Rock Mechanics and Rock Engineering

, Volume 18, Issue 1, pp 37–52 | Cite as

Lower bound solutions for circular tunnels in two and three dimensions

  • H. -B. Mühlhaus
Article

Summary

Complete statically admissible stress fields are evaluated for the problem of tunnel stability. The tunnels are supported by uniform internal pressure due to a lining or rock bolts. In both cases plane deformations are assumed. Additionally, a complete stress field is derived for the problem of the stability of the unsupported span of a tunnel. The latter problem is formulated three dimensionally. In all cases the Mohr Coulomb yield criterion is used. The solution is based on the lower bound theorem of plasticity, which states that the stability of a statical system is proved if at least one admissible stress field exists.

Keywords

Civil Engineer Stress Field Statical System Internal Pressure Yield Criterion 

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References

  1. Atkinson, J. H., Brown, E. T., Potts, M. (1975): collapse of Shallow Unlined Tunnels in Dense Sand. Tunnels and Tunnelling3, 81–87.Google Scholar
  2. Atkinson, J. H., Potts, D. M. (1977): Stability of a Shallow Circular Tunnel in Cohesionless Soil. Géotechnique27, 203–215.Google Scholar
  3. Caquot, A., Kérisel, J. (1967): Grundlagen der Bodenmechanik. Berlin-Heidelberg-New York: Springer.Google Scholar
  4. Davis, E. H., Gunn, M. J., Mair, R. J., Seneviratnes, H. N. (1980): The Stability of Shallow Tunnels and Underground Openings in Cohesive Material. Géotechnique30, 397–416.Google Scholar
  5. Egger, P. (1983): Roof Stability of Shallow Tunnels in Isotropic and Jointed Rock. 5th International Congress on Rock Mechanics, Section C, 295–301.Google Scholar
  6. Egger, P. (1973). Einfluß des Post-Failure-Verhaltens von Fels auf den Tunnelausbau unter besonderer Berücksichtigung des Ankerausbaus. Veröffentlichungen des Institutes für Bodenmechanik und Felsmechanik der Universität Karlsruhe,57.Google Scholar
  7. Graf, B., Lippomann, R., Mélix, P. (1983): Private Communication. Institut für Bodenmechanik und Felsmechanik der Universität Karlsruhe.Google Scholar
  8. Gudehus, G. (1973): Elastoplastische Stoffgleichungen für trockenen Sand. Ingenieur-Archiv42, 151–169.Google Scholar
  9. Jirovec, P. (1979): Untersuchungen zum Tragverhalten von Felsankern. Veröffentlichungen des Institutes für Bodenmechanik und Felsmechanik der Universität Karlsruhe, 79.Google Scholar
  10. Kolymbas, D. (1982): Vereinfachte statische Berechnung der Firste eines Tunnels in massigem Fels. Rock Mechanics14, 201–207.Google Scholar
  11. Mühlhaus, H.-B. (1980): Berechnungen von Gleichgewichtsverzweigungen kristalliner Gesteinskörper. Veröffentlichungen des Institutes für Bodenmechanik und Felsmechanik der Universität Karlsruhe, 85.Google Scholar
  12. Prager, W., Hodge, P. G. (1951): Theory of Perfectly Plastic Solids. New York: John Wiley & Sons.Google Scholar
  13. Tvergaard, V., Needleman, A., Lo, K. K. (1981): Flow Localization in Plain Strain Tensile Test. J. Mech. Phys. Solids29, 115–142.Google Scholar
  14. Wernick, E. (1978): Tragfähigkeit zylindrischer Anker im Sand unter besonderer Berücksichtigung des Dilatanzverhaltens. Veröffentlichungen des Institutes für Bodenmechanik und Felsmechanik der Universität Karlsruhe, 75.Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • H. -B. Mühlhaus
    • 1
  1. 1.Institute for Soil and Rock MechanicsUniversity of KarlsruheFederal Republic of Germany

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