Three-dimensional face stability analysis of twin circular tunnels in double-layered soil based on semidefinite programming of adaptive node-based smoothed upper bound finite element limit analysis

A novel and efficient computational method, adaptive three-dimensional node-based smoothed upper bound finite element limit analysis (adaptive 3D NS-UBFELA), is proposed in this study. The node-based strain smoothing technique is integrated into the semidefinite programming formulation of 3D UBFELA with the Mohr–Coulomb criterion to improve accuracy while ensuring efficiency of linear tetrahedral elements. An adaptive mesh refinement strategy is also introduced, using volumetric strain rate as an error indicator and Octasection refinement to locally refine elements. Validation through three benchmark examples confirms the accuracy, robustness, and efficiency of the proposed method. The method is further applied to analyze a new problem: the face stability of horizontal and vertical twin circular tunnels in double-layered soils. Results show that tunnel interaction effects, soil strength parameters, and cover depth significantly influence the minimal support pressure, safety factor, and overall stability of tunnel faces.