Stability of Unlined Rectangular Tunnels in Rock Masses Subjected to Surcharge Loading
Publication: International Journal of Geomechanics
Volume 21, Issue 1
Abstract
This paper investigates the stability of unlined rectangular tunnels in rock masses subjected to surcharge loading using adaptive finite element limit analysis based on the generalized Hoek-Brown failure criterion. Both upper and lower bound solutions are employed to calculate the stability number of the problem, and the relative errors are found to be within ±7%. A sensitivity study relevant to the Hoek-Brown parameters (σci, GSI, and mi), the normalized cover depth of the tunnel (C/H), and the width to height ratio of tunnels (W/H) are conducted. At a given value of C/H, the stability number is found to be increasing continuously with decreasing W/H and with increasing GSI and mi. The computational results are summarized in the form of design tables and charts for practitioners to use, and potential collapse mechanisms are provided and discussed in detail.
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Acknowledgments
The authors would like to acknowledge the financial support of the Science and Technology Project of the Hunan Provincial Department of Education (Grant No. 19C0167), which made the work presented in this paper possible.
References
Abbo, A. J., D. W. Wilson, S. W. Sloan, and A. V. Lyamin. 2013. “Undrained stability of wide rectangular tunnels.” Comput. Geotech. 53: 46–59. https://doi.org/10.1016/j.compgeo.2013.04.005.
Atkinson, J. H., and A. M. Cairncross. 1973. “Collapse of a shallow tunnel in a Mohr-Coulomb material.” In Proc., Symp. on the Role of Plasticity in Soil Mechanics, edited by A. C. Palmer, 202–206. Cambridge, UK: University of Cambridge.
Bhattacharya, P., and J. Kumar. 2016. “Uplift capacity of anchors in layered sand using finite-element limit analysis: Formulation and results.” Int. J. Geomech. 16 (3): 04015078. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000560.
Ciria, H., J. Peraire, and J. Bonet. 2008. “Mesh adaptive computation of upper and lower bounds in limit analysis.” Int. J. Numer. Methods Eng. 75 (8): 899–944. https://doi.org/10.1002/nme.2275.
Davis, E. H., M. J. Gunn, R. J. Mair, and H. N. Seneviratne. 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.
Fraldi, M., and F. Guarracino. 2009. “Limit analysis of collapse mechanisms in cavities and tunnels according to the Hoek–Brown failure criterion.” Int. J. Rock Mech. Min. Sci. 46 (4): 665–673. https://doi.org/10.1016/j.ijrmms.2008.09.014.
Fraldi, M., and F. Guarracino. 2010. “Analytical solutions for collapse mechanisms in tunnels with arbitrary cross sections.” Int. J. Solids Struct. 47 (2): 216–223. https://doi.org/10.1016/j.ijsolstr.2009.09.028.
Herskovits, J., P. Mappa, E. Goulart, and C. M. M. Soares. 2005. “Mathematical programming models and algorithms for engineering design optimization.” Comput. Methods Appl. Mech. Eng. 194 (30–33): 3244–3268. https://doi.org/10.1016/j.cma.2004.12.017.
Hoek, E., and E. T. Brown. 2019. “The Hoek–Brown failure criterion and GSI—2018 edition.” J. Rock Mech. Geotech. Eng. 11 (3): 445–463. https://doi.org/10.1016/j.jrmge.2018.08.001.
Kiyosumi, M., O. Kusakabe, M. Ohuchi, and F. L. Peng. 2007. “Yielding pressure of spread footing above multiple voids.” J. Geotech. Geoenviron. Eng. 133 (12): 1522–1531. https://doi.org/10.1061/(ASCE)1090-0241(2007)133:12(1522).
Krabbenhoft, K., A. V. Lyamin, M. Hjiaj, and S. W. Sloan. 2005. “A new discontinuous upper bound limit analysis formulation.” Int. J. Numer. Methods Eng. 63 (7): 1069–1088. https://doi.org/10.1002/nme.1314.
Kumar, J., and J. P. Sahoo. 2012. “Upper bound solution for pullout capacity of vertical anchors in sand using finite elements and limit analysis.” Int. J. Geomech. 12 (3): 333–337. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000160.
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., D. L. Jack, and S. W. Sloan. 2001. “Collapse analysis of square tunnels in cohesive–frictional soils.” In Computational mechanics–new frontiers for the new millennium, edited by S. Valliappan, and N. Khalili, 405–414. Amsterdam, Netherlands: Elsevier.
Lyamin, A. V., K. Krabbenhøft, A. J. Abbo, and S. W. Sloan. 2005. “General approach to modelling discontinuities in limit analysis.” In Vol. 1 of Proc., 11th Int. Conf. Int. Assoc. Computer Methods and Advances in Geomechanics, 95–102. Bologna, Italy: Patron editore.
Lyamin, A. V., and S. W. Sloan. 2000. “Stability of a plane strain circular tunnel in a cohesive-frictional soil.” In Proc., Booker Memorial Symp., edited by D. W. Smith and J. P. Carter, 139–153. Rotterdam, The Netherlands: Balkema.
Mair, R. J. 1979. “Centrifugal modelling of tunnel construction in soft clay.” Ph.D. thesis, Engineering Dept., Univ. of Cambridge.
Merifield, R. S., A. V. Lyamin, and S. W. Sloan. 2006. “Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek–Brown criterion.” Int. J. Rock Mech. Min. Sci. 43 (6): 920–937. https://doi.org/10.1016/j.ijrmms.2006.02.001.
Merifield, R. S., S. W. Sloan, and H. S. Yu. 1999. “Rigorous plasticity solutions for the bearing capacity of two-layered clays.” Géotechnique 49 (4): 471–490. https://doi.org/10.1680/geot.1999.49.4.471.
Mühlhaus, H. B. 1985. “Lower bound solutions for circular tunnels in two and three dimensions.” Rock Mech. Rock Eng. 18 (1): 37–52. https://doi.org/10.1007/BF01020414.
Munoz, J. J., J. Bonet, A. Huerta, and J. Peraire. 2009. “Upper and lower bounds in limit analysis: Adaptive meshing strategies and discontinuous loading.” Int. J. Numer. Methods Eng. 77 (4): 471–501. https://doi.org/10.1002/nme.2421.
Osman, A. S., R. J. Mair, and M. D. Bolton. 2006. “On the kinematics of 2D tunnel collapse in undrained clay.” Géotechnique 56 (9): 585–595. https://doi.org/10.1680/geot.2006.56.9.585.
Perrotti, M., P. Lollino, N. L. Fazio, L. Pisano, G. Vessia, M. Parise, A. Fiore, and M. Luisi. 2018. “Finite element–based stability charts for underground cavities in soft calcarenites.” Int. J. Geomech. 18 (7): 04018071. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001175.
Qian, Z. G., A. J. Li, A. V. Lyamin, and C. C. Wang. 2017. “Parametric studies of disturbed rock slope stability based on finite element limit analysis methods.” Comput. Geotech. 81: 155–166. https://doi.org/10.1016/j.compgeo.2016.08.012.
Shiau, J. S., R. S. Merifield, A. V. Lyamin, and S. W. Sloan. 2011. “Undrained stability of footings on slopes.” Int. J. Geomech. 11 (5): 381–390. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000092.
Sloan, S. W. 2013. “Geotechnical stability analysis.” Géotechnique 63 (7): 531–571. 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. 1993. Stability of shallow tunnels in soft ground. Predictive soil mechanics, 644–663. London: Thomas Telford.
Suchowerska, A. M., R. S. Merifield, J. P. Carter, and J. Clausen. 2012. “Prediction of underground cavity roof collapse using the Hoek–Brown failure criterion.” Comput. Geotech. 44: 93–103. https://doi.org/10.1016/j.compgeo.2012.03.014.
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.
Ukritchon, B., and S. Keawsawasvong. 2018. “Three-dimensional lower bound finite element limit analysis of Hoek-Brown material using semidefinite programming.” Comput. Geotech. 104: 248–270. https://doi.org/10.1016/j.compgeo.2018.09.002.
Ukritchon, B., and S. Keawsawasvong. 2019a. “Stability of unlined square tunnels in Hoek-Brown rock masses based on lower bound analysis.” Comput. Geotech. 105: 249–264. https://doi.org/10.1016/j.compgeo.2018.10.006.
Ukritchon, B., and S. Keawsawasvong. 2019b. “Lower bound stability analysis of plane strain headings in Hoek-Brown rock masses.” Tunnelling Underground Space Technol. 84: 99–112. https://doi.org/10.1016/j.tust.2018.11.002.
Ukritchon, B., and S. Keawsawasvong. 2019c. “Lower bound solutions for undrained face stability of plane strain tunnel headings in anisotropic and non-homogeneous clays.” Comput. Geotech. 112: 204–217. https://doi.org/10.1016/j.compgeo.2019.04.018.
Ukritchon, B., and S. Keawsawasvong. 2019d. “Stability of retained soils behind underground walls with an opening using lower bound limit analysis and second-order cone programming.” Geotech. Geol. Eng. 37 (3): 1609–1625. https://doi.org/10.1007/s10706-018-0710-9.
Ukritchon, B., and S. Keawsawasvong. 2020. “Undrained stability of unlined square tunnels in clays with linearly increasing anisotropic shear strength.” Geotech. Geol. Eng. 38 (1): 897–915. https://doi.org/10.1007/s10706-019-01023-8.
Ukritchon, B., S. Keawsawasvong, and K. Yingchaloenkitkhajorn. 2017a. “Undrained face stability of tunnels in Bangkok subsoils.” Int. J. Geotech. Eng. 11 (3): 262–277. https://doi.org/10.1080/19386362.2016.1214773.
Ukritchon, B., K. Yingchaloenkitkhajorn, and S. Keawsawasvong. 2017b. “Three-dimensional undrained tunnel face stability in clay with a linearly increasing shear strength with depth.” Comput. Geotech. 88: 146–151. https://doi.org/10.1016/j.compgeo.2017.03.013.
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.
Wilson, D. W., A. J. Abbo, S. W. Sloan, and K. Yamamoto. 2017. “Undrained stability of rectangular tunnels where shear strength increases linearly with depth.” Can. Geotech. J. 54 (4): 469–480. https://doi.org/10.1139/cgj-2016-0072.
Xiao, Y., M. Zhao, and H. Zhao. 2018a. “Undrained stability of strip footing above voids in two-layered clays by finite element limit analysis.” Comput. Geotech. 97: 124–133. https://doi.org/10.1016/j.compgeo.2018.01.005.
Xiao, Y., M. Zhao, H. Zhao, and R. Zhang. 2018b. “Finite element limit analysis of the bearing capacity of strip footing on a rock mass with voids.” Int. J. Geomech. 18 (9): 04018108. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001262.
Xiao, Y., M. Zhao, R. Zhang, H. Zhao, and G. Wu. 2019a. “Stability of dual square tunnels in rock masses subjected to surcharge loading.” Tunnelling Underground Space Technol. 92: 103037. https://doi.org/10.1016/j.tust.2019.103037.
Xiao, Y., M. Zhao, R. Zhang, H. Zhao, and G. Wu. 2019b. “Undrained bearing capacity of strip footings placed adjacent to two-layered slopes.” Int. J. Geomech. 19 (8): 06019014. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001480.
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., and J. S. Yang. 2010. “Stability of shallow tunnel using rigid blocks and finite-element upper bound solutions.” Int. J. Geomech. 10 (6): 242–247. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000011.
Yang, X. L., and F. Huang. 2011. “Collapse mechanism of shallow tunnel based on nonlinear Hoek–Brown failure criterion.” Tunnelling Underground Space Technol. 26 (6): 686–691. https://doi.org/10.1016/j.tust.2011.05.008.
Yang, X. L., and F. Huang. 2013. “Three-dimensional failure mechanism of a rectangular cavity in a Hoek–Brown rock medium.” Int. J. Rock Mech. Min. Sci. 61: 189–195. https://doi.org/10.1016/j.ijrmms.2013.02.014.
Zhang, R., L. Li, L. Zhao, and G. Tang. 2018. “An adaptive remeshing procedure for discontinuous finite element limit analysis.” Int. J. Numer. Methods Eng. 116 (5): 287–307. https://doi.org/10.1002/nme.5925.
Zhang, R., Y. Xiao, M. Zhao, and J. Jiang. 2020. “Seismic bearing capacity of strip footings placed near c-φ soil slopes.” Soil Dyn. Earthquake Eng. 136: 106221. https://doi.org/10.1016/j.soildyn.2020.106221.
Zhang, R., Y. Xiao, M. Zhao, and H. Zhao. 2019. “Stability of dual circular tunnels in a rock mass subjected to surcharge loading.” Comput. Geotech. 108: 257–268. https://doi.org/10.1016/j.compgeo.2019.01.004.
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Published In
International Journal of Geomechanics
Volume 21 • Issue 1 • January 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Nov 23, 2019
Accepted: Aug 12, 2020
Published online: Oct 23, 2020
Published in print: Jan 1, 2021
Discussion open until: Mar 23, 2021
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