Probabilistic Analysis and Design of Circular Tunnels against Face Stability

This paper presents a reliability-based approach for the three-dimensional analysis and design of the face stability of a shallow circular tunnel driven by a pressurized shield. Both the collapse and the blow-out failure modes of the ultimate limit state are studied. The deterministic models are based on the upper-bound method of the limit analysis theory. The collapse failure mode was found to give the most critical deterministic results against face stability and was adopted for the probabilistic analysis and design. 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 (1) the assumption of negative correlation between the soil shear strength parameters gives a greater reliability of the tunnel face stability with respect to the one of uncorrelated variables; (2) FORM approximation gives accurate results of the failure probability; and (3) the failure probability is much more influenced by the coefficient of variation of the angle of internal friction than that of the cohesion. Finally, a reliability-based design is performed to determine the required tunnel pressure for a target collapse failure probability.