Determination of Support Pressure for the Design of Square Box Culverts
Publication: International Journal of Geomechanics
Volume 23, Issue 1
Abstract
A box culvert is a tunnel under roadways or railways that transports open drains or streams. The geotechnical design of such a structure involves accurate evaluation of the earth pressure on the structure. This short technical note pertains to findings of stability factors in tables and charts as an aid to civil engineers in designing unlined square box culverts. A conventional equation that is similar to Terzaghi's bearing capacity factors (Nc, Ns, and Nγ) is adopted to examine the use of stability factors (Fc, Fs, and Fγ) to estimate the critical support pressures at collapse. Rigorous upper-bound and lower-bound solutions of the stability factors are computed using the adaptive finite-element limit analysis. To validate the present bound solutions, numerical results are compared with those published previously using other methods. Design tables, figures, and examples are presented for practical uses.
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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.
Abousnina, R. M., A. Manalo, J. Shiau, and W. Lokuge. 2016. “An overview on oil contaminated sand and its engineering applications.” Int. J. Geomate. 10 (19): 1615–1622.
Anagnostou, G., and K. Kovári. 1996. “Face stability conditions with earth-pressure-balanced shields.” Tunnelling Underground Space Technol. 11 (2): 165–173. https://doi.org/10.1016/0886-7798(96)00017-X.
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).
Atkinson, J. H., and R. J. Mair. 1981. “Soil mechanics aspects of soft ground tunnelling.” Ground Eng. 14 (5): 20–28.
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.
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.
Dutta, P., and P. Bhattacharya. 2019. “Stability of rectangular tunnel in cohesionless soils.” Int. J. Geotech. Eng. 5 (10): 1–7. https://doi.org/10.1080/19386362.2019.1592874.
Keawsawasvong, S., J. Shiau, C. Ngamkhanong, V. Q. Lai, and C. Thongchom. 2022. “Undrained stability of ring foundations: Axisymmetry, anisotropy, and nonhomogeneity.” Int. J. Geomech. 22 (1): 04021253. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002229.
Krabbenhøft, K., A. V. Lyamin, and S. W. Sloan. 2007. “Formulation and solution of some plasticity problems as conic programs.” Int. J. Solids Struct. 44 (5): 1533–1549. https://doi.org/10.1016/j.ijsolstr.2006.06.036.
Lyamin, A. V., and S. W. Sloan. 2002a. “Lower bound limit analysis using non-linear programming.” Int. J. Numer. Methods Eng. 55 (5): 573–611. https://doi.org/10.1002/nme.511.
Lyamin, A. V., and S. W. Sloan. 2002b. “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.
OptumCE. 2019. Optumg2. Copenhagen, Denmark: Optum Computational Engineering. Accessed August 10, 2019. https://optumce.com/.
Qarmout, M., D. König, P. Gussmann, M. Thewes, and T. Schanz. 2019. “Tunnel face stability analysis using Kinematical Element Method.” Tunnelling Underground Space Technol. 85: 354–367. https://doi.org/10.1016/j.tust.2018.11.024.
Shiau, J., and F. Al-Asadi. 2022. “Stability factors Fc, Fs and Fγ for twin tunnels in three dimensions.” Int. J. Geomech. 22 (3): 04021290. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002264.
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. “Twin tunnels stability factors Fc, Fs and Fγ.” Geotech. Geol. Eng. 39: 335–345. https://doi.org/10.1007/s10706-020-01495-z.
Shiau, J., and F. Al-Asadi. 2020d. “Three-Dimensional analysis of circular tunnel headings using broms and bennermark’s 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. 2021. “Revisiting circular tunnel stability using broms and bennermarks” original stability number.” Int. J. Geomech. 21 (5): 06021009. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001996.
Shiau, J., B. Chudal, K. Mahalingasivam, and S. Keawsawasvong. 2021a. “Pipeline burst-related ground stability in blowout condition.” Transp. Geotech. 29: 100587. https://doi.org/10.1016/j.trgeo.2021.100587.
Shiau, J., S. Keawsawasvong, and J.-S. Lee. 2022. “Three-dimensional stability investigation of trapdoors in collapse and blowout conditions.” Int. J. Geomech. 22 (4): 04022007. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002339.
Shiau, J., B. Lamb, M. Sams, and J. Lobwein. 2017. “Stability charts for unsupported circular tunnels in cohesive soils.” Int. J. Geomate. 13 (39): 95–102.
Shiau, J., J.-S. Lee, and F. Al-Asadi. 2021b. “Three-dimensional stability analysis of active and passive trapdoors.” Tunnelling Underground Space Technol. 107: 103635. https://doi.org/10.1016/j.tust.2020.103635.
Shiau, J., A. V. Lyamin, and S. W. Sloan. 2006a. “Application of pseudo-static limit analysis in geotechnical earthquake design.” In Pro., 6th European Conf. on Numerical Methods in Geotechnical Engineering. Boca Raton, FL: CRC Press.
Shiau, J., S. Pather, and R. Ayers. 2006b. “Developing physical models for geotechnical teaching and research.” In Proc., 6th IC Physical Modelling in Geotechnics, 157–162. Boca Raton, FL: CRC Press.
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.
Shiau, J., and C. Smith. 2006. “Numerical analysis of passive earth pressures with interfaces.” In Proc., of the III European Conf. on Computational Mechanics. Dordrecht, Netherlands: Springer.
Shiau, J., and H. Yu. 2000. “Shakedown analysis of flexible pavements.” In Proc., of the John Booker Memorial Symp., edited by D. W. Smith and J. P. Carter, 643–653. Rotterdam, Netherlands: Balkema.
Shiau, J. S., and J. F. Watson. 2008. “3D bearing capacity of shallow foundations located near deep excavation sites.” In Proc., Int. Conf. on Deep Excavation: Challenges Risk Management of Underground Construction. Piscataway, NJ: IEEE.
Sloan, S. W. 1988. “Lower bound limit analysis using finite elements and linear programming.” Int. J. Numer. Anal. Methods Geomech. 12 (1): 61–77. https://doi.org/10.1002/nag.1610120105.
Sloan, S. W. 1989. “Upper bound limit analysis using finite elements and linear programming.” Int. J. Numer. Anal. Methods Geomech. 13 (3): 263–282. https://doi.org/10.1002/nag.1610130304.
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.
Ukritchon, B., and S. Keawsawasvong. 2020. “Undrained stability of unlined square tunnels in clays with linearly increasing anisotropic shear strength.” Geotech. Geol. Eng. 38 (6): 897–915. https://doi.org/10.1007/s10706-019-01023-8.
Vermeer, P. A., N. Ruse, and T. Marcher. 2002. “Tunnel heading stability in drained ground.” Felsbau 20 (6): 8–18.
Wilson, D. W., A. J. Abbo, S. W. Sloan, and K. Yamamotob. 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.
Yamamoto, K., A. V. Lyamin, D. W. Wilson, S. W. Sloan, and A. J. Abbo. 2011. “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.
Zhang, J., Z. Hang, T. Feng, and F. Yang. 2020. “Assessment of the stability of an unlined rectangular tunnel with an overload on the ground surface.” Adv. Civ. Eng. 2020: 6616067.
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Published In
International Journal of Geomechanics
Volume 23 • Issue 1 • January 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jan 10, 2022
Accepted: Jul 29, 2022
Published online: Oct 21, 2022
Published in print: Jan 1, 2023
Discussion open until: Mar 21, 2023
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Cited by
- G. Gowtham, Jagdish Prasad Sahoo, Seismic Stability Analysis of Square and Rectangular Tunnels in Cohesive-Frictional Soils, Natural Hazards Review, 10.1061/NHREFO.NHENG-1955, 25, 3, (2024).
- Jim Shiau, Suraparb Keawsawasvong, Fadhil Al-Asadi, Use of Terzaghi’s Superposition Approach for Estimating Critical Supporting Pressures in Circular Tunnels, Transportation Infrastructure Geotechnology, 10.1007/s40515-023-00282-6, (2023).