Probabilistic Analysis and Design of Circular Tunnels against Face Stability

Abstract

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.

Face Stability Analysis of Circular Tunnels Driven by a Pressurized Shield

“…As a conclusion, the kinematical limit analysis models by Leca andDormieux ͑1990͒ andMollon et al ͑2009͒ are among the most recent and significant approaches. It should be mentioned here that the upper-bound theorem ͑kinematical approach͒ states that if a work calculation is performed for a kinematically admissible collapse mechanism, then the loads thus deduced will be higher than ͑or equal to͒ those for collapse.…”

“…For the case of a frictional soil, some writers have performed experimental tests ͑cf., Chambon and Corté 1994;Takano et al 2006͒. Others ͑Horn 1961; Leca and Dormieux 1990; Eisenstein and Ezzeldine 1994; Anagnostou and Kovari 1996;Broere 1998;Mollon et al 2009͒ have performed analytical or numerical approaches. The aim of the centrifuge tests by Chambon and Corté ͑1994͒ was to visualize the collapse pattern and to determine the value of the critical face pressure.…”

“…A more rigorous model based on the kinematical method of limit analysis was proposed by Leca and Dormieux ͑1990͒. This model was then improved by Mollon et al ͑2009͒. On the other hand, Eisenstein and Ezzeldine ͑1994͒ have performed a numerical study for the stability analysis of a tunnel face using two models ͑axisymetric and three dimensional͒.…”

“…Thus, the kinematical approach will provide an unsafe estimate of the tunnel pressure required to maintain stability ͑i.e., smaller or equal to that actually required͒. The aim of this paper is to improve the existing solutions given by Leca andDormieux ͑1990͒ andMollon et al ͑2009͒ in the framework of the kinematical approach. The soil considered in the analysis is assumed to be frictional and/or cohesive.…”

“…This improvement required numerical generation "point by point" of complex shapes of failure surfaces instead of simple use of existing standard geometric shapes ͑such as cones or cylinders͒ as it was made in Davis et al ͑1980͒, Leca and Dormieux ͑1990͒, and Mollon et al ͑2009͒. After a short overview of the existing limit analysis failure mechanisms by Leca andDormieux ͑1990͒ andMollon et al ͑2009͒, the proposed mechanism and the corresponding numerical results are presented and discussed.…”