Probabilistic Analysis and Design of Circular Tunnels against Face Stability
Publication: International Journal of Geomechanics
Volume 9, Issue 6
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 (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.
Get full access to this article
View all available purchase options and get full access to this article.
References
Baecher, G. B., and Christian, J. T. (2003). Reliability and statistics in geotechnical engineering, Wiley, New York.
Bhattacharya, G., Jana, D., Ojha, S., and Chakraborty, S. (2003). “Direct search for minimum reliability index of earth slopes.” Comput. Geotech., 30, 455–462.
Chen, W. F. (2008). Limit analysis and soil plasticity, J. Ross Publishing Classics, 637.
Christian, J., Ladd, C., and Baecher, G. (1994). “Reliability applied to slope stability analysis.” J. Geotech. Eng., 120(12), 2180–2207.
Der Kiureghian, A., and Liu, P. L. (1986). “Structural reliability under incomplete probability information.” J. Eng. Mech., 112(1), 85–104.
Ditlevsen, O. (1981). Uncertainty modelling: With applications to multidimensional civil engineering systems, McGraw-Hill, New York.
Fenton, G. A., and Griffiths, D. V. (2003). “Bearing capacity prediction of spatially random C- soils.” Can. Geotech. J., 40, 54–65.
Haldar, A., and Mahadevan, S. (2000). Probability, reliability and statistical methods in engineering design, Wiley, New York.
Hasofer, A. M., and Lind, N. C. (1974). “Exact and invariant second-moment code format.” J. Engrg. Mech. Div., 100(1), 111–121.
Leca, E., and Dormieux, L. (1990). “Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material.” Geotechnique, 40(4), 581–606.
Lemaire, M. (2005). Fiabilité des structures, Hermès, Lavoisier, Paris (in French).
Low, B. K., Lacasse, S., and Nadim, F. (2007). “Slope reliability analysis accounting for spatial variation.” Georisk: Assessment and management of risk for engineered systems and geohazards, 1(4), Taylor & Francis, London, 177–189.
Low, B. K., and Tang, W. H. (1997a). “Efficient reliability evaluation using spreadsheet.” J. Eng. Mech., 123(7), 749–752.
Low, B. K., and Tang, W. H. (1997b). “Reliability analysis of reinforced embankments on soft ground.” Can. Geotech. J., 34, 672–685.
Low, B. K., and Tang, W. H. (2004). “Reliability analysis using object-oriented constrained optimization.” Struct. Safety, 26, 69–89.
Melchers, R. E. (1999). Structural reliability analysis and prediction, 2nd Ed., Wiley, New York.
Mollon, G., Dias, D., and Soubra, A-H. (2009). “Probabilistic analysis of circular tunnels using a response surface methodology.” J. Geotech. Geoenviron. Eng., 135(9), 1314–1325.
Oberlé, S. (1996). “Application de la méthode cinématique à l’étude de la stabilité d’un front de taille de tunnel, Final Project Rep. Prepared for ENSAIS, Strasbourg, France (in French).
Phoon, K. -K., and Kulhawy, F. H. (1999). “Evaluation of geotechnical property variability.” Can. Geotech. J., 36, 625–639.
Rackwitz, R., and Fiessler, B. (1978). “Structural reliability under combined random load sequences.” Comput. Struct., 9(5), 484–494.
Soubra, A. -H. (1999). “Upper-bound solutions for bearing capacity of foundations.” J. Geotech. Geoenviron. Eng., 125(1), 59–68.
Youssef Abdel Massih, D. S. (2007). “Analyse du comportement des fondations superficielles filantes par des approches fiabilistes.” Ph.D. thesis, Université of Nantes, Nantes, France (in French).
Youssef Abdel Massih, D. S., and Soubra, A. -H. (2008). “Reliability-based analysis of strip footings using response surface methodology.” Int. J. Geomech., 8(2), 134–143.
Youssef Abdel Massih, D. S., Soubra, A. -H., and Low, B. K. (2008). “Reliability-based analysis and design of strip footings against bearing capacity failure.” J. Geotech. Geoenviron. Eng., 134(7), 917–928.
Information & Authors
Information
Published In
Copyright
© 2009 ASCE.
History
Received: Apr 25, 2008
Accepted: Jul 1, 2009
Published in print: Nov 2009
Published online: Nov 13, 2009
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.