Revisiting Circular Tunnel Stability Using Broms and Bennermarks’ Original Stability Number
Publication: International Journal of Geomechanics
Volume 21, Issue 5
Abstract
The stability of a single circular tunnel in cohesive undrained soil was investigated under plain strain conditions using a two-dimensional finite-element limit analysis (FELA) program and a shear strength reduction method (SSRM). The stability for this problem was well expressed by using Broms and Bennermarks’ original stability number (N = (σs + γH − σt)/Su) owing to the undrained loading conditions. The variations of the factor of safety and the critical stability number were presented for a series of tunnel cover-to-diameter ratios (C/D) in both collapse and blowout scenarios. Also, the extent of surface failure for some selected depth ratios was determined in the case of tunnel collapse. The obtained results were compared and validated by using the finite-difference method, as well as other existing solutions available in the literature. The dimensionless ratios employed in this study make the design charts suitable to cover a broad range of tunnel geometries and soil parameters.
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References
Assadi, A., and S. W. Sloan. 1991. “Undrained stability of shallow square tunnel.” J. Geotech. Eng. 117 (8): 1152–1173. https://doi.org/10.1061/(ASCE)0733-9410(1991)117:8(1152).
Broms, B. B., and H. Bennermark. 1967. “Stability of clay at vertical openings.” J. Soil Mech. Found. Div. 93: 71–94.
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.
Huang, M., H. Wang, J. Yu, and Z. Tang. 2019. “Undrained stability analysis of a plane strain circular tunnel using streamline velocity fields.” Int. J. Geomech. 19 (5): 06019006. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001395.
Keawsawasvong, S., and B. Ukritchon. 2017a. “Stability of unsupported conical excavations in non-homogeneous clays.” Comput. Geotech. 81: 125–136. https://doi.org/10.1016/j.compgeo.2016.08.007.
Keawsawasvong, S., and B. Ukritchon. 2017b. “Undrained stability of an active planar trapdoor in non-homogeneous clays with a linear increase of strength with depth.” Comput. Geotech. 81: 284–293. https://doi.org/10.1016/j.compgeo.2016.08.027.
Kimura, T., and R. Mair. 1981. “Centrifugal testing of model tunnels in soft clay.” In Proc., 10th Int. Conf. on Soil Mechanics and Foundation Engineering, 319–322. Rotterdam, The Netherlands: A.A. Balkema.
Krabbenhoft, K., and A. V. Lyamin. 2015. “Strength reduction finite-element limit analysis.” Géotechnique Letters 5 (4): 250–253. https://doi.org/10.1680/jgele.15.00110.
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.
Lyamin, A. V., and S. W. Sloan. 2002a. “Upper bound limit analysis using linear finite elements and non-linear programming.” Int. J. Numer. Anal. Methods Geomech. 26 (2): 181–216. https://doi.org/10.1002/nag.198.
Lyamin, A. V., and S. W. Sloan. 2002b. “Lower bound limit analysis using non-linear programming.” Int. J. Numer. Methods Eng. 55 (5): 573–611. https://doi.org/10.1002/nme.511.
Mollon, G., D. Dias, and A.-H. Soubra. 2009. “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. 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. https://doi.org/10.1002/nag.962.
Mollon, G., D. Dias, and A.-H. Soubra. 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. https://doi.org/10.1002/nag.2121.
Peck, R. B. 1969. “Deep excavations and tunneling in soft ground.” In Proc., 7th Int. Conf. on Soil Mechanics and Foundation Engineering, 225–90. Mexico City: Sociedad Mexicans de Mecanica de Suelos.
Schofield, A. N. 1980. “Cambridge geotechnical centrifuge operations.” Géotechnique 30 (3): 227–268. https://doi.org/10.1680/geot.1980.30.3.227.
Shiau, J., and F. Al-Asadi. 2018. “Revisiting Broms and Bennermarks’ original stability number for tunnel headings.” Géotech. Lett. 8 (4): 310–315. https://doi.org/10.1680/jgele.18.00145.
Shiau, J., and F. Al-Asadi. 2020a. “Two-dimensional tunnel heading stability factors Fc, Fs and Fγ.” Tunnelling Underground Space Technol. 97: 103293. https://doi.org/10.1016/j.tust.2020.103293.
Shiau, J., and F. Al-Asadi. 2020b. “Determination of critical tunnel heading pressures using stability factors.” Comput. Geotech. 119: 103345. https://doi.org/10.1016/j.compgeo.2019.103345.
Shiau, J., and F. Al-Asadi. 2020c. “Three-dimensional analysis of circular tunnel headings using Broms and Bennermarks’ original stability number.” Int. J. Geomech. 20 (7): 06020015. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001734.
Shiau, J., and F. Al-Asadi. 2020d. “Three-dimensional heading stability of twin circular tunnels.” Geotech. Geol. Eng. 38 (2): 2973–2988. https://doi.org/10.1007/s10706-020-01201-z.
Shiau, J., and F. Al-Asadi. 2020e. “Stability analysis of twin circular tunnels using shear strength reduction method.” Géotech. Lett. 10 (2): 311–319. https://doi.org/10.1680/jgele.19.00003.
Shiau, J., and F. Al-Asadi. 2021. “Twin tunnels stability factors Fc, Fs and Fr.” Geotech. Geol. Eng. 39: 335–345. https://doi.org/10.1007/s10706-020-01495-z.
Shiau, J., and M. M. Hassan. 2020. “Undrained stability of active and passive trapdoors.” Geotech. Res. 7 (1): 40–48. https://doi.org/10.1680/jgere.19.00033.
Shiau, J., and M. Sams. 2019. “Relating volume loss and greenfield settlement.” Tunnelling Underground Space Technol. 83: 145–152. https://doi.org/10.1016/j.tust.2018.09.041.
Sloan, S. W. 2013. “Geotechnical stability analysis.” Géotechnique 63 (7): 531–572. https://doi.org/10.1680/geot.12.RL.001.
Sloan, S. W., and A. Assadi. 1991. “Undrained stability of a square tunnel in a soil whose strength increases linearly with depth.” Comput. Geotech. 12 (4): 321–346. https://doi.org/10.1016/0266-352X(91)90028-E.
Sloan, S. W., and A. Assadi. 1992. “Stability of shallow tunnels in soft ground.” In Proc., Wroth Memorial Symp. on Predictive Soil Mechanics, edited by G. T. Houlsby and A. N. Schofield, 644–663. London: Thomas Telford.
Ukritchon, B., and S. Keawsawasvong. 2017. “Design equations for undrained stability of opening in underground walls.” Tunnelling Underground Space Technol. 70: 214–220. https://doi.org/10.1016/j.tust.2017.08.004.
Wilson, D. W., A. J. Abbo, S. W. Sloan, and A. V. Lyamin. 2011. “Undrained stability of a circular tunnel where the shear strength increases linearly with depth.” Can. Geotech. J. 48 (9): 1328–1342. https://doi.org/10.1139/t11-041.
Wilson, D. W., A. J. Abbo, S. W. Sloan, and A. V. Lyamin. 2013. “Undrained stability of a square tunnel where the shear strength increases linearly with depth.” Comput. Geotech. 49: 314–325. https://doi.org/10.1016/j.compgeo.2012.09.005.
Yamamoto, K., A. V. Lyamin, D. W. Wilson, S. W. Sloan, and A. J. Abbo. 2011a. “Stability of a circular tunnel in cohesive–frictional soil subjected to surcharge loading.” Comput. Geotech. 38 (4): 504–514. https://doi.org/10.1016/j.compgeo.2011.02.014.
Yamamoto, K., A. V. Lyamin, D. W. Wilson, S. W. Sloan, and A. J. Abbo. 2011b. “Stability of a single tunnel in cohesive–frictional soil subjected to surcharge loading.” Can. Geotech. J. 48 (12): 1841–1854. https://doi.org/10.1139/t11-078.
Yang, F., J. Zhang, J. Yang, L. Zhao, and X. Zheng. 2015. “Stability analysis of unlined elliptical tunnel using finite element upper-bound method with rigid translatory moving elements.” Tunnelling Underground Space Technol. 50: 13–22. https://doi.org/10.1016/j.tust.2015.06.005.
Zhang, C., K. Han, and D. Zhang. 2015. “Face stability analysis of shallow circular tunnels in cohesive–frictional soils.” Tunnelling Underground Space Technol. 50: 345–357. https://doi.org/10.1016/j.tust.2015.08.007.
Zhang, F., Y. F. Gao, Y. X. Wu, and N. Zhang. 2018. “Upper-bound solutions for face stability of circular tunnels in undrained clays.” Géotechnique 68 (1): 76–85. https://doi.org/10.1680/jgeot.16.T.028.
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Published In
International Journal of Geomechanics
Volume 21 • Issue 5 • May 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Mar 4, 2020
Accepted: Dec 2, 2020
Published online: Feb 19, 2021
Published in print: May 1, 2021
Discussion open until: Jul 19, 2021
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