Reliability Analysis of Tunnel Face in Broken Soft Rocks Using Improved Response Surface Method
Publication: International Journal of Geomechanics
Volume 18, Issue 5
Abstract
An improved response surface method (RSM) is presented for reliability analysis of a tunnel face in broken soft rocks. To fully consider the variation of the slip surface caused by the random variables in the process of reliability analysis, the method uses an implicit performance function, and it is adjustable according to each possible combination of the random variables. The improved RSM and the traditional method, which is based on a deterministic performance function (a fixed slip surface), are compared. In practical projects, random variables are often correlated, and normal distributions are not advisable under some circumstances. To satisfy the practical requirements, the proposed method was extended into the space of nonnormal correlated random variables. Sensitivity analysis was performed by examining different combinations of the coefficient of variation (COV) of random variables. Results show the following: (1) A significant improvement was observed in the reliability analysis using the proposed method, especially when a large uniform force was applied to the tunnel face. (2) Beta distributions are suggested in lieu of normal distributions to exclude the negative values that probably occur as random data. (3) The stability of the tunnel face tended to be underestimated without consideration of negative correlation of random variables. (4) The stability of the tunnel face was more sensitive to the internal friction angle than to the cohesion, and the sensitivity was intensified when the negative correlation was considered. In summary, the improved RSM adequately considers the uncertainties in engineering and leads to a more reliable stability assessment of the tunnel face.
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Acknowledgments
The preparation of the article has received financial support from the National Basic Research 973 Program of China (2013CB036004) and the National Natural Science Foundation (51378510). The financial supports are greatly appreciated.
References
Chen, W. F. (1975). Limit analysis and soil plasticity, Elsevier, Amsterdam, Netherlands.
Cherubini, C. (2000). “Reliability evaluation of shallow foundation bearing capacity on c'φ' soils.” Can. Geotech. J., 37(1), 264–269.
Ditlevsen, O. (1981). Uncertainty modeling with applications to multidimensional civil engineering systems, McGraw-Hill, New York.
Drucker, D. C., Prager, W., and Greenberg, H. J. (1951). “Extended limit design theorems for continuous media.” Q. Appl. Math., 9, 381–389.
Guharay, A., and Baidya, D. K. (2015). “Reliability based analysis of cantilever sheet pile walls backfilled with different soil types using finite element approach.” Int. J. Geomech., 06015001.
Hasofer, A. M. (1974). “Exact and invariant second-moment code format.” J. Eng. Mech. Div., 100(1), 111–121.
Jimenez-Rodriguez, R., Sitar, N., and Chacón, J. (2006). “System reliability approach to rock slope stability.” Int. J. Rock Mech. Min. Sci., 43(6), 847–859.
Langford, J. C., and Diederichs, M. S. (2013). “Reliability based approach to tunnel lining design using a modified point estimate method.” Int. J. Rock Mech. Min. Sci., 60(8), 263–276.
Li, D., Chen, Y., and Lu, W. (2011). “Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables.” Comput. Geotech., 38(1), 58–68.
Li, D. Q., Jiang, S. H., and Cao, Z. J. (2015). “A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties.” Eng. Geol., 187, 60–72.
Li, H. Z., and Low, B. K. (2010). “Reliability analysis of circular tunnel under hydrostatic stress field.” Comput. Geotech., 37(1–2), 50–58.
Low, B. K., and Tang, W. H. (2004). “Reliability analysis using object-oriented constrained optimization.” Struct. Saf., 26(1), 69–89.
Lü, Q., and Low, B. K. (2011). “Probabilistic analysis of underground rock excavations using response surface method and SORM.” Comput. Geotech., 38(8), 1008–1021.
Mollon, G., Dias, D., and Soubra, A. H. (2009). “Probabilistic analysis and design of circular tunnels against face stability.” Int. J. Geomech., 237–249.
Pan, Q., and Dias, D. (2017a). “An efficient reliability method combining adaptive support vector machine and Monte Carlo simulation.” Struct. Saf., 67, 85–95.
Pan, Q., and Dias, D. (2017b). “Sliced inverse regression-based sparse polynomial chaos expansions for reliability analysis in high dimensions.” Reliab. Eng. Syst. Saf., 167, 484–493.
Wolff, T. F. (1985). Analysis and design of embankment dam slopes: A probabilistic approach, Univ. Microfilms, Ann Arbor, MI.
Wong, F. S. (1985). “Slope reliability and response surface method.” J. Geotech. Eng., 32–53.
Yang, X. L., and Li, W. T. (2017). “Reliability analysis of shallow tunnel with surface settlement.” Geomech. Eng., 12(2), 313–326.
Yang, Z. H. (2017). “Upper bound analysis for supporting pressure of tunnel face and stability of confining rocks.” Ph.D. thesis, Central South Univ., China (in Chinese).
Yang, X. L., and Yao, C. (2018). “Stability of tunnel roof in nonhomogeneous soils.” Int. J. Geomech.,, 06018002.
Zhao, L. H., Zuo, S., and Li, L. (2016). “System reliability analysis of plane slide rock slope using Barton-Bandis failure criterion.” Int. J. Rock Mech. Min. Sci., 88, 1–11.
Zhao, H., Ru, Z., Chang, X., Yin, S., and Li, S. (2014). “Reliability analysis of tunnel using least square support vector machine.” Tunnelling Underground Space Technol., 41, 14–23.
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Published In
International Journal of Geomechanics
Volume 18 • Issue 5 • May 2018
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Jun 29, 2017
Accepted: Nov 1, 2017
Published online: Feb 22, 2018
Published in print: May 1, 2018
Discussion open until: Jul 22, 2018
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