Meshless numerical manifold method with novel subspace tracking and CSS locating techniques for slope stability analysis

Abstract

The meshless numerical manifold method (MNMM) inherits the advantages of handling continuous and discontinuous problems uniformly, improving interpolation precision, and avoiding linear dependence issues. This paper refines the MNMM method for slope stability analysis to overcome the dependence and sensitivity of the strength reduction method of the finite element method on the number of finite element meshes and the algorithm for solving the nonlinear equations when calculating slopes with soft and weak interlayers. First, the strength reduction method (SRM) was incorporated into MNMM to create the numerical model called MNMM-SRM. Based on the MNMM-SRM, a complementary Mohr-Coulomb (M−C) control equation compliant with Koiter's rule of multi-yielding surfaces was established. In the principal stress space, the subspace tracking method was used to track the eigenvalues and eigenvectors of the stress tensor, thereby addressing the corner problem of M−C multi-yield surfaces. Combining the k-means clustering algorithm with wavelet transformation and employing the slope's total nodal displacement field as an input variable, an intelligent and efficient critical slip surface (CSS) automatic extraction method was developed. Three typical cases were used to validate the accuracy of the numerical model. This numerical model has a wide range of potential applications in slope stability research.