Skip to main content
SpringerLink
Log in

Development of an adaptive CTM–RPIM method for modeling large deformation problems in geotechnical engineering

  • Research Paper
  • Published:
Acta Geotechnica Aims and scope Submit manuscript

Abstract

In this paper, a meshfree method called adaptive CTM–RPIM is developed to model geotechnical problems with large deformation. The developed adaptive CTM–RPIM is a combination of the Cartesian transformation method (CTM), the radial point interpolation method (RPIM) and the alpha shape method. To reduce the requirement for meshes, the CTM is adopted to transform domain integrals into line integrals, and the RPIM is applied to construct interpolation functions. The alpha shape method, which is capable of capturing severe boundary evolution due to large deformations, is then introduced into the CTM–RPIM to form the adaptive CTM–RPIM. The accuracy of CTM–RPIM is first verified by considering a cantilever beam under small deformation, where the influence of key parameters on the simulation results is explored. Afterward, the ability of the adaptive CTM–RPIM to handle large deformation problems is demonstrated by simulating cantilever beams with large deformations for which analytical solutions are available. Finally, the ability of the proposed method to model the geotechnical large deformations is illustrated from both quasi-static and dynamic aspects, where a slope failure problem and a footing bearing capacity problem are modeled to evaluate the stability of geotechnical structures; and a 2-D soil collapse experiment using small aluminum bars is simulated to show the method capability in describing the soil flows. These benchmark examples demonstrate that the adaptive CTM–RPIM is a numerical method with broad application prospects for modeling large deformation problems in geotechnical engineering.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28

Similar content being viewed by others

References

  1. Abdollahifar A, Nami MR, Shafiei AR (2012) A new MLPG method for elastostatic problems. Eng Anal Bound Elem 36(3):451–457

    Article  MathSciNet  Google Scholar 

  2. Ákos T, Arpad B, Gyula B, Tamas L, Arpad S, Péter G (2018) Slope stability and rockfall assessment of volcanic tuffs using RPAS with 2-D FEM slope modelling. Nat Hazard Earth Sys 18(2):583–597

    Article  Google Scholar 

  3. Alba Y, Eduardo A, Núria P (2015) The material point method for unsaturated soils. Géotechnique 65(3):201–217

    Article  Google Scholar 

  4. Amir K, Hematiyan M (2010) A new method for meshless integration in 2-D and 3-D Galerkin meshfree methods. Eng Anal Bound Elem 34:30–40

    Article  MathSciNet  Google Scholar 

  5. Bishop AW, Morgenstern NR (1960) Stability coefficients for earth slopes. Géotechnique 10(4):129–147

    Article  Google Scholar 

  6. Bui HH, Fukagawa R, Sako K, Ohno S (2010) Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic-plastic soil constitutive mode. Int J Numer Anal Met 32(12):1537–1570

    Article  Google Scholar 

  7. Cheng L, Liu YR, Yang Q, Pan YW, Lv Z (2017) Mechanism and numerical simulation of reservoir slope deformation during impounding of high arch dams based on nonlinear FEM. Comput Geotech 81:143–154

    Article  Google Scholar 

  8. Cruden DM (1991) A simple definition of a landslide. B Eng Geol Environ 43:27–29

    Google Scholar 

  9. Gu YT (2011) An enriched radial point interpolation method based on weak-form and strong-form. Mech Adv Mater Struct 18(8):578–584

    Article  Google Scholar 

  10. Hematiyan M, Amir K, Liu GR (2014) A background decomposition method for domain integration in weak-form meshfree methods. Compute Struct 142:64–78

    Article  Google Scholar 

  11. Hungr O, Leroueil S, Picarelli L (2014) The Varnes classification of landslide types, an update. Landslides 11(2):167–194

    Article  Google Scholar 

  12. Jameel A, Harmain GA (2015) Fatigue crack growth in presence of material discontinuities by EFGM. Int J Fatigue 81:105–116

    Article  Google Scholar 

  13. Jin YF, Yin ZY, Yuan WH (2020) Simulating retrogressive slope failure using two different smoothed particle finite element methods: a comparative study. Eng Geol 279:105870

    Article  Google Scholar 

  14. John N (2013) Modeling imperfect interfaces in the material point method using multimaterial methods. Cmes Comp Model Eng 92(3):271–299

    MathSciNet  Google Scholar 

  15. Li Y, Liu GR, Yue J (2018) A novel node-based smoothed radial point interpolation method for 2-D and 3-D solid mechanics problems. Comput Struct 196:157–172

    Article  Google Scholar 

  16. Lian YP, Zhang X, Liu Y (2012) An adaptive finite element material point method and its application in extreme deformation problems. Comput Method Appl M 241–24:275–285

    Article  Google Scholar 

  17. Liu GR, Yan L, Wang JG, Gu YT (2002) Point interpolation method based on local residual formulation using radial basis functions. Struct Eng Mech 14(6):713–732

    Article  Google Scholar 

  18. Locat A, Leroueil S, Bernander S, Demers D, Jostad HP, Ouehb L (2011) Progressive failures in eastern Canadian and Scandinavian sensitive clays. Can Geotech J 48(11):1696–1712

    Article  Google Scholar 

  19. Ma YC, Su PD, Li YG (2020) Three-dimensional nonhomogeneous slope failure analysis by the strength reduction method and the local strength reduction method. Arab J Geosci 13(2):1–7

    Google Scholar 

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

    Article  Google Scholar 

  21. Meral G, Tezer-Sezgin M (2010) DRBEM solution of exterior nonlinear wave problem using FDM and LSM time integrations. Eng Anal Bound Elem 34(6):574–580

    Article  MathSciNet  Google Scholar 

  22. Monforte L, Arroyo M, Carbonell JM, Gens A (2017) Numerical simulation of undrained insertion problems in geotechnical engineering with the particle finite element method (PFEM). Comput Geotech 82:144–156

    Article  Google Scholar 

  23. Pai PF, Palazotto AN (1996) Large-deformation analysis of flexible beams. Int J Solids Struct 33(9):1335–1370

    Article  Google Scholar 

  24. Pant M, Singh IV, Mishra BK (2011) Evaluation of mixed mode stress intensity factors for interface cracks using EFGM. App Math Model 35(7):3443–3459

    Article  MathSciNet  Google Scholar 

  25. Prandtl L (1920) Über die Härte plastischer Körper. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen Mathematisch-physikalische Klasse 1920:74–85

    Google Scholar 

  26. Rao X, Cheng LS, Cao RY, Jiang J, Li N, Fang SD, Jia P, Wang LZ (2018) A novel green element method by mixing the idea of the finite difference method. Eng Anal Bound Elem 95:238–247

    Article  MathSciNet  Google Scholar 

  27. Stephen B, Ted B (1996) Nodal integration of the element-free Galerkin method. Comput Method Appl M 139:49–74

    Article  MathSciNet  Google Scholar 

  28. Tinesh P, Andrea B-B, Rastogi A, Eldho TI (2019) Simulation of groundwater flow in an unconfined sloping aquifer using the element-free galerkin method. Water Resour Manag 33(2):2827–2845

    Google Scholar 

  29. Xu DD, Yang YT, Zheng H, Wu AQ (2017) A high order local approximation free from linear dependency with quadrilateral mesh as mathematical cover and applications to linear elastic fractures. Compute Struct 178:1–16

    Article  Google Scholar 

  30. Yang YT, Sun GH, Zheng H, Fu XD (2016) A four-node quadrilateral element fitted to numerical manifold method with continuous nodal stress for crack analysis. Compute Struct 177:69–82

    Article  Google Scholar 

  31. Zahra K, Hematiyan M, Reza V (2017) Meshfree radial point interpolation method for analysis of viscoplastic problems. Eng Anal Bound Elem 82:172–184

    Article  MathSciNet  Google Scholar 

  32. Zhang X, Krabbenhoft K, Pedroso DM, Lyamin AV, Sheng D, da Silva MV, Wang D (2013) Particle finite element analysis of large deformation and granular flow problems. Comput Geotechn 54:133–142

    Article  Google Scholar 

  33. Zhang W, Yuan WH, Dai BB (2018) Smoothed particle finite-element method for large-deformation problems in geomechanics. Int J Geomech 18(4):04018010

    Article  Google Scholar 

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

    Article  Google Scholar 

  35. Zhao GF (2014) Development of the distinct lattice spring model for large deformation analyses. Int J Numer Anal Met 38:1078–1100

    Article  Google Scholar 

Download references

Acknowledgements

The authors wish to acknowledge the National Natural Science Foundation of China (Grant Nos. 51979270 and 51709258) and the CAS Pioneer Hundred Talents Program for their financial support.

Author information

Authors and Affiliations

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

    Jianguo Li, Bin Wang & Quan Jiang

  2. University of Chinese Academy of Sciences, Beijing, China

    Jianguo Li, Bin Wang & Quan Jiang

  3. Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines, Northeastern University, Shenyang, China

    Benguo He

  4. Department of Civil Engineering and Industrial Design, University of Liverpool, Liverpool, UK

    Xue Zhang

  5. Geo-Engineering Section, Delft University of Technology, Delft, The Netherlands

    Philip J. Vardon

Authors
  1. Jianguo Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Quan Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Benguo He
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xue Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Philip J. Vardon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Bin Wang or Quan Jiang.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, J., Wang, B., Jiang, Q. et al. Development of an adaptive CTM–RPIM method for modeling large deformation problems in geotechnical engineering. Acta Geotech. 17, 2059–2077 (2022). https://doi.org/10.1007/s11440-021-01416-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11440-021-01416-1

Keywords

Search

Navigation