Skip to main content
Log in

Appropriate Uses and Practical Limitations of 2D Numerical Analysis of Tunnels and Tunnel Support Response

  • Original paper
  • Published:
Geotechnical and Geological Engineering Aims and scope Submit manuscript

Abstract

In spite of the gradual development of three-dimensional analysis packages utilizing finite element models or finite difference algorithms for stress–strain calculations, two-dimensional (2D) analysis is still used as the primary engineering tool for practical analysis of tunnel behavior and tunnel support performance for design—particularly at the preliminary stage of a project. The applicability of 2D finite element analysis or analytical convergence confinement solutions to staged support installation depend on the application of an assumed or validated longitudinal displacement profile. Convergence in commonly applied 2D staged models is controlled by boundary displacement or internal pressure relaxation. While there have been developments to improve this methodology, this often assumes independence between the ground reaction curve and the support resistance, independence between the longitudinal displacement profile to support application, and the assumption that non-isotropic stresses and non-circular geometries can be handled in the same way as circular tunnels in isotropic conditions. This paper examines the validity of these assumptions and the error inherent in these extensions to 2D tunnel analysis. Anisotropic stresses and lagged (staged) excavation present a particular problem. Practical solutions are proposed for support longitudinal displacement LDPs in simplified conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  • Bernaud D, Rousset G (1996) The ‘New Implicit Method’ for tunnel analysis. Int J Numer Anal Methods Geomech 20(9):673–690. doi:10.1002/(SICI)1096-9853(199609)20:9<673::AID-NAG845>3.0.CO;2-9

  • Brady BHG, Brown ET (1993) Rock mechanics for underground mining. Chapman and Hall 1993:571

    Google Scholar 

  • Cai M (2008) Influence of stress path on tunnel excavation response—numerical tool selection and modeling strategy. Tunn Undergr Sp Technol 23(2008):618–628

    Article  Google Scholar 

  • Cantieni L, Anagnostou G (2009) The effect of the stress path on squeezing behaviour in tunnelling. Rock Mech Rock Eng 42(2):289–318

    Article  Google Scholar 

  • Carranza-Torres C, Fairhurst C (2000) Application of the convergence–confinement method of tunnel design to rock masses that satisfy the Hoek-Brown failure criterion. Tunn Undergr Sp Technol 15(2):187–213

    Article  Google Scholar 

  • Chen WF (1982) Plasticity in Reinforced Concrete. McGraw Hill, New York, p 465p

    Google Scholar 

  • Corbetta F, Bernaud D, Nguyen-Minh D (1991) Contribution a‘la method convergerce–confinement par le principe de la similitude. Rev Fr Geotech 54:5–11

    Google Scholar 

  • Duncan Fama ME (1993) Numerical modelling of yield zones in weak rocks. In: Hudson JA (ed) Comprehensive rock engineering, vol 2. Pergamon, Oxford, pp 49–75

  • Eberhardt E (2001) Numerical modeling of three-dimensional stress rotation ahead of an advancing tunnel face. Int J Rock Mech Min Sci 38(4):499–518

    Article  Google Scholar 

  • Hoek E, Diederichs MS (2006) Empirical estimation of rock mass modulus. Int J Rock Mech Min Sci 43(2):203–215

    Article  Google Scholar 

  • Hoek E, Carranza-Torres C, Corkum B. (2002) Hoek-Brown criterion-2002 edition. In: Proceedings of NARMS-TAC conference, Toronto, vol 1, pp 267–273

  • Hoek E, Carranza-Torres C. Diederichs, M.S. and Corkum B. (2008). Kersten lecture: Integration of geotechnical and structural design in tunnelling. In: Proceedings university of Minnesota 56th annual geotechnical engineering conference. Minneapolis, 29 Feb 2008, pp 1–53

  • Itasca (2002) FLAC3D Numercial Software Package. Itasca Consulting Group Inc, Lagrangian Analysis of Contiuna

  • Itasca (2005) FLAC3D Numercial Software Package. Itasca Consulting Group Inc, Lagrangian Analysis of Contiuna

    Google Scholar 

  • Karakus M (2006) Appraising the methods accounting for 3D tunneling effects in 2D plain strain FE analysis. Tunn Undergr Sp Technol 22:47–56

    Article  Google Scholar 

  • Nguyen-Minh D, Guo C (1996) Recent progress in convergence confinement method. In: Barla G (ed) Prediction and performance in rock mechanics and rock engineering: EUROCK’96, Balkema, Rotterdam, pp 855–860

  • Owen DRJ, Hinton E (1980) Finite Elements in Plasticity. Pineridge Press, Swansea, p 589

    Google Scholar 

  • Panet M (1993) Understanding deformations in tunnels. In: Hudson JA, Brown ET, Fairhurst C, Hoek E (eds) Comprehensive rock engineering, vol 1. Pergamon, London, pp 663–690

  • Panet M (1995) Le calcul des tunnels par la me′thode convergence–confinement. Presses de l’Ecole Nationale des Ponts et Chausse′es, Paris ISBN 2-85978-230-3. 187 p

  • Rocscience Inc. (2004) Phase2, 5. Rocscience Inc., Toronto, www.rocscience.com

  • Unlu T, Gercek H (2003) Effect of Poisson’s ratio on the normalized radial displacements occurring around the face of a circular tunnel. Tunn Undergr Sp Technol 18:547–553

    Article  Google Scholar 

  • Vlachopoulos N, Diederichs MS (2009) Improved longitudinal displacement profiles for convergence confinement analysis of deep tunnels. Journal of rock mechanics and rock engineering, vol 42, Number 2, April 2009. pp 131–146

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nicholas Vlachopoulos.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vlachopoulos, N., Diederichs, M.S. Appropriate Uses and Practical Limitations of 2D Numerical Analysis of Tunnels and Tunnel Support Response. Geotech Geol Eng 32, 469–488 (2014). https://doi.org/10.1007/s10706-014-9727-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10706-014-9727-x

Keywords

Navigation