Probabilistic Stability Analysis of Subway Tunnels Combining Multiple Failure Mechanisms and Response Surface Method
Publication: International Journal of Geomechanics
Volume 18, Issue 12
Abstract
A probabilistic approach is proposed for face stability analysis of subway tunnels, which begins with establishment of multiple failure mechanisms, including active failure and passive failure. In terms of the complex conditions during subway construction, the buried depth, surcharge load imposed on the ground, and pore water pressure are introduced to account for the extrinsic factors that probably affect the face stability. The probabilistic analysis is performed by consolidating the multiple failure mechanisms into response surface method (RSM). The cohesion and internal friction angle of soils are considered as random variables, and the remaining parameters are considered as nonrandom variables due to their low variability or determinacy for specific projects. The influence of nonrandom variables and random variables on failure probability is investigated in detail. Finally, a reliability-based design chart is provided to evaluate the target supporting pressure against tunnel face according to different coefficients of variation of random variables. In short, by taking into account of all the possible face failures in one performance function, the proposed approach has the virtue of catching the global behaviors of face failure when multiple failure mechanisms occur at tunnel face.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The preparation of the paper has received financial supports from National Natural Science Foundation (Grant 51378510). The financial supports are greatly appreciated.
References
Anagnostou, G., and K. Kovári. 1996. “Face stability conditions with earth-pressure-balanced shields.” Tunnelling Underground Space Technol. 11 (2): 165–173. https://doi.org/10.1016/0886-7798(96)00017-X.
Berthoz, N., D. Branque, D. Subrin, H. Wong, and E. Humbert. 2012. “Face failure in homogeneous and stratified soft ground: Theoretical and experimental approaches on 1g EPBS reduced scale model.” Tunnelling Underground Space Technol. 30: 25–37. https://doi.org/10.1016/j.tust.2012.01.005.
Bishop, A. W. 1954. “The use of pore-pressure coefficients in practice.” Géotechnique 4 (4): 148–152. https://doi.org/10.1680/geot.1954.4.4.148.
Cardoso, A. S., and M. M. Fernandes 2001. “Characteristic values of ground parameters and probability of failure in design according to Eurocode 7.” Géotechnique 51 (6): 519–531. https://doi.org/10.1680/geot.2001.51.6.519.
Chen, W. F. 1975. Limit analysis and soil plasticity. Amsterdam, Netherlands: Elsevier Science.
Cherubini, C. 2000. “Reliability evaluation of shallow foundation bearing capacity on c′, φ′ soils.” Can. Geotech. J. 37 (1): 264–269. https://doi.org/10.1139/t99-096.
Drucker, D. C., and W. Prager. 1952. “Soil mechanics and plastic analysis or limit design.” Q. Appl. Math. 10 (2): 157–165. https://doi.org/10.1090/qam/48291.
GuhaRay, A., and D. K. Baidya. 2015. “Reliability-based analysis of cantilever sheet pile walls backfilled with different soil types using finite element approach.” Int. J. Geomech. 15 (6): 06015001. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000475.
Huang, M., and C. Song. 2013. “Upper-bound stability analysis of a plane strain heading in non-homogeneous clay.” Tunnelling Underground Space Technol. 38 (9): 213–223. https://doi.org/10.1016/j.tust.2013.07.012.
Ibrahim, E., A.-H. Soubra, G. Mollon, W. Raphael, D. Dias, and A. Reda. 2015. “Three-dimensional face stability analysis of pressurized tunnels driven in a multilayered purely frictional medium.” Tunnelling Underground Space Technol. 49 (1): 18–34. https://doi.org/10.1016/j.tust.2015.04.001.
Leca, E., and L. Dormieux. 1990. “Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material.” Géotechique 40 (4): 581–606. https://doi.org/10.1680/geot.1990.40.4.581.
Low, B. K., and W. H. Tang. 1997. “Efficient reliability evaluation using spreadsheet.” J. Eng. Mech. 123 (7): 749–752. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:7(749).
Low, B. K., and W. H. Tang. 2004. “Reliability analysis using object-oriented constrained optimization.” Struct. Saf. 26 (1): 69–89. https://doi.org/10.1016/S0167-4730(03)00023-7.
Lü, Q., C. L. Chan, and B. K. Low. 2013. “System reliability assessment for a rock tunnel with multiple failure modes.” Rock Mech. Rock Eng. 46 (4): 821–833. https://doi.org/10.1007/s00603-012-0285-3.
Lu, X., Y. Zhou, M. Huang, and F. Li. 2017. “Computation of the minimum limit support pressure for the shield tunnel face stability under seepage condition.” Int. J. Civ. Eng. 15 (6): 849–863. https://doi.org/10.1007/s40999-016-0116-0.
Lyamin, A. V., R. Salgado, S. W. Sloan, and M. Prezzi. 2007. “Two- and three-dimensional bearing capacity of footings in sand.” Géotechnique 57 (8): 647–662. https://doi.org/10.1680/geot.2007.57.8.647.
Lyamin, A. V., and S. W. Sloan. 2001. “Upper bound limit analysis using linear finite elements and non-linear programming.” Int. J. Numer. Anal. Methods Geomech. 26 (2): 181–216. https://doi.org/10.1002/nag.198.
Michalowski, R. L., and A. Drescher. 2009. “Three-dimensional stability of slopes and excavations.” Géotechnique 59 (10): 839–850. https://doi.org/10.1680/geot.8.P.136.
Michalowski, R. L., and S. S. Nadukuru. 2013. “Three-dimensional limit analysis of slopes with pore pressure.” J. Geotech. Geoenviron. Eng. 139 (9): 1604–1610. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000867.
Mollon, G., D. Dias, and A.-H. Soubra. 2009. “Probabilistic analysis of circular tunnels in homogeneous soil using response surface methodology.” J. Geotech. Geoenviron. Eng. 135 (9): 1314–1325. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000060.
Mollon, G., D. Dias, and A. H. Soubra. 2011. “Probabilistic analysis of pressurized tunnels against face stability using collocation-based stochastic response surface method.” J. Geotech. Geoenviron. Eng. 137 (4): 385–397. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000443.
Nagel, F., and G. Meschke. 2011. “Grout and bentonite flow around a TBM: Computational modeling and simulation-based assessment of influence on surface settlements.” Tunnelling Underground Space Technol. 26 (3): 445–452. https://doi.org/10.1016/j.tust.2010.12.001.
Pan, Q., and D. Dias. 2016. “Face stability analysis for a shield-driven tunnel in anisotropic and nonhomogeneous soils by the kinematical approach.” Int. J. Geomech. 16 (3): 04015076. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000569.
Pan, Q., and D. Dias. 2017. “Probabilistic evaluation of tunnel face stability in spatially random soils using sparse polynomial chaos expansion with global sensitivity analysis.” Acta Geotech. 12 (6): 1415–1429. https://doi.org/10.1007/s11440-017-0541-5.
Qin, C. B., and S. C. Chian 2018. “Revisiting crown stability of tunnels deeply buried in non-uniform rock surrounds.” Tunnelling Underground Space Technol. 73: 154–161. https://doi.org/10.1016/j.tust.2017.12.006.
Wolff, T. F. 1985. “Analysis and design of embankment dam slopes: A probabilistic approach.” Ph.D. thesis, Purdue Univ. https://www.researchgate.net/publication/35471497_Analysis_and_design_of_embankment_dam_slopes_a_probabilistic_approach.
Xu, J.-S., and X.-L. Yang. 2018a. Three-dimensional stability analysis of slope in unsaturated soils considering strength nonlinearity under water drawdown. Eng. Geol. 237 (10): 102–115. https://doi.org/10.1016/j.enggeo.2018.02.010.
Xu, J.-S., and X.-L. Yang. 2018b. “Seismic and static stability analysis for 3D reinforced slope in nonhomogeneous and anisotropic soils.” Int. J. Geomech. 18 (7): 04018065. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001177.
Yang, X. L., and Z. W. Li. 2018. “Factor of safety of three-dimensional stepped slopes.” Int. J. Geomech. 18 (6): 04018036. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001154.
Yang, X. L., C. Yao, and J. H. Zhang. 2016. “Safe retaining pressures for pressurized tunnel face using nonlinear failure criterion and reliability theory.” J. Cent. South Univ. 23 (3): 708–720. https://doi.org/10.1007/s11771-016-3116-y.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 18 • Issue 12 • December 2018
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Jan 17, 2018
Accepted: Jun 8, 2018
Published online: Sep 24, 2018
Published in print: Dec 1, 2018
Discussion open until: Feb 24, 2019
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.