Upper-bound stability analysis of dual unlined horseshoe-shaped tunnels subjected to gravity

This study investigates the stability of dual horseshoe-shaped tunnels in cohesive-frictional soils subjected to gravity using an upper-bound finite element method combined with a plastic-dissipation-based mesh adaptive strategy. The results are presented in the form of dimensionless stability numbers, which decrease with C/D and increase with phi. The results indicate that the interaction between dual horseshoe-shaped tunnels disappears when their dimensionless center-to-center distance S/D lies approximately in any of the following ranges for C/D: (i) 3.5-4.5 for C/D = 1, (ii) 3.5-6.5 for C/D = 2, (iii) 3.5-9 for C/D = 3, (iv) 4-11 for C/D = 4, and (v) 4-13.5 for C/D = 5.