The aim of this paper is to determine the face collapse pressure of a circular tunnel driven by a pressurized shield. The analysis is performed in the framework of the kinematical approach of limit analysis theory. It is based on a translational three-dimensional multiblock failure mechanism. The present failure mechanism has a significant advantage with respect to the existing limit analysis mechanisms developed in the case of a frictional soil: it takes into account the entire circular tunnel face and not only an inscribed ellipse to this circular area. This was made possible by the use of a spatial discretization technique. Hence, the three-dimensional failure surface was generated “point by point” instead of simple use of existing standard geometric shapes such as cones or cylinders. The numerical results have shown that a multiblock mechanism composed of three blocks is a good compromise between computation time and results accuracy. The present method significantly improves the best available soluti...

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 ...

A probabilistic analysis of a shallow circular tunnel driven by a pressurized shield in a frictional and/or cohesive soil is presented. Both the ultimate limit state (ULS) and serviceability limit state (SLS) are considered in the analysis. Two deterministic models based on numerical simulations are used. The first one computes the tunnel collapse pressure and the second one calculates the maximal settlement due to the applied face pressure. The response surface methodology is utilized for the assessment of the Hasofer-Lind reliability index for both limit states. Only the soil shear strength parameters are considered as random variables while studying the ULS. However, for the SLS, both the shear strength parameters and Young’s modulus of the soil are considered as random variables. For ULS, the assumption of uncorrelated variables was found conservative in comparison to the one of negatively correlated parameters. For both ULS and SLS, the assumption of nonnormal distribution for the random variables ha...