A node-based Smoothed Finite Element Method for Stability Analysis of Dual Square Tunnels in Cohesive-frictional Soils

Document Type: Article


1 Department of Civil Engineering, Ho Chi Minh City University of Technology, HCMUT, Vietnam

2 Department of Civil Engineering, HCMC University of Technology, Hutech, Vietnam


This paper presents an upper bound limit analysis procedure using the node-based smoothed finite element method (NS-FEM) and second order cone programming (SOCP) to evaluate the stability of dual square tunnels in cohesive-frictional soils subjected to surcharge loading. The displacement field of the tunnel problems is approximated by using NS-FEM triangular elements (NS-FEM-T3). Next, commercial software Mosek is employed to deal with optimization problems, which are formulated as second order cone. Collapse loads and failure mechanisms of dual square tunnels were performed by solving the optimization problems with a series of size-to-depth ratios and soil properties. For dual square tunnels, the distance between centers of two parallel tunnels is the major parameter used to determine the stability. In this study, surcharge loading is applied to the ground surface and drained conditions are considered. Numerical results are verified with those available to demonstrate the accuracy of the proposed method.


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