This paper investigates the stability of a plain strain circular tunnel in an undrained clay. Using finite element limit analysis, upper and lower bounds on the stability of the tunnel are determined for a range of tunnel geometries and soil conditions. These results are verified using semi-analytical rigid block upper bound methods. The numerical formulation of the finite element limit analysis techniques are based upon the upper and lower bounds theorems of classical plasticity. Solutions, that provide upper and lower bounds on the true collapse loads, are obtained using advanced conic programming schemes to solve the resulting optimisation problems. Results from this study, in which the two bounds differ by at most 5%, are summarised in the form of stability charts. Finally, an expression that approximates the undrained stability of a circular tunnel has been formulated for use by practicing engineers.
2nd International Conference on Computational Methods in Tunnelling (EURO:TUN 2009). EURO:TUN 2009 Computational Methods in Tunnelling: Proceedings of the Second International Conference on Computational Methods in Tunnelling (Ruhr University Bochum 9-11 September, 2009) p. 857-864