Three-Dimensional Stability Investigation of Trapdoors in Collapse and Blowout Conditions
Publication: International Journal of Geomechanics
Volume 22, Issue 4
Abstract
Road-related sinkholes are of great concerns nowadays, appearing frequently in media stories. In the undrained stability analysis, a dimensionless stability number that is known as Broms and Bennermark’s original stability number expresses the combined effect of surface surcharge pressure, self-weight of the soil, and the supporting pressure. This “critical” undrained stability number, Nc, is used in this paper to formulate three-dimensional (3D) upper-bound and lower-bound solutions in active (collapse) and passive (blowout) scenarios of sinkhole stability using the classic trapdoor problem. Design charts, tables, and equations were developed to cover a wide range of practical design parameters. Together with modern geophysics techniques for the detection of underground cavity as well as the findings of the associated failure patterns in this paper, the study should, therefore, be of value to practitioners in their daily decision making.
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References
Broms, B. B., and H. Bennermark. 1967. “Stability of clay at vertical openings’, J. Soil Mech. Found. Div. 93: 71–94.
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: 899–944. https://doi.org/10.1002/nme.2275.
Costa, Y., J. Zornberg, B. Bueno, and C. Costa. 2009. “Failure mechanisms in sand over a deepactive trapdoor.” J. Geotech. Geoenviron. Eng. 135 (11): 1741–1753. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000134.
Davis, E. H. 1968. “Theories of plasticity and the failure of soil masses.” In Soil mechanics: Selected topics, edited by I. K. Lee, 341–380. London: Butterworths.
Enstad, G. 1975. “On the theory of arching in mass flow hoppers.” Chem. Eng. Sci. 30 (10): 1273–1283. https://doi.org/10.1016/0009-2509(75)85051-2.
Gunn, M. 1980. “Limit analysis of undrained stability problems using a very small computer.” In Proc. Symp. on Computer Applications to Geotechnical Problems in Highway Engineering, 5–30. Cambridge, UK: Dept. of Engineering, Univ. of Cambridge
Jenike, A. W. 1964. “Steady gravity flow of frictional-cohesive solids in converging channels.” J. Appl. Mech. 31 (1): 5–11. https://doi.org/10.1115/1.3629571.
Keawsawasvong, S., and B. Ukritchon. 2017. “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.
Koutsabeloulis, N. C., and D. V. Griffiths. 1989. “Numerical modelling of the trap door problem.” Geotechnique 39 (1): 77–89. https://doi.org/10.1680/geot.1989.39.1.77.
Ladanyi, B., and B. J. Hoyaux. 1969. “A study of the trap-door problem in a granular mass.” Can. Geotech. J. 6 (1): 1–14. https://doi.org/10.1139/t69-001.
Martin, C. M. 2009. “Undrained collapse of a shallow plane-strain trapdoor.” Géotechnique 59 (10): 855–863. https://doi.org/10.1680/geot.8.T.023.
Merifield, R. S., S. W. Sloan, and H. S. Yu. 2001. “Stability of plate anchors in undrained clay.” Geotechnique 51 (2): 141–153. https://doi.org/10.1680/geot.2001.51.2.141.
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.” Numer. Anal. Methods Geomech. 37 (13): 2061–2083. https://doi.org/10.1002/nag.2121.
OptumCE. 2020. Optumg3. Copenhagen, Denmark: Optum Computational Engineering.
Sahoo, J. P., and S. Khuntia. 2018. “Lower bound solutions for uplift capacity of strip anchors adjacent to sloping ground in clay.” Mar. Georesour. Geotechnol. 36 (4): 405–416. https://doi.org/10.1080/1064119X.2017.1322647.
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. “‘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. 2020b. “Three-Dimensional heading stability of twin circular tunnels.” Geotech. Geol. Eng. 38: 2973–2988, https://doi.org/10.1007/s10706-020-01201-z.
Shiau, J., and F. Al-Asadi. 2020c. “Stability analysis of twin circular tunnels using shear strength reduction method’.” Geotech. Lett. 10 (2): 311–319. https://doi.org/10.1680/jgele.19.00003.
Shiau, J., and F. Al-Asadi. 2020d. “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. 2020e. “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. 2020f. “Twin tunnels stability factors Fc, Fs and Fγ.” Geotech. Geol. Eng. 39 (1): 335–345. https://doi.org/10.1007/s10706-020-01495-z.
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., 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., B. Lamb, and M. Sams. 2016. “The use of sinkhole models in advanced geotechnical engineering teaching.” Int. J. Geomate 10 (2): 1718–1724.
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.
Sloan, S. W. 2013. “Geotechnical stability analysis.” Géotechnique 63 (7): 531–572. https://doi.org/10.1680/geot.12.RL.001.
Sloan, S. W., A. Assadi, and N. Purushothaman. 1990. “Undrained stability of a trapdoor.” Géotechnique 40 (1): 45–62. https://doi.org/10.1680/geot.1990.40.1.45.
Soliman, M. H., R. Shamet, Y. J. Kim, H. Youn, and B. H. Nam. 2019. “Numerical investigation on the mechanical behaviour of karst sinkholes.” Environ. Geotech. 40:, 1–15.
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.
Tanaka, T., and T. Sakai. 1993. “Progressive failure and scale effect of trap-door problems with granular materials.” Soils Found. 33 (1): 11–22. https://doi.org/10.3208/sandf1972.33.11.
Terzaghi, K. 1936. “Stress distribution in dry and saturated sand above a yielding trapdoor.” In Vol. 1 of Proc., Int. Conf. of Soil Mechanic, 307–311. Cambridge: Harvard University Press.
Terzaghi, K. 1943. Theoretical soil mechanics, 11–15. New York: Wiley.
Tharp, T. 1999. “Mechanics of upward propagation of cover-collapse sinkholes.” Eng. Geol. 52 (1–2): 23–33. https://doi.org/10.1016/S0013-7952(98)00051-9.
Ukritchon, B., S. Yoang, and S. Keawsawasvong. 2019. “Three-dimensional stability analysis of the collapse pressure on flexible pavements over rectangular trapdoors.” Transp. Geotech. 21: 100277. https://doi.org/10.1016/j.trgeo.2019.100277.
Van Rooy, J. L. 2018. “Editorial.” Environ. Geotech. 5 (1): 1–2. https://doi.org/10.1680/jenge.2018.5.1.1.
Vardoulakis, I., B. Graf, and G. Gudehus. 1981. “Trap-door problem with dry sand: A statical approach based upon model test kinematics.” Numer. Anal. Methods Geomech. 5 (1): 57–78. https://doi.org/10.1002/nag.1610050106.
Wang, L., B. Leshchinsky, T. M. Evans, and Y. Xie. 2017. “Active and passive arching stresses in c′-ϕ′ soils: A sensitivity study using computational limit analysis.” Comput. Geotech. 84: 47–57. https://doi.org/10.1016/j.compgeo.2016.11.016.
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 22 • Issue 4 • April 2022
Copyright
© 2022 American Society of Civil Engineers.
History
Received: May 11, 2021
Accepted: Dec 6, 2021
Published online: Jan 28, 2022
Published in print: Apr 1, 2022
Discussion open until: Jun 28, 2022
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