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Undrained stability of dual square tunnels

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Abstract

In this paper, finite element limit analysis (FELA) and semi-analytical rigid block techniques are used to investigate the influence of tunnel spacing on the undrained stability of two unlined square tunnels constructed side by side. The tunnels, which are assumed to be straight and infinitely long, are modelled under conditions of plane strain. Upper and lower bounds on the stability of the tunnels are obtained using FELA; the numerical formulation of which is based upon the bounds theorems of classical plasticity. These bounds, which bracket the true collapse load from above and below, are found to be in good agreement with one another. Rigid block methods also provided an upper bound estimate on tunnel stability which was generally higher than, but still in good agreement with, the FELA upper bound. Failure mechanisms associated with the collapse of the dual tunnels were investigated, and for deeper tunnels, it was found that mechanisms extend much deeper below the tunnels than the collapse mechanisms associated with a single tunnel. Results from this study are summarised in dimensionless stability charts for use by practitioners.

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Acknowledgments

The research reported in this paper was made possible by the Australian Laureate Fellowship Grant FL0992039 awarded to Professor Scott Sloan by the Australian Research Council. The Authors are grateful for this support.

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Authors and Affiliations

  1. ARC Centre of Excellence in Geotechnical Science and Engineering, School of Engineering, University of Newcastle, Newcastle, Australia

    Daniel W. Wilson, Andrew J. Abbo, Scott W. Sloan & Andrei V. Lyamin

Authors
  1. Daniel W. Wilson
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  2. Andrew J. Abbo
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  3. Scott W. Sloan
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  4. Andrei V. Lyamin
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Corresponding author

Correspondence to Andrew J. Abbo.

Appendix 1

Appendix 1

Table 1 in this appendix gives the values used to generate the stability charts in Figs. 6, 7, 8, 9, 10 and 11. The superscripts identify the rigid block failure mechanism that provided the minimum rigid block solution. Rigid block solutions governed by a dual tunnel collapse modes are annotated with a numeral that specifies the critical rigid block mechanism as shown in Fig. 4. Solutions governed by single tunnel collapse modes are annotated with a letter that refers to a mechanism shown in Fig. 5.

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Wilson, D.W., Abbo, A.J., Sloan, S.W. et al. Undrained stability of dual square tunnels. Acta Geotech. 10, 665–682 (2015). https://doi.org/10.1007/s11440-014-0340-1

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