Abstract
The stability analysis of a rectangular tunnel with a horizontal base in sloping ground has been carried out by using lower and upper bound finite element limit analysis (FELA). It is intended to compute the required lining pressure to support the tunnel without causing any shear failure (collapse) in cohesive-frictional soil media. The lining pressure becomes an important parameter while designing the liner element for any tunnel. The required lining pressure becomes a function of ground slope inclination and soil shear strength parameters. All the numerical results are presented in the form of non-dimensional parameters. It is found that the magnitude of the lining compressive pressure increases continuously with increases in the ground inclination (\(\beta\)) as well as the cover (H) to height (D) ratio of the tunnel. The failure mechanisms have also been examined in order to assess the geometry of the plastic zones during the tunnel collapse. It is noted that the lateral spread of the failure zone increases continuously with an increase in the value of H/D. The results will be useful for performing the design of any rectangular tunnel on a sloping ground surface.
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Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
References
Abbo, A.J., Wilson, D.W., Sloan, S.W., Lyamin, A.V.: Undrained stability of wide rectangular tunnels. Comput. Geotech. 1(53), 46–59 (2013)
Assadi, A., Sloan, S.W.: Undrained stability of shallow square tunnel. J. Geotech. Eng. 117(8), 1152–1173 (1991)
Atkinson, J.H., Potts, D.M.: Stability of a shallow circular tunnel in cohesionless soil. Geotechnique 27(2), 203–215 (1977)
Banerjee, S.K., Chakraborty, D.: Stability of long circular tunnels in sloping ground. Geomech. Geoeng. 13(2), 104–114 (2018)
Broms, B.B., Bennermark, H.: Stability of clay at vertical opening. J. Soil Mech. Found. Div. 93(1), 71–94 (1967)
Chambon, P., Corte, J.F.: Shallow tunnels in cohesionless soil: stability of tunnel face. J. Geotech. Eng. 120(7), 1148–1165 (1994)
Dutta, P., Bhattacharya, P.: Stability of rectangular tunnel in cohesionless soils. Int. J. Geotech. Eng. (2019)
Keawsawasvong, S., Lai, V.Q.: End bearing capacity factor for annular foundations embedded in clay considering the effect of the adhesion factor. Int J Geosynth. Ground Eng. 7(1), 1 (2021)
Keawsawasvong, S., Thongchom, C., Likitlersuang, S.: Bearing capacity of strip footing on Hoek-Brown rock mass subjected to eccentric and inclined loading. Transp. Infrastruct. Geotechnol. 8(2), 189–202 (2021)
Keawsawasvong, S., Ukritchon, B.: Undrained stability of a spherical cavity in cohesive soils using finite element limit analysis. J. Rock Mech. Geotech. Eng. 11(6), 1274–1285 (2019)
Keawsawasvong, S., Ukritchon, B.: Undrained basal stability of braced circular excavations in non-homogeneous clays with linear increase of strength with depth. Comput. Geotech. 115, 103180 (2019)
Keawsawasvong, S., Ukritchon, B.: Design equation for stability of a circular tunnel in anisotropic and heterogeneous clay. Undergr. Space. 7(1), 76–93 (2022)
Krabbenhoft, K., Lyamin, A., Krabbenhoft, J.: Optum computational engineering (OptumG2). Available on:< www. optumce. com. 2019. (2015)
Kumar, B., Sahoo, J.P.: Stability of square tunnels in two layered clayey soil. Lect. Notes Civ. Eng. 85, 493–502 (2020)
Leca, E., Dormieux, L.: Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material. Géotechnique 40(4), 581–606 (1990)
Mollon, G., Dias, D., Soubra, A.H.: Probabilistic analysis and design of circular tunnels against face stability. Int. J. Geomech. 9(6), 237–249 (2009)
Mollon, G., Dias, D., Soubra, A.H.: Face stability analysis of circular tunnels driven by a pressurized shield. J. Geotech. Geoenviron. Eng. 136(1), 215–229 (2010)
Mühlhaus, H.B.: Lower bound solutions for circular tunnels in two and three dimensions. Rock Mech. Rock Eng. 18(1), 37–52 (1985)
Sahoo, J.P., Kumar, J.: Seismic stability of a long unsupported circular tunnel. Comput. Geotech. 1(44), 109–115 (2012)
Sahoo, J.P., Kumar, J.: Stability of long unsupported twin circular tunnels in soils. Tunn. Undergr. Space Technol. 1(38), 326–335 (2013)
Sahoo, J.P., Kumar, J.: Stability of a circular tunnel in presence of pseudostatic seismic body forces. Tunn. Undergr. Space Technol. 1(42), 264–276 (2014)
Sahoo, J.P., Kumar, J.: Required lining pressure for the stability of twin circular tunnels in soils. Int. J. Geomech. 18(7), 04018069 (2018)
Shiau, J., Al-Asadi, F.: Revisiting circular tunnel stability using Broms and Bennermarks’ original stability number. Int. J. Geomech. 21(5), 06021009 (2021)
Shiau, J., Keawsawasvong, S.: Producing undrained stability factors for various tunnel shapes. Int. J. Geomech. 22(8), 06022017 (2022)
Shiau, J., Keawsawasvong, S., Yodsomjai, W.: Determination of support pressure for the design of square box culverts. Int. J. Geomech. 23(1), 06022035 (2023)
Sloan, S.W.: Geotechnical stability analysis. Géotechnique 63(7), 531–571 (2013)
Sloan, S.W., Assadi, A.: Stability of shallow tunnels in soft ground. In Predictive soil mechanics: Proceedings of the Wroth Memorial Symposium held at St Catherine’s College, Oxford, 27–29 July 1992 (pp. 644–663). Thomas Telford Publishing. (1992)
Wilson, D.W., Abbo, A.J., Sloan, S.W., Lyamin, A.V.: Undrained stability of a circular tunnel where the shear strength increases linearly with depth. Can. Geotech. J. 48(9), 1328–1342 (2011)
Wilson, D.W., Abbo, A.J., Sloan, S.W., Lyamin, A.V.: Undrained stability of a square tunnel where the shear strength increases linearly with depth. Comput. Geotech. 1(49), 314–325 (2013)
Yamamoto, K., Lyamin, A.V., Wilson, D.W., Sloan, S.W., Abbo, A.J.: Stability of a single tunnel in cohesive–frictional soil subjected to surcharge loading. Can. Geotech. J. 48(12), 1841–1854 (2011)
Yodsomjai, W., Keawsawasvong, S., Lai, V.Q.: Limit analysis solutions for bearing capacity of ring foundations on rocks using Hoek-Brown failure criterion. Int. J. Geosynth. Ground Eng. 7(2), 1 (2021)
Yodsomjai, W., Keawsawasvong, S., Likitlersuang, S.: Stability of unsupported conical slopes in Hoek-Brown rock masses. Transp. Infrastruct. Geotechnol. 8(2), 279–295 (2021)
Acknowledgements
This study was supported by Bualuang ASEAN Chair Professor Fund. Also, this study was supported by Thammasat University Research Fund, Contract No. TUFT 19/2566.
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Wittaya Jitchaijaroen acquired methodology and software and contributed to investigation, data curation, and writing—original draft.
Suraparb Keawsawasvong acquired conceptualization, methodology and software and contributed to investigation, data curation, and writing—original draft.
Jyant Kumar acquired conceptualization, methodology, supervision, resource, project administration, and writing—reviewing and editing.
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Jitchaijaroen, W., Keawsawasvong, S. & Kumar, J. Required Supporting Lining Pressure for the Stability of a Rectangular Tunnel in Sloping Ground. Transp. Infrastruct. Geotech. (2023). https://doi.org/10.1007/s40515-023-00313-2
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DOI: https://doi.org/10.1007/s40515-023-00313-2