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

Jianguo Li, Bin Wang*, Quan Jiang, Benguo He, Xue Zhang, Philip J. Vardon

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)
35 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)2059-2077
Number of pages19
JournalActa Geotechnica
Issue number6
Publication statusPublished - 2021

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Alpha shape method
  • Cartesian transformation method
  • Geotechnical engineering
  • Large deformation
  • Radial point interpolation method


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