P, Sanavia L, López-Querol S et al (2018) Explicit meshfree solution for large deformation dynamic problems in saturated porous media. Acta Geotechnica 13:227–242

    MATH  Google Scholar 

  39. O\(\check{n}\)ate E, Idelsohn SR, Del Pin F et al (2004) The particle finite element methodan overview. Int J Comput Methods 32(2):267–307

  40. O\(\check{n}\)ate E, Idelsohn SR, Celigueta MA et al (2011) Advances in the particle finite element method (PFEM) for solving coupled problems in engineering. Springer, Netherlands

  41. Pastor M, Li T, Liu X et al (2000) A fractional step algorithm allowing equal order of interpolation for coupled analysis of saturated soil problems. Mech Cohes-Frict Mater 5:511–534

    Google Scholar 

  42. Pastor M, Blanc T, Haddad B et al (2014) Application of a SPH depth-integrated model to landslide run-out analysis. Landslides 11(5):793–812

    Google Scholar 

  43. Pastor M, Yague A, Stickle M et al (2018) A two-phase SPH model for debris flow propagation. Int J Numer Anal Methods Geomech 42(3):418–448

    Google Scholar 

  44. Preisig M, Prevost JH (2011) Stabilization procedures in coupled poromechanics problems: a critical assessment. Int J Numer Anal Methods Geomech 35(3):1207–1225

    Google Scholar 

  45. Sabetamal H, Nazem M, Sloan SW et al (2016) Frictionless contact formulation for dynamic analysis of nonlinear saturated porous media based on the mortar method. Int J Numer Anal Meth Geomech 40:25–61

    Google Scholar 

  46. Sloan S, Abbo JA (1999) Biot consolidation analysis with automatic time stepping and error control part 1: theory and implementation. Int J Numer Anal Methods Geomech 23:467–492

    MATH  Google Scholar 

  47. Sloan S, Abbo JA (1999) Biot consolidation analysis with automatic time stepping and error control part 2: applications. Int J Numer Anal Methods Geomech 23:493–529

    MATH  Google Scholar 

  48. Sulsky D, Chen Z, Schreyer HL (1994) A particle method for history-dependent materials. Comput Method Appl M 118(1–2):179–196

    MathSciNet  MATH  Google Scholar 

  49. Sulsky D, Zhou SJ, Schreyer HL (1995) Application of a particle-in-cell method to solid mechanics. Comput Phys Commun 87(1–2):236–252

    MATH  Google Scholar 

  50. Sun WC, Ostien JT, Salinger A (2013) A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain. Int J Numer Anal Methods Geomech 37(16):2755–2788

    Google Scholar 

  51. Sun W (2015) A stabilized finite element formulation for monolithic thermo-hydro-mechanical simulations at finite strain. Int J Numer Meth Eng 103(11):798–839

    MathSciNet  MATH  Google Scholar 

  52. Vermeer PA, Verruijt A (1981) An accuracy condition for consolidation by finite elements. Int J Numer Anal Methods Geomech 5(1):1–14

    MathSciNet  MATH  Google Scholar 

  53. Wang D, Bienen B, Nazem M et al (2015) Large deformation finite element analyses in geotechnical engineering. Comput Geotech 65:104–114

    Google Scholar 

  54. Wang L, Zhang X, Zhang S et al (2021) A generalized Hellinger-Reissner variational principle and its PFEM formulation for dynamic analysis of saturated porous media. Comput Geotech 132:103994

    Google Scholar 

  55. White JA, Borja RI (2008) Stabilized low-order finite elements for coupled solid-deformation/fluid-diffusion and their application to fault zone transients. Comput Methods Appl Mech Engrg 197(49–50):4353–4366

    MATH  Google Scholar 

  56. Xie K, Leo CJ (2004) Analytical solutions of one-dimensional large strain consolidation of saturated and homogeneous clays. Comput Geotech 31(4):301–314

    Google Scholar 

  57. Yuan WH, Zhang W, Dai BB et al (2019) Application of the particle finite element method for large deformation consolidation analysis. Eng Comput 36:3138–3163

    Google Scholar 

  58. Yuan WH, Wang B, Zhang W et al (2019) Development of an explicit smoothedparticle finite element method for geotechnical applications. Comput Geotech 106:42–51

    Google Scholar 

  59. Yuan WH, Liu K, Zhang W et al (2020) Dynamic modeling of large deformation slope failure using smoothed particle finite element method. Landslides 17(2):1–13

    Google Scholar 

  60. Yuan WH, Wang HC, Zhang W et al (2021) Particle finite element method implementation for large deformation analysis using Abaqus. Acta Geotech 12:1–14

    Google Scholar 

  61. Yuan WH, Wang HC, Liu K et al (2021) Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method. J Zhejiang Univ Sci A 22:909–923

    Google Scholar 

  62. Yuan WH, Zhu JX, Liu K et al (2022) Dynamic analysis of large deformation problems in saturated porous media by smoothed particle finite element method. Comput Methods Appl Mech Engrg 392:114724

    MathSciNet  MATH  Google Scholar 

  63. Zhao Y, Choo J (2020) Stabilized material point methods for coupled large deformation and fluid flow in porous materials. Comput Method Appl Mech Eng 362:112742

    MathSciNet  MATH  Google Scholar 

  64. Zhang X, Krabbenhoft K, Pedroso DM et al (2013) Particle finite element analysis of large deformation and granular flow problems. Comput Geotech 54:133–142

    Google Scholar 

  65. Zhang X, Sheng DC, Sloan SW et al (2016) Second-order cone programming formulation for consolidation analysis of saturated porous media. Comput Mech 58(1):29–43

    MathSciNet  MATH  Google Scholar 

  66. Zhang W, Dai BB, Liu Z et al (2016) Modeling discontinuous rock mass based on smoothed finite element method. Comput Geotech 79:22–30

    Google Scholar 

  67. Zhang X, Krabbenhoft K, Sheng DC (2017) Lagrangian modelling of large deformation induced by progressive failure of sensitive clays with elastoviscoplasticity. Int J Numer Method Eng 112(8):963–989

    MathSciNet  Google Scholar 

  68. Zhang W, Dai BB, Liu Z et al (2018) Numerical algorithm of reinforced concrete lining cracking process for pressure tunnels. Eng Computations 35:91–107

    Google Scholar 

  69. Zhang W, Yuan WH, Dai BB (2018) Smoothed particle finite-element method for large-deformation problems in geomechanics. Int J Geome 18(4):4018010

    Google Scholar 

  70. Zhang X, Sloan SW, Onate E (2018) Dynamic modelling of retrogressive landslides with emphasis on the role of clay sensitivity. Int J Numer Analyt Method Geomech 42(15):1806–1822

    Google Scholar 

  71. Zhang X, Onate E, Torres SAG et al (2019) A unified Lagrangian formulation for solid and fluid dynamics and its possibility for modelling submarine landslides and their consequences. Comput Method Appl M 343:314–338

    MathSciNet  MATH  Google Scholar 

  72. Zhang W, Zou JQ, Zhang XW et al (2021) Interpretation of cone penetration test in clay with smoothed particlefinite element method. Acta Geotech 16:2593–2607

    Google Scholar 

  73. Zhang W, Zhong ZH, Peng C, et al (2021) GPU-accelerated smoothed particle finite element method for large deformation analysis in geomechanics. Comput Geotech 129:103856

    Article  Google Scholar 

  74. Zheng X, Pisano F, Vardon PJ et al (2021) An explicit stabilised material point method for coupled hydromechanical problems in two-phase porous media. Comput Geotech 135:104112

    Google Scholar 

  75. Zienkiewicz OC, Shiomi T (1984) Dynamic behaviour of saturated porous media: the generalized Biot formulation and its numerical solution. Int J Num Anal Geomech 8:71–96

    MATH  Google Scholar 

  76. Zienkiewicz OC, Chan AHC, Pastor M et al (1999) Computational Geomechanics. John Wiley, UK

    MATH  Google Scholar 

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Acknowledgements

The research is supported by the characteristic innovation project of Guangdong Provincial Department of Education (No. 2022KTSCX013), the Natural Science Foundation of China (No. 41807223, No. 41972285), the Fundamental Research Funds for the Central Universities (No. B210202096), the Natural Science Foundation of Guangdong Province (No. 2018A030310346), and the Water Conservancy Science and Technology Innovation Project of Guangdong Province (No. 2020-11).

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Authors and Affiliations

  1. College of Mechanics and Materials, Hohai University, Nanjing, 210098, China

    Wei-Hai Yuan & Ming Liu

  2. State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, 430071, China

    Xian-Wei Zhang

  3. College of Water Conservancy and Civil Engineering, South China Agricultural University, Guangzhou, 510642, China

    Hui-Lin Wang & Wei Zhang

  4. Institut für Geotechnik, Universität für Bodenkultur, Feistmantelstrasse 4, Vienna, 1180, Austria

    Wei Wu

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  1. Wei-Hai Yuan
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Yuan, WH., Liu, M., Zhang, XW. et al. Stabilized smoothed particle finite element method for coupled large deformation problems in geotechnics. Acta Geotech. 18, 1215–1231 (2023). https://doi.org/10.1007/s11440-022-01691-6

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