Skip to main content

Three-Dimensional Circular Trapdoor Stability


The stability of a circular opening trapdoor in undrained cohesive soils is numerically investigated using three-dimensional (3D) numerical simulations. FLAC3D, a finite difference program using the shear strength reduction method (SSRM), is employed to determine the factor of safety (FoS) solutions that are a function of the depth ratio and the shear strength ratio. Numerical results from the current FoS study suggest that the 3D circular opening results are almost twice larger than those in 2D study. The strong arching effects have been noted for deeper cases, and the corresponding global failure mechanism is observed. The results are compared with published solutions in the literature. Practical examples are used to demonstrate how to use the design charts and equations in practice.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Data Availability

The data and materials in this paper are available.


  • Abbasi, B., Russell, D., Taghavi, R.: FLAC 3D mesh and zone quality. Proceedings of the 3rd International FLAC/DEM Symposium, China (2013)

  • Augarde, C.E., Lyamin, A.V., Sloan, S.W.: Prediction of undrained sinkhole collapse. J. Geotech. Geoenviron. Eng. 129(3), 197–205 (2003)

    Article  Google Scholar 

  • Baker, R.: A second look at Taylor’s stability chart. J. Geotech. Geoenviron. Eng. 129(12), 1102–1108 (2003)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Keawsawasvong, S.: Limit analysis solutions for spherical cavities in sandy soils under overloading. Innov Infrastruct Solut. 6, 33 (2021)

    Article  Google Scholar 

  • Keawsawasvong, S., Likitlersuang, S.: Undrained stability of active trapdoors in two-layered clays. Undergr Space. (2021).

  • Keawsawasvong, S., Ukritchon, B.: Undrained stability of an active planar trapdoor in non-homogeneous clays with a linear increase of strength with depth. Comput. Geotech. 81, 284–293 (2017)

    Article  Google Scholar 

  • 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)

    Article  Google Scholar 

  • Keawsawasvong, S., Ukritchon, B.: Undrained stability of plane strain active trapdoors in anisotropic and non-homogeneous clays. Tunn. Undergr. Space Technol. 107, 103628 (2021)

    Article  Google Scholar 

  • Martin, C.: Undrained collapse of a shallow plane-strain trapdoor. Geotechnique. 59(10), 855–863 (2009)

    Article  Google Scholar 

  • McCarthy, D.F.: Essentials of soil mechanics and foundations, Sixth edn. Prentice Hall, Hoboken (2002)

    Google Scholar 

  • Shiau, J., Al-Asadi, F.: Two-dimensional tunnel heading stability factors Fc, Fs and Fγ. Tunn Undergr Space Technol. 97, 103293 (2020a)

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Shiau, J., Al-Asadi, F.: Twin tunnels stability factors Fc, Fs and Fγ. Geotech Geol Eng. 39, 335–345 (2020c).

    Article  Google Scholar 

  • Shiau, J., Al-Asadi, F.: Three-dimensional analysis of circular tunnel headings using Broms and Bennermarks’ original stability number. Int J Geomech. 20(7), 06020015 (2020d)

    Article  Google Scholar 

  • Shiau, J., Hassan, M.M.: Undrained stability of active and passive trapdoors. Geotech Res. 7(1), 40–48 (2019)

    Article  Google Scholar 

  • Shiau, J., Pather, S., Ayers, R.: Developing physical models for geotechnical teaching and research’, Proc. 6th IC Physical Modelling in Geotechnics, 157–162 (2006)

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

    Google Scholar 

  • Shiau, J., Lamb, B., Sams, M.: The use of sinkhole models in advanced geotechnical engineering teaching. Int. J. Geomate. 10(2), 1718–1724 (2016b)

    Google Scholar 

  • Shiau, J., Hassan, M.M., Hossein, Z.: Stability charts for unsupported square tunnels in homogeneous undrained clay. Int J Geomate. 15(48), 195–201 (2018)

    Article  Google Scholar 

  • Taylor, D.W.: Stability of earth slopes. J Boston Soc Civil Eng. 24(3), 197–247 (1937)

    Google Scholar 

  • Terzaghi K.: 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 (1936)

  • Ukritchon, B., Yoang, S., Keawsawasvong, S.: Three-dimensional stability analysis of the collapse pressure on flexible pavements over rectangular trapdoors. Transp Geotech. 21, 100277 (2019)

    Article  Google Scholar 

  • Yang, M.Z., Drumm, E.C.: Stability evaluation for the siting of municipal landfills in karst. Eng. Geol. 65(2–3), 185–195 (2002)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations



Jim Shiau acquired supervision, methodology, and contributed to conceptualization, writing—original draft

Suraparb Keawsawasvong contributed to writing—review and editing

Ji-Sung Lee acquired methodology and software and contributed to investigation and data curation

Mohammad Mirza Hassan acquired methodology and software and contributed to investigation and data curation

Corresponding author

Correspondence to Suraparb Keawsawasvong.

Ethics declarations

Conflict of Interest

The authors no competing interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Shiau, J., Keawsawasvong, S., Lee, JS. et al. Three-Dimensional Circular Trapdoor Stability. Transp. Infrastruct. Geotech. 9, 173–184 (2022).

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Sinkhole
  • Circular opening
  • FLAC 3D
  • Finite difference method
  • Surface failure extent