Abstract
Notwithstanding its complexity in terms of numerical implementation and limitations in coping with problems involving extreme deformation, the finite element method (FEM) offers the advantage of solving complicated mathematical problems with diverse boundary conditions. Recently, a version of the particle finite element method (PFEM) was proposed for analyzing large-deformation problems. In this version of the PFEM, the finite element formulation, which was recast as a standard optimization problem and resolved efficiently using advanced optimization engines, was adopted for incremental analysis whilst the idea of particle approaches was employed to tackle mesh issues resulting from the large deformations. In this paper, the numerical implementation of this version of PFEM is detailed, revealing some key numerical aspects that are distinct from the conventional FEM, such as the solution strategy, imposition of displacement boundary conditions, and treatment of contacts. Additionally, the correctness and robustness of this version of PFEM in conducting failure and post-failure analyses of landslides are demonstrated via a stability analysis of a typical slope and a case study on the 2008 Tangjiashan landslide, China. Comparative studies between the results of the PFEM simulations and available data are performed qualitatively as well as quantitatively.
Highlights
As a widely found geophysical phenomenon, the term “landslide” refers to various mass movements on slopes, including rockfalls, topples, debris flows, etc. (Varnes 1978)
This paper focuses on the numerical implementation of a version of particle finite element method (PFEM) in which the finite element formulation is transformed into a second-order cone programming (SOCP-finite element method (FEM)), and on its application to failure and post-failure analysis of landslides
Based on the Hellinger–Reissner variational principle, the finite element formulation for static/dynamic elastoplastic analyses with interactions between deformable bodies and a rigid surface can be cast into equivalent optimization programs and resolved efficiently using available advanced optimization engines
Summary
As a widely found geophysical phenomenon, the term “landslide” refers to various mass movements on slopes, including rockfalls, topples, debris flows, etc. (Varnes 1978). The traditional Lagrangian FEM performs well for slope stability analysis, it cannot capture the motion and deposition stages, since severe mesh distortion is encountered when the sliding mass experiences large changes in geometry To tackle this issue, the particle finite element method (PFEM), which combines standard finite element analysis and a particle-based technique, was proposed by Idelsohn et al (2004). The PFEM developed by Oñate et al (2004) and by Cremonesi et al (2010) belongs to the first category that solves the resulting nonlinear finite element equations using a nested scheme based on Newton’s scheme or a variant thereof In this solution scheme, iterations are carried out between the level of global structures (where the unbalanced force is minimized) and the level of material points such as the stress integration points (where the stress–strain relationship is fulfilled). This work aims to contribute to fill these gaps with a twofold objective: (1) to detail the numerical implementation of the optimization-based PFEM to assist researchers from geoscience in developing their own version, and (2) to provide a quantitative comparison between the optimization-based PFEM and the techniques commonly adopted in geosciences to treat landslides, including both stability analysis and post-failure analysis
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