Comparison of Modeling Soil Parameters Using Random Variables and Random Fields in Reliability Analysis of Tunnel Face
Publication: International Journal of Geomechanics
Volume 19, Issue 1
Abstract
Uncertainty is a notable feature of the geotechnical field. Reliability analysis methods provide a more rational solution than deterministic ones in the presence of the spatial variability of soil properties. Two types of reliability analysis methods were employed in the face stability analysis of pressurized tunnels in this study: the random variable method (RVM), which ignores spatial autocorrelation of soil parameters, and the random finite-difference method (RFDM), which considers spatial autocorrelation. In the RVM, the first-order second-moment (FOSM) method was adopted to calculate the reliability index with less computational effort. Then, the computational efficiency and accuracy of the two types of reliability analysis methods were systematically compared through a typical tunnel problem. Further sensitivity studies using the RFDM were performed to explore the effects of the scale of the fluctuation and autocorrelation functions. The authors found the probability of failure predicted by the RVM to be significantly overestimated because the spatial structure of soil parameters were ignored. Finally, using equivalent soil parameters instead of realistic ones, the corresponding results predicted by the equivalent FOSM method were found to be consistent with those of the RFDM, but they required far less computational effort. Thus, the equivalent FOSM method can be used to efficiently predict the stability of the tunnel face in variable soils, and it provides a practical tool for designers.
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Acknowledgments
This work was financially supported by the National Natural Science Foundation of China (41807512), the Science and Technology Service Network Initiative (KFJ-EW-STS-122), the National Key Research and Development Program of China (2016YFC0800207), and the Provincial Key Research and Development Program of Hunan (0105679005).
References
Broere, W. 2001. “Tunnel face stability & new CPT applications.” Ph.D. thesis, Delft Univ. https://repository.tudelft.nl/islandora/object/uuid%3A0323c1da-7428-44be-9f4d-90024eafba24.
Chambon, P., and J. F. Corté. 1994. “Shallow tunnels in cohesionless soil: Stability of tunnel face.” J. Geotech. Eng. 120 (7): 1148–1165. https://doi.org/10.1061/(ASCE)0733-9410(1994)120:7(1148).
Chen, R. P., L. J. Tang, D. S. Ling, and Y. M. Chen. 2011. “Face stability analysis of shallow shield tunnels in dry sandy ground using the discrete element method.” Comput. Geotech. 38 (2): 187–195. https://doi.org/10.1016/j.compgeo.2010.11.003.
Chenari, R. J., and R. Alaie. 2015. “Effects of anisotropy in correlation structure on the stability of an undrained clay slope.” Georisk 9 (2): 109–123. https://doi.org/10.1080/17499518.2015.1037844.
Davis, E. H., M. J. Gunn, R. J. Mair, and H. N. Seneviratine. 1980. “The stability of shallow tunnels and underground openings in cohesive material.” Géotechnique 30 (4): 397–416. https://doi.org/10.1680/geot.1980.30.4.397.
Eshraghi, A., and S. Zare. 2015. “Face stability evaluation of a TBM-driven tunnel in heterogeneous soil using a probabilistic approach.” Int. J. Geomech. 15 (6): 04014095. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000452.
Fenton, G. A., and D. V. Griffiths. 2003. “Bearing capacity prediction of spatially random c–φ soils.” Can. Geotech. J. 40 (1): 54–65. https://doi.org/10.1139/t02-086.
Fenton, G. A., and D. V. Griffiths. 2008. Risk assessment in geotechnical engineering. New York: John Wiley & Sons.
Griffiths, D. V., and G. A. Fenton. 2009. “Probabilistic settlement analysis by stochastic and random finite-element methods.” J. Geotech. Geoenviron. Eng. 135 (11): 1629–1637. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000126.
Griffiths, D. V., J. S. Huang, and G. A. Fenton. 2009. “Influence of spatial variability on slope reliability using 2-D random fields.” J. Geotech. Geoenviron. Eng. 135 (10): 1367–1378. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000099.
Hasofer, A. M., and N. C. Lind. 1974. “Exact and invariant second-moment code format.” J. Eng. Mech. Div. 100 (1): 111–121.
Hicks, M. A., and K. Samy. 2002. “Influence of heterogeneity on undrained clay slope stability.” Q. J. Eng. Geol. Hydrogeol. 35 (1): 41–49. https://doi.org/10.1144/qjegh.35.1.41.
Huang, J. S., D. V. Griffiths, and G. A. Fenton. 2010. “System reliability of slopes by RFEM.” Soils Found. 50 (3): 343–353. https://doi.org/10.3208/sandf.50.343.
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 (Jun): 18–34. https://doi.org/10.1016/j.tust.2015.04.001.
Ji, J.,. H. J. Liao, and B. K. Low. 2012. “Modeling 2-D spatial variation in slope reliability analysis using interpolated autocorrelations.” Comput. Geotech. 40 (Mar): 135–146. https://doi.org/10.1016/j.compgeo.2011.11.002.
Jiang, S. H., D. Q. Li, Z. J. Cao, C. B. Zhou, and K. K. Phoon. 2015. “Efficient system reliability analysis of slope stability in spatially variable soils using Monte Carlo simulation.” J. Geotech. Geoenviron. Eng. 141 (2): 04014096. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001227.
Kirsch, A. 2010. “Experimental investigation of the face stability of shallow tunnels in sand.” Acta Geotech. 5 (1): 43–62. https://doi.org/10.1007/s11440-010-0110-7.
Leca, E., and L. Dormieux. 1990. “Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material.” Géotechnique 40 (4): 581–606. https://doi.org/10.1680/geot.1990.40.4.581.
Li, D. Q., S. H. Jiang, Z. J. Cao, W. Zhou, C. B. Zhou, and L. M. Zhang. 2015. “A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties.” Eng. Geol. 187 (Mar): 60–72. https://doi.org/10.1016/j.enggeo.2014.12.003.
Lu, X., H. Wang, and M. Huang. 2014. “Upper bound solution for the face stability of shield tunnel below the water table.” Math. Prob. Eng. 2014 (Oct): 727964. https://doi.org/10.1155/2014/727964.
Luo, Z., S. Atamturktur, Y. Cai, and C. H. Juang. 2012. “Reliability analysis of basal-heave in a braced excavation in a 2-D random field.” Comput. Geotech. 39 (Jan): 27–37. https://doi.org/10.1016/j.compgeo.2011.08.005.
Mollon, G., D. Dias, and A. H. Soubra. 2009a. “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. 2009b. “Probabilistic analysis and design of circular tunnels against face stability.” Int. J. Geomech. 9 (6): 237–249. https://doi.org/10.1061/(ASCE)1532-3641(2009)9:6(237).
Mollon, G., D. Dias, and A. H. Soubra. 2010. “Face stability analysis of circular tunnels driven by a pressurized shield.” J. Geotech. Geoenviron. Eng. 136 (1): 215–229. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000194.
Mollon, G., D. Dias, and A. H. Soubra. 2011a. “Extension of CSRSM for the parametric study of the face stability of pressurized tunnels.” In GeoRisk 2011: Geotechnical risk assessment and management, Geotechnical Special Publication 224. Reston, VA: ASCE. https://doi.org/10.1061/41183(418)126.
Mollon, G., D. Dias, and A. H. Soubra. 2011b. “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.
Mollon, G., K. K. Phoon, D. Dias, and A. H. Soubra. 2011c. “Influence of the scale of fluctuation of the friction angle on the face stability of a pressurized tunnel in sands.” In GeoRisk 2011: Geotechnical risk assessment and management, Geotechnical Special Publication 224. Reston, VA: ASCE. https://doi.org/10.1061/41183(418)14.
Mollon, G., K. K. Phoon, D. Dias, and A. H. Soubra. 2011d. “Validation of a new 2D failure mechanism for the stability analysis of a pressurized tunnel face in a spatially varying sand.” J. Eng. Mech. 137 (1): 8–21. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000196.
Suchomel, R., and D. Mašı´n. 2010. “Comparison of different probabilistic methods for predicting stability of a slope in spatially variable c-φ soil.” Comput. Geotech. 37 (1–2): 132–140. https://doi.org/10.1016/j.compgeo.2009.08.005.
Tang, X. S., D. Q. Li, G. Rong, K. K. Phoon, and C. B. Zhou. 2013. “Impact of copula selection on geotechnical reliability under incomplete probability information.” Comput. Geotech. 49 (Apr): 264–278. https://doi.org/10.1016/j.compgeo.2012.12.002.
Vanmarcke, E. H. 1977. “Probabilistic modeling of soil profiles.” J. Geotech. Eng. Div. 103 (11): 1227–1246. http://cedb.asce.org/CEDBsearch/record.jsp?dockey=0007734.
Vanmarcke, E. H. 1983. Random fields: Analysis and synthesis. Cambridge, MA: MIT Press.
Vermeer, P. A., N. Ruse, and T. Marcher. 2002. “Tunnel heading stability in drained ground.” Felsbau 20 (6): 1–17.
Zhang, J., H. Z. Chen, H. W. Huang, and Z. Luo. 2015. “Efficient response surface method for practical geotechnical reliability analysis.” Comput. Geotech. 69 (Sep): 496–505. https://doi.org/10.1016/j.compgeo.2015.06.010.
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Published In
International Journal of Geomechanics
Volume 19 • Issue 1 • January 2019
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Sep 7, 2017
Accepted: Jul 12, 2018
Published online: Oct 18, 2018
Published in print: Jan 1, 2019
Discussion open until: Mar 18, 2019
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