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

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.