Probabilistic Analysis of the Face Stability of Circular Tunnels

Abstract

This paper presents a reliability-based approach for the three-dimensional analysis of the face stability of a shallow circular tunnel driven by a pressurized shield. Only the collapse failure mode of the ultimate limit state is studied. The deterministic model is based on the upper-bound method of the limit analysis theory. The random variables used are the soil shear strength parameters. The Hasofer-Lind reliability index and the failure probability were determined. A sensitivity analysis was also performed. It was shown that (i) the assumption of negative correlation between the soil shear strength parameters gives a greater reliability of the tunnel face against collapse, with respect to the hypothesis of uncorrelated variables, (ii) the failure probability is much more influenced by the coefficient of variation of the angle of internal friction than that of the cohesion and (iii) when no correlation between shear strength parameters is considered, a more spread out CDF of the tunnel pressure was obtained in comparison to the case of correlated shear strength parameters.