Upper bound analysis of stability of dual circular tunnels subjected to surcharge loading in cohesive-frictional soils

The stability of dual circular tunnels subjected to surcharge loading in cohesive-frictional soils, obeying the Mohr-Coulomb failure criterion, is determined by an upper bound finite element method combined with rigid translatory moving elements (UBFEM-RTME). The stability results, which are considered to be influenced by the soil internal friction angle (ϕ), ratio of the tunnel cover to the tunnel diameter (C/D), ratio of the tunnels' center-to-center distance to the tunnel diameter (S/D), and ratio of the product of the soil unit weight and the tunnel diameter to the soil cohesion (γD/c), are presented in the form of dimensionless stability numbers (σs/c) and failure mechanisms. The results reveal that the values of stability numbers decrease continuously with increasing γD/c and increase with increasing C/D, S/D, and ϕ, except in the cases of moderate depth and close proximity. Most of the obtained failure mechanisms are constituted by two wedge-shaped areas composed of two groups of crossed slip lines and a complete rigid area. The results of this study compare reasonably well with the solutions reported in the literature.