Undrained Stability of Dual Circular Tunnels

Abstract

In this paper, numerical limit analysis and semianalytical rigid block techniques are used to investigate the effect of the tunnel spacing on the stability of two circular tunnels excavated side by side. The tunnels are modeled under plane-strain conditions, which implies that they are assumed to be infinitely long. Bounds on the stability of the tunnels are obtained using finite-element limit analysis, the numerical formulation of which is based on the upper and lower bounds theorems of classical plasticity. Solutions are obtained using advanced conic programming schemes to solve the resulting optimization problems, and upper and lower bound estimates on the stability of the tunnels are obtained for a range of geometries. These bounds, which bracket the true collapse load from above and below, are found to differ by at most 5% for the cases where the solution does not approach zero. Results from this study are summarized in stability charts for use by practitioners.