failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield. International Journal for Numerical and Analytical Methods in Geomechanics, Wiley, 2011Wiley, , 35 (12), pp.1363Wiley, -1388Wiley, . 10.1002 Rotational failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield Nantes, Bd. de l'université, BP 152, cedex, France The aim of this paper is to determine the collapse and blow-out face pressures of a circular tunnel driven by a pressurized shield. The analysis is performed in the framework of the kinematical approach of the limit analysis theory. Two rotational failure mechanisms are proposed for the active and passive cases. These mechanisms have two significant advantages with respect to the available ones: (i) they take into account the entire circular tunnel face instead of an inscribed ellipse to this circular area, and (ii) they are more consistent with the rotational rigid-block movement observed in the experimental tests. For both the active and passive cases, the three-dimensional failure surface was generated 'point by point' instead of simple use of the existing standard geometric shapes such as cones or cylinders. This was achieved by employing a spatial discretization technique. The numerical results have shown that the present rotational mechanisms provide, in the case of frictional soils (with or without cohesion), a significant improvement with respect to the translational mechanisms. Finally, an extension of the proposed collapse mechanism to include a tension cut-off in the classical Mohr-Coulomb failure criterion is presented and discussed.

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 ͑1͒ 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; ͑2͒ FORM approximation gives accurate results of the failure probability; and ͑3͒ 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.

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Abstract: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 solutions of the collapse pressure given by other kinematical approaches. Design charts are given in the case of a frictional and cohesive soil for practical use in geotechnical engineering.

A probabilistic analysis of the face stability of a tunnel driven by a compressed-air pressurized shield is presented. The collocation-based stochastic response surface methodology (CSRSM) is used. The deterministic model employed in the probabilistic analysis is analytical. A translational multiblock collapse mechanism in the framework of the kinematic theorem of limit analysis forms the basis of the analysis. The soil friction angle and cohesion are considered as random variables. CSRSM was first validated by the comparison of the results obtained from the original analytical deterministic model. Then, the influence of the probabilistic characteristics of the uncertain variables was studied. Contrary to the correlation between c and φ and the coefficients of variation of these variables, which have a significant effect on the variability of the critical collapse pressure, the nonnormality of the distributions of the random variables was shown not to have a considerable effect on the distribution of the output.

SUMMARY Face stability analysis of tunnels excavated under pressurized shields is a major issue in real tunnelling projects. Most of the failure mechanisms used for the stability analysis of tunnels in purely cohesive soils were derived from rigid block failure mechanisms that were developed for frictional soils, by imposing a null friction angle. For a purely cohesive soil, this kind of mechanism is quite far from the actual velocity field. This paper aims at proposing two new continuous velocity fields for both collapse and blowout of an air‐pressurized tunnel face. These velocity fields are much more consistent with the actual failures observed in undrained clays. They are based on the normality condition, which states that any plastic deformation in a purely cohesive soil develops without any volume change. The numerical results have shown that the proposed velocity fields significantly improve the best existing bounds for collapse pressures and that their results compare reasonably well with the collapse and blowout pressures provided by a commercial finite difference software, for a much smaller computational cost. A design chart is provided for practical use in geotechnical engineering. Copyright © 2012 John Wiley & Sons, Ltd.

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 ͑ULS͒ and serviceability limit state ͑SLS͒ 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 has almost no effect on the reliability index for the practical range of values of the applied pressure. Finally, it was found that the system reliability depends on both limit states. Notice however that the contribution of ULS to the system reliability was not significant. Thus, SLS can be used alone for the assessment of the tunnel reliability.

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