Limit Analysis of Active and Passive Mechanisms of Shallow Tunnels in Nonassociative Soil with Changing Water Table
Publication: International Journal of Geomechanics
Volume 18, Issue 7
Abstract
The evaluation of the failure mechanism of a shallow tunnel is very significant in geotechnical engineering. In this literature an analytical methodology for determining the plane strain limit failure mechanism for a shallow tunnel with an arbitrary cross section is presented. The paper presents active and passive failure modes for the shallow tunnels in linear and nonlinear soils. By variation calculus, the effects of dilation on the failure mechanism of the shallow tunnel are explored based on the nonassociative flow rule in the present work. Within the upper bound theorem different curve functions are obtained to describe the different failure mechanisms up and down the water level. Good agreement is demonstrated in both active and passive failure mechanisms with the lower bound solution solved in the similar trapdoor/anchor problem in linear Mohr-Coulomb soils. To analyze the influence of the dilatancy coefficient and position of the water table on the potential failure range, some examples and sensitivity analysis are conducted, which shows great consistency with existing research findings.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Financial support was received from the National Natural Science Foundation (51378510) and Innovation Foundation for postgraduates of the Central South University (2017zzts157) for the preparation of this manuscript. This financial support is greatly appreciated.
References
Anyaegbunam, A. (2015). “Nonlinear power-type failure laws for geomaterials: Synthesis from triaxial data, properties, and applications.” Int. J. Geomech., 04014036.
Babiker, A., Smith, C. C., Matthew, G., and John, P. A. (2014). “Nonassociative limit analysis of the toppling-sliding failure of rock slopes.” Int. J. Rock Mech. Min. Sci., 71(1), 1–11.
Baker, R. (2004). “Nonlinear Mohr envelopes based on triaxial data.” J. Geotech. Geoenviron. Eng., 498–506.
Chen, W. F. (1975). Limit analysis and soil plasticity, Elsevier, Amsterdam, Netherlands.
Davis, E. H., Gunn, M. J., Mair, R. J., and Seneviratine, H. N. (1980). “The stability of shallow tunnels and underground openings in cohesive material.” Géotechnique, 30(4), 397–416.
Drescher, A., and Detourany, E. (1993). “Limit load in translational failure mechanisms for associative and nonassociative materials.” Géotechnique, 43(3), 443–456.
Drucker, D. C. (1954). “Coulomb friction, plastic, and limit loads.” J. Appl. Math., 21(1), 71–74.
Fahimifar, A., Ghadami, H., and Ahmadvand, M. (2015). “The ground response curve of underwater tunnels, excavated in a strain-softening rock mass.” Geomech. Eng., 8(3), 323–359.
Feng, K., He, C., Zhou, J. M., and Zhang, Z. (2012). “Model test on impact of surrounding rock deterioration on segmental lining structure for underwater shield tunnel with large cross-section.” Procedia Environ. Sci., 12(Part B), 891–898.
Fraldi, M., and Guarracino, F. (2010). “Analytical solutions for collapse mechanisms in tunnels with arbitrary cross sections.” Int. J. Solid Struct., 47(2), 216–223.
Hoek, E., and Brown, E. T. (1997). “Practical estimates of rock mass strength.” Int. J. Rock Mech. Min. Sci., 34(8), 1165–1186.
Huang, F. M., Wang, M. S., Tan, Z. S., and Wang, X. Y. (2010). “Analytical solutions for stead seepage into an underwater circular tunnel.” Tunnelling Underground Space Technol., 25(4), 391–396.
Kumar, J. (2004). “Stability factors for slopes with nonassociated flow rule using energy consideration.” Int. J. Geomech., 264–272.
Lee, Y. J. (2016). “Determination of tunnel support pressure under the pile tip using upper and lower bounds with a superimposed approach.” Geomech. Eng., 11(4), 587–605.
Li, T., and Yang, X. (2018). “Reliability analysis of tunnel face in broken soft rocks using improved response surface method.” Int. J. Mech., 04018021.
LimitState:GEO 3.2e [Computer software]. LimitState, Ltd., Sheffield, U.K.
LimitState Ltd. (2015). LimitState:GEO, manual version 2.0, Sheffield, U.K.
Lu, A., Zhang, N., Wang, S., and Zhang, X. (2017). “Analytical solution for a lined tunnel with arbitrary cross sections excavated in orthogonal anisotropic rock mass.” Int. J. Geomech., 04017044.
Mohammadi, M., and Tavakoli, H. (2015). “Comparing the generalized Hoek-Brown and Mohr-Coulomb failure criteria for stress analysis on the rocks failure plane.” Geomech. Eng., 9(1), 115–124.
Mollon, G., Dias, D., and Soubra, A. (2009). “Probabilistic analysis of circular tunnels in homogeneous soil using response surface methodology.” J. Geotech. Geoenviron. Eng., 1314–1325.
Pan, Q., and Dias, D. (2016). “Face stability analysis for a shield-driven tunnel in anisotropic and nonhomogeneous soils by the kinematical approach.” Int. J. Geotech., 04015076.
Saada, Z., Maghous, S., and Garnier, D. (2012). “Stability analysis of rock slopes subjected to seepage forces using the modified Hoek-Brown criterion.” Int. J. Rock Mech. Min. Sci., 55(Oct), 45–54.
Smith, C. C. (1998). “Limit loads for an anchor/trapdoor embedded in an associative Coulomb soil.” Int. J. Numer. Anal. Methods Geomech., 22(11), 855–865.
Smith, C. C. (2012). “Limit loads for a shallow anchor/trapdoor embedded in a non-associative Coulomb soil.” Géotechnique, 62(7), 563–571.
Smith, C. C., and Gilbert, M. (2007). “Application of discontinuity layout optimization to plane plasticity problems.” Proc. R. Soc. London, Ser A, 462(2086), 2461–2484.
Sokolovskii, V. V. (1965). Statics of granular media, Pergamon Press, Oxford, U.K.
Soubra, A. H. (2000). Three-dimensional face stability analysis of shallow circular tunnels. Proc., Int. Conf. on Geotechnical and Geological Engineering, International Society for Rock Mechanics and Rock Engineering, Melbourne, Australia, ISRM-IS-2000-594.
Taylor, R. K. (1978). Properties of mining wastes with respect to foundations: Foundation engineering in difficult ground, F. G. Bell, ed., Newnes-Butterworth, London, 175–203.
Vu, M., Broere, W., and Bosch, J. (2017). “Structural analysis for shallow tunnels in soft soils.” Int. J. Geomech., 04017038.
Xu, J., Pan, Q., Yang, X., and Li, W. (2018). “Stability charts for rock slopes subjected to water drawdown based on the modified nonlinear Hoek-Brown failure criterion.” Int. J. Geomech., 04017133.
Yang, X., and Yao, C. (2018). “Stability of tunnel roof in nonhomogeneous soils.” Int. J. Geomech., 06018002.
Yang, X. L., and Zhang, R. (2017). “Collapse analysis of shallow tunnel subjected to seepage in layered soils considering joined effects of settlement and dilation.” Geomech. Eng., 13(2), 217–235.
Zhang, X. J., and Chen, W. F. (1987). “Stability analysis of slopes with general nonlinear failure criterion.” Int. J. Numer. Anal. Geomech., 11(1), 33–50.
Information & Authors
Information
Published In
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Jun 20, 2017
Accepted: Dec 19, 2017
Published online: Apr 24, 2018
Published in print: Jul 1, 2018
Discussion open until: Sep 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.