Stability of Horseshoe Tunnel in Cohesive-Frictional Soil
Publication: International Journal of Geomechanics
Volume 20, Issue 9
Abstract
The stability of long horseshoe tunnels in cohesive-frictional soils is examined by using lower bound finite element limit analysis. Its stability is assessed by determining the magnitude of uniform internal normal pressure required to be applied along the tunnel peripheral face. If the pressure required to be applied to the tunnel peripheral face at a particular soil cover depth and soil condition is compressive in nature, then it indicates that the tunnel is unstable without the lining pressure at that particular condition. The analysis has been done for different combinations of (i) soil cover depth (H), (ii) ratio of tunnel height to width (h/B), (iii) peak soil friction angle ϕ, and (iv) γB/c where c refers to soil cohesion, γ is soil unit weight, and B is the tunnel width. The results are presented here in terms of normalized compressive internal pressure (σt /c) for both smooth and rough tunnel boundary conditions. The magnitude of σt /c appeared to (a) increase with an increase in γB/c, h/B, and H/B and (b) decrease with an increase in ϕ and roughness condition of the tunnel boundary. The results are presented in the form of dimensionless charts.
Get full access to this article
View all available purchase options and get full access to this article.
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 D. M. Potts. 1977. “Stability of a shallow circular tunnel in cohesionless soil.” Géotechnique 27 (2): 203–215. https://doi.org/10.1680/geot.1977.27.2.203.
Bottero, A., R. Negre, J. Pastor, and S. Turgeman. 1980. “Finite element method and limit analysis theory for soil mechanics problems.” Comput. Methods Appl. Mech. Eng. 22 (1): 131–149. https://doi.org/10.1016/0045-7825(80)90055-9.
Chen, R. P., J. Zhu, W. Liu, and X. W. Tang. 2011. “Ground movement induced by parallel EPB tunnels in silty soils.” Tunnelling Underground Space Technol. 26 (1): 163–171. https://doi.org/10.1016/j.tust.2010.09.004.
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.
Klar, A., A. S. Osman, and M. D. Bolton. 2007. “2D and 3D upper bound solutions for tunnel excavation using “elastic” flow fields.” Int. J. Numer. Anal. Methods Geomech. 31 (12): 1367–1374. https://doi.org/10.1002/nag.597.
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.
Lee, C. J., B. R. Wu, H. T. Chen, and K. H. Chiang. 2006. “Tunnel stability and arching effects during tunneling in soft clayey soil.” Tunnelling Underground Space Technol. 21 (2): 119–132. https://doi.org/10.1016/j.tust.2005.06.003.
Li, P., F. Wang, and Q. Fang. 2018. “Undrained analysis of ground reaction curves for deep tunnels in saturated ground considering the effect of ground reinforcement.” Tunnelling Underground Space Technol. 71: 579–590. https://doi.org/10.1016/j.tust.2017.11.001.
Mair, R. J. 1979. “Centrifugal modelling of tunnel construction in soft clay.” Ph.D. thesis, Engineering Dept., Univ. of Cambridge.
Osman, A. S. 2010. “Stability of unlined twin tunnels in undrained clay.” Tunnelling Underground Space Technol. 25 (3): 290–296. https://doi.org/10.1016/j.tust.2010.01.004.
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.
Sahoo, J. P., and B. Kumar. 2019. “Stability of circular tunnels in clay with an overlay of sand.” Int. J. Geomech. 19 (3): 06018039. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001360.
Sahoo, J. P., and J. Kumar. 2014. “Stability of a circular tunnel in presence of pseudostatic seismic body forces.” Tunnelling Underground Space Technol. 42: 264–276. https://doi.org/10.1016/j.tust.2014.03.003.
Sahoo, J. P., and J. Kumar. 2018. “Required lining pressure for the stability of twin circular tunnels in soils.” Int. J. Geomech. 18 (7): 04018069. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001196.
Shen, S.-L., H.-N. Wu, Y.-J. Cui, and Z.-J. Yin. 2014. “Long-term settlement behaviour of metro tunnels in the soft deposits of Shanghai.” Tunnelling Underground Space Technol. 40: 309–323. https://doi.org/10.1016/j.tust.2013.10.013.
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.” In Predictive soil mechanics, edited by G. T. Holsby, and A. N. Schofield, 644–663. London: Thomas Telford.
Ukritchon, B., and S. Keawsawasvong. 2019a. “Undrained stability of unlined square tunnels in clays with linearly increasing anisotropic shear strength.” Geotech. Geol. 105: 249–264.
Ukritchon, B., and S. Keawsawasvong. 2019b. “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. 2019c. “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.
Wilson, D. W., A. J. Abbo, and S. W. Sloan. 2014b. “Undrained stability of tall tunnels.” Computer methods and recent advances in geomechanics. Edited by Fusao Oka, Akira Murakami, Ryosuke Uzuoka, Sayuri Kimoto, 447–452. London: CRC Press.
Wilson, D. W., A. J. Abbo, S. W. Sloan, and A. V. Lyamin. 2014a. “Undrained stability of dual square tunnels.” Int. J. Geomech. 14 (1): 69–79. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000288.
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 A. V. Lyamin. 2015. “Undrained stability of dual square tunnels.” Acta Geotech 10: 665–682. https://doi.org/10.1007/s11440-014-0340-1.
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.
Wu, B. R., and C. J. Lee. 2003. “Ground movements and collapse mechanisms induced by tunneling in clayey soil.” Int. J. Phys. Modell. Geotech. 3 (4): 15–29. https://doi.org/10.1680/ijpmg.2003.030402.
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., X. Sun, X. Zheng, and J. Yang. 2017. “Stability analysis of a deep buried elliptical tunnel in cohesive-frictional (c–ϕ) soils with a nonassociated flow rule.” Can. Geotech. J. 54 (5): 736–741. https://doi.org/10.1139/cgj-2016-0523.
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, 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, J., T. Feng, J. Yang, F. Yang, and Y. Gao. 2018a. “Upper-bound finite-element analysis of characteristics of critical settlement induced by tunneling in undrained clay.” Int. J. Geomech. 18 (9): 04018110. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001224.
Zhang, J., T. Feng, J. Yang, Y. Feng, and Y. Gao. 2018b. “Upper-bound stability analysis of dual unlined horseshoe-shaped tunnels subjected to gravity.” Comput. Geotech. 97: 103–110. https://doi.org/10.1016/j.compgeo.2018.01.006.
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.
Zhang, J., F. Yang, J. Yang, X. Zheng, and F. Zeng. 2016. “Upper-bound stability analysis of dual unlined elliptical tunnels in cohesive-frictional soils.” Comput. Geotech. 80: 283–289. https://doi.org/10.1016/j.compgeo.2016.08.023.
Zhang, J., J. Yang, F. Yang, X. Zhang, and X. Zheng. 2017. “Upper-bound solution for stability number of elliptical tunnel in cohesionless soils.” Int. J. Geomech. 17 (1): 06016011. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000689.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 20 • Issue 9 • September 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Feb 16, 2019
Accepted: Mar 24, 2020
Published online: Jun 19, 2020
Published in print: Sep 1, 2020
Discussion open until: Nov 19, 2020
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.