Advertisement

Frontiers of Structural and Civil Engineering

, Volume 13, Issue 2, pp 337–352 | Cite as

A three-dimensional two-level gradient smoothing meshfree method for rainfall induced landslide simulations

  • Dongdong WangEmail author
  • Jiarui Wang
  • Junchao Wu
  • Junjun Deng
  • Ming Sun
Research Article
  • 43 Downloads

Abstract

A three-dimensional two-level gradient smoothing meshfree method is presented for rainfall induced landslide simulations. The two-level gradient smoothing for meshfree shape function is elaborated in the three-dimensional Lagrangian setting with detailed implementation procedure. It is shown that due to the successive gradient smoothing operation without the requirement of derivative computation in the present formulation, the two-level smoothed gradient of meshfree shape function is capable of achieving a given influence domain more efficiently than the standard gradient of meshfree shape function. Subsequently, the two-level smoothed gradient of meshfree shape function is employed to discretize the weak form of coupled rainfall seepage and soil motion equations in a nodal integration format, as provides an efficient three-dimensional regularized meshfree formulation for large deformation rainfall induced landslide simulations. The exponential damage and pressure dependent plasticity relationships are utilized to describe the failure evolution in landslides. The plastic response of soil is characterized by the true effective stress measure, which is updated according to the rotationally neutralized objective integration algorithm. The effectiveness of the present three-dimensional two-level gradient smoothing meshfree method is demonstrated through numerical examples.

Keywords

meshfree method landslide rainfall three-dimensional two-level gradient smoothing nodal integration 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The support of this work by the National Natural Science Foundation of China (Grant Nos. 11772280 and 11472233) and the Program for Scientific and Technological Innovation Leading Talents of Fujian Province is gratefully acknowledged.

References

  1. 1.
    Zienkiewicz O C, Taylor R L, Fox D D. The Finite Element Method for Solid and Structural Mechanics. 7th ed. Oxford: Butterworth-Heinemann, 2013Google Scholar
  2. 2.
    Lucy L B. A numerical approach to the testing of the fission hypothesis. Astronomical Journal, 1977, 82: 1013–1024Google Scholar
  3. 3.
    Gingold R A, Monaghan J J. Smoothed particle hydrodynamics: Theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society, 1977, 181(3): 375–389zbMATHGoogle Scholar
  4. 4.
    Liu M B, Liu G R. Smoothed particle hydrodynamics (SPH): An overview and recent developments. Archives of Computational Methods in Engineering, 2010, 17(1): 25–76MathSciNetzbMATHGoogle Scholar
  5. 5.
    Belytschko T, Lu Y Y, Gu L. Element-free Galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37(2): 229–256MathSciNetzbMATHGoogle Scholar
  6. 6.
    Liu W K, Jun S, Zhang Y F. Reproducing kernel particle methods. International Journal for Numerical Methods in Fluids, 1995, 20(8–9): 1081–1106MathSciNetzbMATHGoogle Scholar
  7. 7.
    Belytschko T, Lu Y Y, Gu L. Crack propagation by element-free Galerkin methods. Engineering Fracture Mechanics, 1995, 51(2): 295–315Google Scholar
  8. 8.
    Chen J S, Pan C, Wu C T, Liu W K. Reproducing kernel particle methods for large deformation analysis of non-linear structures. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1–4): 195–227MathSciNetzbMATHGoogle Scholar
  9. 9.
    Libersky L D, Randles P W, Carney T C, Dickinson D L. Recent improvements in SPH modeling of hypervelocity impact. International Journal of Impact Engineering, 1997, 20(6–10): 525–532Google Scholar
  10. 10.
    Liu W K, Jun S. Multiple-scale reproducing kernel particle methods for large deformation problems. International Journal for Numerical Methods in Engineering, 1998, 41(7): 1339–1362MathSciNetzbMATHGoogle Scholar
  11. 11.
    Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799MathSciNetzbMATHGoogle Scholar
  12. 12.
    Vidal Y, Bonet J, Huerta A. Stabilized updated Lagrangian corrected SPH for explicit dynamic problems. International Journal for Numerical Methods in Engineering, 2007, 69(13): 2687–2710MathSciNetzbMATHGoogle Scholar
  13. 13.
    Wang D, Li Z, Li L, Wu Y. Three dimensional efficient meshfree simulation of large deformation failure evolution in soil medium. Science China. Technological Sciences, 2011, 54(3): 573–580zbMATHGoogle Scholar
  14. 14.
    Ren B, Li S, Qian J, Zeng X. Meshfree simulations of spall fracture. Computer Methods in Applied Mechanics and Engineering, 2011, 200(5–8): 797–811MathSciNetzbMATHGoogle Scholar
  15. 15.
    Wu Y, Wang D, Wu C T. Three dimensional fragmentation simulation of concrete structures with a nodally regularized meshfree method. Theoretical and Applied Fracture Mechanics, 2014, 72: 89–99Google Scholar
  16. 16.
    Drathi R, Das A J M, Rangarajan A. Meshfree simulation of concrete structures and impact loading. International Journal of Impact Engineering, 2016, 91: 194–199Google Scholar
  17. 17.
    Wu C T, Wu Y, Crawford J E, Magallanes J M. Three-dimensional concrete impact and penetration simulations using the smoothed particle Galerkin method. International Journal of Impact Engineering, 2017, 106: 1–17Google Scholar
  18. 18.
    Atluri S N, Shen S P. The Meshless Local Petrov-Galerkin (MLPG) Method. Henderson: Tech Science Press, 2002zbMATHGoogle Scholar
  19. 19.
    Li S F, Liu W K. Meshfree Particle Methods. New York: Springer, 2004zbMATHGoogle Scholar
  20. 20.
    Zhang X, Liu Y. Meshless Methods. Beijing: Tsinghua University Press, 2004 (in Chinese)Google Scholar
  21. 21.
    Nguyen V P, Rabczuk T, Bordas S, Duflot M. Meshless methods: A review and computer implementation aspects. Mathematics and Computers in Simulation, 2008, 79(3): 763–813MathSciNetzbMATHGoogle Scholar
  22. 22.
    Liu G R. Meshfree Methods: Moving Beyond the Finite Element Method. 2nd ed. Boca Raton: CRC Press, 2009Google Scholar
  23. 23.
    Chen J S, Hillman M, Chi S W. Meshfree methods progress made after 20 years. Journal of Engineering Mechanics, 2017, 143(4): 04017001Google Scholar
  24. 24.
    Bui H H, Fukagawa R, Sako K, Wells J C. Slope stability analysis and discontinuous slope failure simulation by elasto-plastic smoothed particle hydrodynamics (SPH). Geotechnique, 2011, 61 (7): 565–574Google Scholar
  25. 25.
    Pastor M, Blanc T, Haddad B, Petrone S, Sanchez Morles M, Drempetic V, Issler D, Crosta G B, Cascini L, Sorbino G, Cuomo S. Application of a SPH depth-integrated model to landslide run-out analysis. Landslides, 2014, 11(5): 793–812Google Scholar
  26. 26.
    Hu M, Liu M B, Xie M W, Liu G R. Three-dimensional run-out analysis and prediction of flow-like landslides using smoothed particle hydrodynamics. Environmental Earth Sciences, 2015, 73 (4): 1629–1640Google Scholar
  27. 27.
    Dai Z, Huang Y. A three-dimensional model for flow slides in municipal solid waste landfills using smoothed particle hydrodynamics. Environmental Earth Sciences, 2016, 75(2): 132Google Scholar
  28. 28.
    Rabczuk T, Areias P M A. A new approach for modelling slip lines in geological materials with cohesive models. International Journal for Numerical and Analytical Methods in Geomechanics, 2006, 30 (11): 1159–1172zbMATHGoogle Scholar
  29. 29.
    Zheng W, Zhuang X, Tannant D, Cai Y, Nunoo S. Unified continuum/discontinuum modeling framework for slope stability assessment. Engineering Geology, 2014, 179: 90–101Google Scholar
  30. 30.
    Liu G, Zhuang X, Cui Z. Three-dimensional slope stability analysis using independent cover based numerical manifold and vector method. Engineering Geology, 2017, 225: 83–95Google Scholar
  31. 31.
    Dolbow J, Belytschko T. Numerical integration of the Galerkin weak form in meshfree methods. Computational Mechanics, 1999, 23(3): 219–230MathSciNetzbMATHGoogle Scholar
  32. 32.
    Chen J S, Hillman M, Rüter M. An arbitrary order variationally consistent integration for Galerkin meshfree methods. International Journal for Numerical Methods in Engineering, 2013, 95(5): 387–418MathSciNetzbMATHGoogle Scholar
  33. 33.
    Duan Q, Gao X, Wang B, Li X, Zhang H, Belytschko T, Shao Y. Consistent element free Galerkin method. International Journal for Numerical Methods in Engineering, 2014, 99(2): 79–101MathSciNetzbMATHGoogle Scholar
  34. 34.
    Hematiyan M R, Khosravifard A, Liu G R. A background decomposition method for domain integration in weak-form meshfree methods. Computers & Structures, 2014, 142: 64–78Google Scholar
  35. 35.
    Joldes G R, Wittek A, Miller K. Adaptive numerical integration in element-free Galerkin methods for elliptic boundary value problems. Engineering Analysis with Boundary Elements, 2015, 51: 52–63MathSciNetzbMATHGoogle Scholar
  36. 36.
    Wang D, Wu J. An efficient nesting sub-domain gradient smoothing integration algorithm with quadratic exactness for Galerkin meshfree methods. Computer Methods in Applied Mechanics and Engineering, 2016, 298: 485–519MathSciNetGoogle Scholar
  37. 37.
    Wei H, Chen J S, Hillman M. A stabilized nodally integrated meshfree formulation for fully coupled hydro-mechanical analysis of fluid-saturated porous media. Computers & Fluids, 2016, 141: 105–115MathSciNetzbMATHGoogle Scholar
  38. 38.
    Wu C T, Chi S W, Koishi M, Wu Y. Strain gradient stabilization with dual stress points for the meshfree nodal integration method in inelastic analyses. International Journal for Numerical Methods in Engineering, 2016, 107(1): 3–30MathSciNetzbMATHGoogle Scholar
  39. 39.
    Wu J, Deng J, Wang J, Wang D. A review of numerical integration approaches for Galerkin meshfree methods. Chinese Journal of Solid Mechanics, 2016, 37: 208–233 (in Chinese)Google Scholar
  40. 40.
    Beissel S, Belytschko T. Nodal integration of the element-free Galerkin method. Computer Methods in Applied Mechanics and Engineering, 1996, 139(1–4): 49–74MathSciNetzbMATHGoogle Scholar
  41. 41.
    Chen J S, Wu C T, Yoon S, You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering, 2001, 50(2): 435–466zbMATHGoogle Scholar
  42. 42.
    Chen J S, Yoon S P, Wu C T. Non-linear version of stabilized conforming nodal integration for Galerkin mesh-free methods. International Journal for Numerical Methods in Engineering, 2002, 53(12): 2587–2615zbMATHGoogle Scholar
  43. 43.
    Kwok O L A, Guan P C, Cheng W P, Sun C T. Semi-Lagrangian reproducing kernel particle method for slope stability analysis and post-failure simulation. KSCE Journal of Civil Engineering, 2015, 19(1): 107–115Google Scholar
  44. 44.
    Guan P C, Chen J S, Wu Y, Teng H, Gaidos J, Hofstetter K, Alsaleh M. Semi-Lagrangian reproducing kernel formulation and application to modeling earth moving operations. Mechanics of Materials, 2009, 41(6): 670–683Google Scholar
  45. 45.
    Lian Y, Zhang X, Liu Y. Coupling between finite element method and material point method for problems with extreme deformation. Theoretical and Applied Mechanics Letters, 2012, 2(2): 021003Google Scholar
  46. 46.
    Zhang X, Krabbenhoft K, Sheng D, Li W. Numerical simulation of a flow-like landslide using the particle finite element method. Computational Mechanics, 2015, 55(1): 167–177MathSciNetzbMATHGoogle Scholar
  47. 47.
    Belytschko T, Bažant Z P, Yul-Woong H, Ta-Peng C. Strainsoftening materials and finite-element solutions. Computers & Structures, 1986, 23(2): 163–180Google Scholar
  48. 48.
    Chen J S, Wu C T, Belytschko T. Regularization of material instabilities by meshfree approximations with intrinsic length scales. International Journal for Numerical Methods in Engineering, 2000, 47(7): 1303–1322zbMATHGoogle Scholar
  49. 49.
    Chen J S, Zhang X, Belytschko T. An implicit gradient model by a reproducing kernel strain regularization in strain localization problems. Computer Methods in Applied Mechanics and Engineering, 2004, 193(27–29): 2827–2844zbMATHGoogle Scholar
  50. 50.
    Askes H, Pamin J, de Borst R. Dispersion analysis and element-free Galerkin solutions of second-and fourth-order gradient-enhanced damage models. International Journal for Numerical Methods in Engineering, 2000, 49(6): 811–832zbMATHGoogle Scholar
  51. 51.
    Wang D, Li Z. A two-level strain smoothing regularized meshfree approach with stabilized conforming nodal integration for elastic damage analysis. International Journal of Damage Mechanics, 2013, 22(3): 440–459Google Scholar
  52. 52.
    Wang D, Li L, Li Z. A regularized Lagrangian meshfree method for rainfall infiltration triggered slope failure analysis. Engineering Analysis with Boundary Elements, 2014, 42: 51–59MathSciNetzbMATHGoogle Scholar
  53. 53.
    Rabczuk T, Belytschko T, Xiao S P. Stable particle methods based on Lagrangian kernels. Computer Methods in Applied Mechanics and Engineering, 2004, 193(12–14): 1035–1063MathSciNetzbMATHGoogle Scholar
  54. 54.
    Maxars J. Mechanical damage and fracture of concrete structures.In: Proceedings of the 5th International Conference of Fracture. Cannes, 1981, 4: 1499–1506Google Scholar
  55. 55.
    Simo J C, Ju J W. Strain-and stress-based continuum damage models—II. Computational aspects. International Journal of Solids and Structures, 1987, 23(7): 841–869zbMATHGoogle Scholar
  56. 56.
    Ju J W. On energy-based coupled elastoplastic damage theories: Constitutive modeling and computational aspects. International Journal of Solids and Structures, 1989, 25(7): 803–833zbMATHGoogle Scholar
  57. 57.
    Simo J C, Hughes T J R. Computational Inelasticity. New York: Springer, 1998zbMATHGoogle Scholar
  58. 58.
    Fredlund D G, Rahardjo H. Soil Mechanics for Unsaturated Soils. New York: John Wiley & Sons, 1993Google Scholar
  59. 59.
    Song X, Borja R I. Mathematical framework for unsaturated flow in the finite deformation range. International Journal for Numerical Methods in Engineering, 2014, 97(9): 658–682MathSciNetzbMATHGoogle Scholar
  60. 60.
    Cho S E, Lee S R. Instability of unsaturated soil slopes due to infiltration. Computers and Geotechnics, 2001, 28(3): 185–208Google Scholar
  61. 61.
    Borja R I, White J A. Continuum deformation and stability analyses of a steep hillside slope under rainfall infiltration. Acta Geotechnica, 2010, 5(1): 1–14Google Scholar
  62. 62.
    Jacquard C. Experimental study in laboratory of a capillary barrier. Dissertation for the Doctoral Degree. Paris: Ecole Mines Paris, 1988 (in French)Google Scholar
  63. 63.
    Bourgeois M. The concept of capillary barrier: Study by numerical model. Dissertation for the Doctoral Degree. Paris: Ecole Mines Paris, 1986 (in French)Google Scholar
  64. 64.
    Wei P, Xiao W. Area calculation of three dimensional polygon. Chinese Mathematics Bulletin, 1984, 2: 18–21 (in Chinese)Google Scholar
  65. 65.
    Wang D, Xie P, Lu H. Meshfree consolidation analysis of saturated porous media with stabilized conforming nodal integration formulation. Interaction and Multiscale Mechanics, 2013, 6(2): 107–125Google Scholar
  66. 66.
    Chi S W, Siriaksorn T, Lin S P. Von Neumann stability analysis of the u-p reproducing kernel formulation for saturated porous media. Computational Mechanics, 2017, 59(2): 335–357MathSciNetzbMATHGoogle Scholar
  67. 67.
    Kawamura S, Miura S, Ishikawa T, Yokohama S. Rainfall-induced failure of unsaturated volcanic slope subjected to freeze-thaw action and its mechanism. JSCE Journal of Geotechnical and Geoenvironmental Engineering, 2010, 66(3): 577–594Google Scholar
  68. 68.
    Li W C, Li H J, Dai F C, Lee L M. Discrete element modeling of a rainfall-induced flowslide. Engineering Geology, 2012, 149–150: 22–34Google Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Dongdong Wang
    • 1
    • 2
    Email author
  • Jiarui Wang
    • 1
  • Junchao Wu
    • 1
  • Junjun Deng
    • 1
  • Ming Sun
    • 1
  1. 1.Department of Civil Engineering and Xiamen Engineering Technology Center for Intelligent Maintenance of InfrastructuresXiamen UniversityXiamenChina
  2. 2.Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputationXiamen UniversityXiamenChina

Personalised recommendations