A sixfold-path discontinuity topology with through-type triangular mesh: Numerical implementation in the upper-bound finite element method

Yang, Feng; Qin, Aohan; Zheng, Xiangcou; Ding, Zhanheng; Osman, Ashraf

Abstract

Given the complementary strengths of plastic elements and velocity discontinuities in capturing characteristics such as plastic zones and slip surfaces, the mesh topology structure becomes a critical factor in influencing the accuracy of the analysis. This study proposes a sixfold-path discontinuity topology structure integrated with a uniform through-type triangular mesh. Serving as the foundation, the initial triangular mesh is conceptualized as a truss and iteratively refined through nodal position adjustments to achieve enhanced mesh regularity and boundary conformity. Subsequently, each element in the uniform mesh is subdivided into six segments using the element’s centroid and its edge midpoints. Leveraging the proposed energy dissipation density factor and discontinuity-based dissipation proportion, numerical validations across diverse scenarios, including slope stability, bearing capacity of slope foundations, and strip footing above asymmetric square dual-voids, demonstrate the superior performance in identifying failure mechanisms dominated by single slip surfaces, coexisting plastic zones and slip surfaces, and multiple slip surfaces. Notably, the sixfold discontinuity path effectively aligns with potential slip surface orientations, thereby improving computational accuracy and reducing computational costs. Moreover, based on stable convergence properties of the uniform meshes, multiple predictive equations for upper-bound solutions of stability coefficients are proposed.

Citation

Yang, F., Qin, A., Zheng, X., Ding, Z., & Osman, A. (2025). A sixfold-path discontinuity topology with through-type triangular mesh: Numerical implementation in the upper-bound finite element method. Computers and Geotechnics, 187, 107453. https://doi.org/10.1016/j.compgeo.2025.107453

• Journal Article Type: Article
• Acceptance Date: Jun 24, 2025
• Online Publication Date: Jul 8, 2025
• Publication Date: 2025-11
• Deposit Date: Jul 16, 2025
• Journal: Computers and Geotechnics
• Print ISSN: 0266-352X
• Electronic ISSN: 1873-7633
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 187
• Pages: 107453
• DOI: https://doi.org/10.1016/j.compgeo.2025.107453
• Public URL: https://durham-repository.worktribe.com/output/4264285