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Numerical modelling of three-dimensional sinkhole stability using finite different method

Innovative Infrastructure Solutions volume 6, Article number: 183 (2021) Cite this article

Abstract

The stability of a cavity underlying homogeneous clay in an unsupported greenfield condition is examined in this paper using the finite difference program, FLAC. Shear strength reduction method (SSRM) is utilised to study two- and three-dimensional failure mechanisms of a horizontal trapdoor. Stability results are presented in the forms of factors of safety (FoS) and failure extent ratios for various dimensionless ratios. Numerical results are compared with the finite element limit analysis technique with upper and lower bound theorems, and a good agreement is found between the solutions. Several practical examples are provided to demonstrate the use of design charts and tables.

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References

  1. Abbasi B, Russell D, Taghavi R (2013) 'FLAC 3D mesh and zone quality. Itasca Consulting Group, Minneapolis, Minnesota, USA

  2. Abdulla WA, Goodings DJ (1996) Modeling of sinkholes in weakly cemented sand. J Geotech Eng 122(12):998–1005

    Article  Google Scholar 

  3. Atkinson J, Potts D (1977) Stability of a shallow circular tunnel in cohesionless soil. Geotechnique 27(2):203–215

    Article  Google Scholar 

  4. Augarde CE, Lyamin AV, Sloan SW (2003) Prediction of undrained sinkhole collapse. J Geotech Geoenviron Eng 129(3):197–205

    Article  Google Scholar 

  5. Broms BB, Bennermark H (1967) ‘Stability of clay at vertical openings’, Journal of the Soil Mechanic & Foundations Division. Proc Am Soc Civ Eng 93:71–93

    Google Scholar 

  6. Craig W (1990) Collapse of cohesive overburden following removal of support. Can Geotech J 27(3):355–364

    Article  Google Scholar 

  7. Davis E, Gunn M, Mair R, Seneviratine H (1980) The stability of shallow tunnels and underground openings in cohesive material. Geotechnique 30(4):397–416

    Article  Google Scholar 

  8. Drumm EC, Aktürk Ö, Akgün H, Tutluoğlu L (2009) Stability charts for the collapse of residual soil in karst. J Geotech Geoenviron Eng 135(7):925–931

    Article  Google Scholar 

  9. Itasca (2002) Fast Lagrangian analysis of continua, FLAC3D Version 2.0, Itasca Consulting Group, Minneapolis, Minnesota, USA

  10. Itasca (2003) Fast Lagrangian analysis of continua, FLAC2D Version 5.0, Itasca Consulting Group, Minneapolis, Minnesota, USA

  11. Jacobsz SW (2016) Trapdoor experiments studying cavity propagation. In: Proceedings of the 1st Southern African geotechnical conference. CRC Press, Taylor & Francis Group, pp 159–165

  12. Keawsawasvong S, Ukritchon B (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

    Article  Google Scholar 

  13. Krabbenhoft K, Lyamin AV (2015) Strength reduction finite-element limit analysis. Géotech Lett 5(4):250–253

    Article  Google Scholar 

  14. Leca E, Dormieux L (1990) Upper and lower bound solutions for the face stability of shallow circular tunnels in frictional material. Geotechnique 40(4):581–606

    Article  Google Scholar 

  15. Mettler K (2015) Seffner sinkhole’, Tampa Bay Times, Florida, United States, viewed 26 June 2018. http://www.tampabay.com/news/publicsafety/report-new-hole-opens-at-site-of-2013-fatal-sinkhole-in-seffner/2241

  16. Mühlhaus H-B (1985) Lower bound solutions for circular tunnels in two and three dimensions. Rock Mech Rock Eng 18(1):37–52

    Article  Google Scholar 

  17. OptumG2 (2018) Optum computational engineering. https://optumce.com/

  18. Shiau J, Pather S, Ayers R (2006) Developing physical models for geotechnical teaching and research. In: Proceedings of 6th IC physical modelling in geotechnics, pp 157–162

  19. Shiau J, Sams M, Lamb B (2016) Introducing advanced topics in geotechnical engineering teaching–Tunnel modelling. Int J GEOMATE 10(1):1698–1705

    Google Scholar 

  20. Shiau J, Al-Asadi F (2018) Revisiting Broms and Bennermarks’ original stability number for tunnel headings. Geotech Lett 8(4):310–315

    Article  Google Scholar 

  21. Shiau JS, Sams MS (2019) Relating volume loss and greenfieldsettlement. Tunn Undergr Space Technol 83:145–152

    Article  Google Scholar 

  22. Shiau J, Hassan MM (2020) Undrained stability of active and passive trapdoors. Geotech Res. https://doi.org/10.1680/jgere.19.00033

  23. Shiau J, Al-Asadi F (2020) Determination of critical tunnel heading pressures using stability factors. Comput Geotech 119:103345

    Article  Google Scholar 

  24. Shiau J, Hassan MM (2020) Undrained stability of active and passive trapdoors. Geotech Res 7(1):40–48

    Article  Google Scholar 

  25. Shiau J, Lee J-S, Al-Asadi F (2021) Three-dimensional stability analysis of active and passive trapdoors. Tunn Undergr Space Technol 107:103635

    Article  Google Scholar 

  26. Shiau J, Al-Asadi F (2021) Revisiting circular tunnel stability using Broms and Bennermarks’ original stability number. Int J Geomech 21(5):06021009

    Article  Google Scholar 

  27. Sloan S, Assadi A, Purushothaman N (1990) Undrained stability of a trapdoor. Geotechnique 40(1):45–62

    Article  Google Scholar 

  28. Taylor DW (1937) Stability of earth slopes. J Boston Soc Civ Eng 24(3):197–247

    Google Scholar 

  29. Terzaghi K (1936) Stress distribution in dry and saturated sand above a yielding trap-door. In: Proceedings of the international conference of soil mechanic. Harvard University Press, Cambridge, vol. 1, no. 4, pp 307–311

  30. Tharp TM (2003) Cover-collapse sinkhole formation and soil plasticity. In: Sinkholes and the engineering and environmental impacts of Karst, pp 110–23

  31. Vaziri HH, Jalali JS, Islam R (2001) An analytical model for stability analysis of rock layers over a circular opening. Int J Solids Struct 38(21):3735–3757

    Article  Google Scholar 

  32. Yang MZ, Drumm EC (2002) Stability evaluation for the siting of municipal landfills in karst. Eng Geol 65(2):185–195

    Article  Google Scholar 

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Authors and Affiliations

  1. School Civil Engineering and Surveying, Faculty of Health, Engineering and Sciences, University of Southern Queensland, West Street, Toowoomba, QLD, 4350, Australia

    Jim Shiau & Mohammad Mirza Hassan

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  1. Jim Shiau
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  2. Mohammad Mirza Hassan
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Correspondence to Jim Shiau.

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Shiau, J., Hassan, M.M. Numerical modelling of three-dimensional sinkhole stability using finite different method. Innov. Infrastruct. Solut. 6, 183 (2021). https://doi.org/10.1007/s41062-021-00559-0

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  • DOI: https://doi.org/10.1007/s41062-021-00559-0

Keywords

  • Sinkhole
  • Factor of safety
  • Strength reduction method
  • Clay
  • Finite different method
  • FLAC