A meshfree large-deformation analysis method for geotechnical engineering based on the RBF field variable mapping technology

Abstract

In this paper, a practical meshfree large deformation method (MFLDM) is proposed for numerical analysis in geotechnical engineerings, including: soil foundation, slop, dam, etc. The MFLDM leverages both the flexible nodal distribution in the meshfree method and the high stability in the arbitrary Lagrangian–Eulerian (ALE) framework. In each calculation step, two sets of Gauss points, fixed and moving Gauss points, are generated in the background mesh. In addition, the radial basis function (RBF) is used to map field variables, including stress, stain, and constitutive variables, between the fixed and moving Gauss points to achieve the field variable redistribution during the large-deformation analysis. The proposed MFLDM, which is written in C++ using the object-oriented programming approach, can be completely integrated into the self-development calculating system named GEODYNA and coupled with the finite element method (FEM) at the matrix level, which significantly broadens its practical application. The proposed model is verified by several numerical examples and compared with different constitutive models, including the linear elasticity model, ideal elastic–plastic model, and generalized elastic–plastic model. The comparison results verify the high accuracy, fast convergence, and good robustness of the proposed MFLDM. Finally, the proposed MFLDM is applied to a local large deformation analysis between the cut-off wall and the core wall on a deep overburden.