Upper-Bound Limit Analysis of Shield Tunnel Stability in Undrained Clays Using Complex Variable Solutions for Different Ground-Loss Scenarios
Publication: International Journal of Geomechanics
Volume 17, Issue 9
Abstract
Continuum upper-bound limit analyses in existing literature are based on empirical formulas or singular analytical solutions for a uniform-convergence type of tunnel boundary condition. This paper presents an upper-bound limit analysis of shield tunnel stability in undrained clays using complex variable displacement fields for four different ground-loss scenarios. The upper-bound theorem was applied on a prescribed perfect plastic Tresca kinematic zone with a slip line boundary to seek the supremum (minimal upper bound) of the tunnel stability number, which should not be exceeded to avoid collapse. For an imposed identical volume of ground loss, the maximum ground surface settlement was found to be the smallest for ground-loss Scenario A (circular convergence), larger for Scenario B (downward oval convergence), and much larger for Scenario C (halved oval convergence), which is slightly smaller than Scenario D (mixed oval convergence); the opposite is true for comparisons of the widths of the settlement troughs. Ground-loss Scenario A presents the worst case in terms of tunnel stability, with the smallest allowable stability number and the widest spread of the least favorable slip line boundary, while Scenario D is the second worst case with the second-smallest allowable stability number. Similar results were found, in sequential order, for Scenarios B and C. The presented approach, because of the complex variable solutions used, may extend upper-bound limit analyses to more complicated tunnel boundary conditions.
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Acknowledgments
This study was sponsored by the China National Key Basic Research and Development Project (973 Project) under Grant 2015CB057800.
References
Anagnostou, G., and Kovári, K. (1994). “The face stability of slurry-shield driven tunnels.” Tunnelling Underground Space Technol., 9(2), 165–174.
Anagnostou, G., and Kovári, K. (1996). “Face stability conditions with earth-pressure-balanced shields.” Tunnelling Underground Space Technol., 11(2), 165–173.
Broere, W. (2015). “On the face support of microtunnelling TBMs.” Tunnelling Underground Space Technol., 46(Feb), 12–17.
Broere, W., and van Tol, A. F. (2000). “Influence of infiltration and groundwater flow on tunnel face stability.” Geotechnical aspects of underground construction in soft ground, O. Kusakabe, K. Fujita, and Y. Miyazaki, eds., A. A. Balkema, Rotterdam, Netherlands, 339–344.
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.
Klar, A., and Klein, B. (2014). “Energy-based volume loss prediction for tunnel face advancement in clays.” Géotechnique, 64(10), 776–786.
Klar, A., Osman, A. S., and Bolton, M. (2007). “2D and 3D upper bound solutions for tunnel excavation using ‘elastic’ flow field.” Int. J. Numer. Anal. Methods Geomech., 31(12), 1367–1374.
Leca, E., and Dormieux, L. (1990). “Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material.” Géotechnique, 40(4), 581–606.
Mair, R. J. (1979). “Centrifugal modeling of tunnel construction in soft clay.” Ph.D. thesis, Univ. of Cambridge, Cambridge, U.K.
Mollon, G., Dias, D., and Soubra, A.-H. (2011). “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.
Mollon, G., Dias, D., and Soubra, A.-H. (2013). “Continuous velocity fields for collapse and blowout of a pressurized tunnel face in purely cohesive soil.” Int. J. Numer. Anal. Methods Geomech., 37(13), 2061–2083.
Osman A. S., Bolton M. D., Mair R. J. (2006a). “Predicting 2D ground movements around tunnels in undrained clay.” Géotechnique, 56(9): 597–604.
Osman, A. S., Mair, R. J., and Bolton, M. D. (2006b). “On the kinematics of 2D tunnel collapse in undrained clay.” Géotechnique, 56(9), 585–595.
Park, K. H. (2004). “Elastic solution for tunneling-induced ground movements in clays.” Int. J. Geomech., 4(4), 310–318.
Perazzelli, P., Leone, T., and Anagnostou, G. (2014). “Tunnel face stability under seepage flow conditions.” Tunnelling Underground Space Technol., 43, 459–469.
Sagaseta, C. (1987). “Analysis of undraind soil deformation due to ground loss.” Géotechnique, 37(3), 301–320.
Sagaseta, C. (1998). “On the role of analytical solutions for the evaluation of soil deformation around tunnels.” Application of numerical methods to geotechnical problems, A. Cividini, ed., 397, Springer, London, 3–24.
Verruijt, A. (1997). “A complex variable solution for a deforming circular tunnel in an elastic half-plane.” Int. J. Numer. Anal. Methods Geomech., 21(2), 77–89.
Verruijt, A., and Booker, J. R. (1996). “Surface settlements due to deformation of a tunnel in an elastic half plane.” Géotechnique, 46(4), 753–756.
Wang, L., and Lv, X. (2007). “A complex variable solution for different kinds of oval deformation around circular tunnel in an elastic half plane.” Chin. J. Geotech. Eng., 29(3), 319–327 (in Chinese).
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© 2017 American Society of Civil Engineers.
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Received: Aug 17, 2016
Accepted: Feb 17, 2017
Published online: Jun 1, 2017
Published in print: Sep 1, 2017
Discussion open until: Nov 1, 2017
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