A stable node-based smoothed finite element method for stability analysis of two circular tunnels at different depths in cohesive-frictional soils

Abstract

This paper investigates the stability of two circular tunnels at different depths in cohesive-frictional soils subjected to surcharge loading using a stable node-based smoothed finite element method (SNS-FEM). In the present method, the numerical integration domains are approximately circular regions of the node-based smoothing domain by the node-based smoothed finite element method (NS-FEM). Four additional integration points are employed for each node to form the stabilization items associated with the variance of the smoothed shape function gradient. The tunnels are modelled under plane strain conditions, and the soil is described as a uniform Mohr-Coulomb material, and it obeys an associated flow rule. The stability numbers of two circular tunnels are obtained directly by solving the optimization problems. In this study, the effects of soil properties (γD/c), the ratio of tunnel diameter to its depth (H/D), the horizontal and vertical spacing ratio (S/D, L/D) and soil internal friction angle (ϕ) on the stability numbers (σs/c) are investigated. Several numerical results of two circular tunnels have been carried out showing that the proposed approach can demonstrate the efficiency and reliability solutions. Based on upper bound limit analysis using SNS-FEM, the results are presented in the form of design tables and charts for engineers to use.