Probabilistic Analysis of a Rock Tunnel Face Using Polynomial Chaos Expansion Method
Publication: International Journal of Geomechanics
Volume 18, Issue 4
Abstract
The polynomial chaos expansion method was used to perform probabilistic analysis on a tunnel face driven in rock masses. The generalized Hoek-Brown (HB) failure criterion was used to characterize the strength of rock masses. Deterministic calculations of required face pressures were based on the upper bound limit analysis theory. Four HB input parameters, the geological strength index (GSI), the uniaxial compressive strength σc of the intact rock, the constant mi, and the disturbance factor Di, were considered as random variables. The influence of HB input parameter uncertainties on probability density functions of the required face pressures, sensitivity analysis, and failure probabilities were discussed with respect to different coefficients of variance (COVs), distribution types, and correlation coefficients. A reliability-based design was performed to compute probabilistic face pressures under different COVs at a target safety level. The obtained results show uncertainties in the input random variables have an important influence on the required face pressures, and it is necessary to analyze the problem in the probabilistic framework.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The first author thanks the China Scholarship Council for providing him with a Ph.D. scholarship for his research work.
References
Ahmed, A. (2012). “Simplified and advanced approaches for the probabilistic analysis of shallow foundations.” Ph.D. thesis, Univ. of Nantes, Nantes, France.
Au, S. K., and Beck, J. L. (2001). “Estimation of small failure probabilities in high dimensions by subset simulation.” Probab. Eng. Mech., 16(4), 263–277.
Baecher, G. B., and Christian, J. T. (2005). Reliability and statistics in geotechnical engineering, John Wiley & Sons, New York.
Berveiller, M., Sudret, B., and Lemaire, M. (2006). “Stochastic finite element: A non intrusive approach by regression.” Eur. J. Comput. Mech., 15(1–3), 81–92.
Blatman, G. (2009). “Adaptive sparse polynomial chaos expansions for uncertainty propagation and sensitivity analysis.” Ph.D. thesis, Univ. Blaise Pascal, Clermont-Ferrand, France.
Blatman, G., and Sudret, B. (2010). “An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis.” Probab. Eng. Mech., 25(2), 183–197.
Blatman, G., and Sudret, B. (2011). “Adaptive sparse polynomial chaos expansion based on least angle regression.” J. Comput. Phys., 230(6), 2345–2367.
Hoek, E. (1998). “Reliability of Hoek-Brown estimates of rock mass properties and their impact on design.” Int. J. Rock Mech. Min. Sci., 35(1), 63–68.
Hoek, E., Carranza-Torres, C., and Corkum, B. (2002). “Hoek-Brown failure criterion–2002 edition.” Proc., NARMS-Tac, Univ. of Toronto, Toronto, 1, 267–273.
Huang, S., Liang, B., and Phoon, K. K. (2009). “Geotechnical probabilistic analysis by collocation-based stochastic response surface method: An EXCEL add-in implementation.” Georisk, 3(2), 75–86.
Isukapalli, S. S. (1999). “Uncertainty analysis of transport-transformation models.” Ph.D. thesis, State Univ. of New Jersey, New Brunswick, NJ.
Kamata, H., and Mashimo, H. (2003). “Centrifuge model test of tunnel face reinforcement by bolting.” Tunnelling Underground Space Technol., 18(2), 205–212.
Kirsch, A. (2010). “Experimental investigation of the face stability of shallow tunnels in sand.” Acta Geotech., 5(1), 43–62.
Li, A., Cassidy, M., Wang, Y., Merifield, R., and Lyamin, A. (2012). “Parametric Monte Carlo studies of rock slopes based on the Hoek–Brown failure criterion.” Comput. Geotech., 45(Sep), 11–18.
Li, D., Chen, Y., Lu, W., and Zhou, C. (2011). “Stochastic response surface method for reliability analysis of rock slopes involving correlated non-normal variables.” Comput. Geotech., 38(1), 58–68.
Liu, L. L., Cheng, Y. M., Wang, X. M., Zhang, S. H., and Wu, Z. H. (2017). “System reliability analysis and risk assessment of a layered slope in spatially variable soils considering stratigraphic boundary uncertainty.” Comput. Geotech., 89(Sep), 213–225.
Low, B. K. (2014). “FORM, SORM, and spatial modeling in geotechnical engineering.” Struct. Saf., 49(Jul), 56–64.
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.
Mao, N., Al-Bittar, T., and Soubra, A. H. (2012). “Probabilistic analysis and design of strip foundations resting on rocks obeying Hoek-Brown failure criterion.” Int. J. Rock Mech. Min. Sci., 49(Jan), 45–58.
Mollon, G., Dias, D., and Soubra, A. (2009a). “Probabilistic analysis and design of circular tunnels against face stability.” Int. J. Geomech., 237–249.
Mollon, G., Dias, D., and Soubra, A. (2009b). “Probabilistic analysis of circular tunnels in homogeneous soil using response surface methodology.” J. Geotech. Geoenviron. Eng., 1314–1325.
Mollon, G., Dias, D., and Soubra, A. (2011a). “Probabilistic analysis of pressurized tunnels against face stability using collocation-based stochastic response surface method.” J. Geotech. Geoenviron. Eng., 385–397.
Mollon, G., Dias, D., and Soubra, A. H. (2011b). “Rotational failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield.” Int. J. Numer. Anal. Methods Geomech., 35(12), 1363–1388.
Oreste, P., and Dias, D. (2012). “Stabilisation of the excavation face in shallow tunnels using fibreglass dowels.” Rock Mech. Rock Eng., 45(4), 499–517.
Pan, Q., and Dias, D. (2017a). “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.
Pan, Q., and Dias, D. (2017b). “Upper-bound analysis on the face stability of a non-circular tunnel.” Tunnelling Underground Space Technol., 62(Feb), 96–102.
Pan, Q., and Dias, D. (2018). “Three dimensional face stability of a tunnel in weak rock masses subjected to seepage forces.” Tunnelling Underground Space Technol., 71(Jan), 555–566.
Pan, Q., Jiang, Y., and Dias, D. (2017a). “Probabilistic stability analysis of a three-dimensional rock slope characterized by the Hoek-Brown failure criterion.” J. Comput. Civil Eng., 04017046.
Pan, Q., Xu, J., and Dias, D. (2017b). “Three-dimensional stability of a slope subjected to seepage forces.” Int. J. Geomech., 04017035.
Phoon, K. K., and Kulhawy, F. H. (1999). “Characterization of geotechnical variability.” Can. Geotech. J., 36(4), 612–624.
Qin, C. B., Yang, X. L., Pan, Q. J., Sun, Z. B., Wang, L. L., and Miao, T. (2015). “Upper bound analysis of progressive failure mechanism of tunnel roofs in partly weathered stratified Hoek-Brown rock masses.” Int. J. Rock Mech. Min. Sci., 74(Feb), 157–162.
Rajashekhar, M. R., and Ellingwood, B. R. (1993). “A new look at the response surface approach for reliability analysis.” Struct. Saf., 12(3), 205–220.
Saada, Z., Maghous, S., and Garnier, D. (2013). “Pseudo-static analysis of tunnel face stability using the generalized Hoek–Brown strength criterion.” Int. J. Numer. Anal. Methods Geomech., 37(18), 3194–3212.
Shen, J., and Karakus, M. (2014). “Simplified method for estimating the Hoek-Brown constant for intact rocks.” J. Geotech. Geoenviron. Eng., 04014025.
Sudret, B. (2008). “Global sensitivity analysis using polynomial chaos expansions.” Reliab. Eng. Syst. Saf., 93(7), 964–979.
Sudret, B., and Caniou, Y. (2013). Analysis of covariance (ANCOVA) using polynomial chaos expansions, Eidgenössische Technische Hochschule Zürich, Zürich, Switzerland.
Vermeer, P. A., Ruse, N., and Marcher, T. (2002). “Tunnel heading stability in drained ground.” Felsbau, 20(6), 8–18.
Webster, M. D., Tatang, M. A., and McRae, G. J. (1996). “Application of the probabilistic collocation method for an uncertainty analysis of a simple ocean model.” Tech. Rep., MIT Joint Program on the Science and Policy of Global Change Reports Series No. 4, Massachusetts Institute of Technology, Cambridge, MA.
Xiu, D., and Karniadakis, G. E. (2002). “The Wiener-Askey polynomial chaos for stochastic differential equations.” SIAM J. Sci. Comput., 24(2), 619–644.
Yang, X. L., and Pan, Q. (2015). “Three dimensional seismic and static stability of rock slopes.” Geomech. Eng., 8(1), 97–111.
Zeng, P., Senent, S., and Jimenez, R. (2016). “Reliability analysis of circular tunnel face stability obeying Hoek–Brown failure criterion considering different distribution types and correlation structures.” J. Comput. Civil Eng., 04014126.
Zhao, L. H., Zuo, S., Lin, Y. L., Li, L., and Zhang, Y. (2016). “Reliability back analysis of shear strength parameters of landslide with three-dimensional upper bound limit analysis theory.” Landslides, 13(4), 711–724.
Zou, J., and Xia, M. (2017). “A new approach for the quasi-plane strain-softening problem of cylindrical cavity expansion based on generalized Hoek-Brown failure criterion.” Geomech. Eng., 12(2), 257–263.
Zou, J., and Zuo, S. (2017). “Similarity solution for the synchronous grouting of shield tunnel under the vertical non-axisymmetric displacement boundary condition.” Adv. Appl. Math. Mech., 9(1), 205–232.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 18 • Issue 4 • April 2018
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Mar 24, 2017
Accepted: Oct 20, 2017
Published online: Jan 24, 2018
Published in print: Apr 1, 2018
Discussion open until: Jun 24, 2018
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.