Finite Element Analysis of Time Dependent Effects in Tunnels

  • G. Gioda
  • A. Cividini
Part of the International Centre for Mechanical Sciences book series (CISM, volume 350)


A discussion is presented of the numerical analysis, based on the finite element method, of the time dependent effects that develop when a tunnel is driven in a rock mass characterized by a viscous behaviour. First, the so called swelling and squeezing phenomena are described considering in particular rocks containing clay minerals. Subsequently the discussion is focused on the squeezing behaviour, i.e. on the time dependent increase of the shear deformation which develops with minor volume changes. Some simple linear and nonlinear constitutive laws are presented able to describe this phenomenon and their use in the solution of boundary value problems by means of the finite element method is discussed. Finally, the results of some numerical analyses are presented that illustrate the effects taking place around tunnels driven into squeezing rocks.


Rock Mass Creep Strain Vertical Stress Radial Displacement Unconfined Compression Strength 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Aiyer A.K., An analytical study of the time-dependent behaviour of underground openings, Ph.D.Thesis, University of Illinois at Urbana-Champaign, Department of Civil Enginering, 1969.Google Scholar
  2. [2]
    Fossum A.F., Visco-plastic behaviour during the excavation phase of a salt cavity, Int.J.Numer.Anal.Methods in Geomechanics, Vol. 1, 4555, 1977.CrossRefGoogle Scholar
  3. [3]
    Cristescu N., Rock rheology, Kluwer Academic Publ., Dordrecht, 1989.CrossRefGoogle Scholar
  4. [4]
    Ottosen N.S., Viscoelastic-viscoplastic formulas for analysis of cavities in rock salt. Int.J.Rock Mech.Min.Sci. & Geomech.Abstract, Vol. 23, 201–212, 1986.CrossRefGoogle Scholar
  5. [5]
    Nakano R., On the design of water tunnels in relation with the type and magnitude of rock load with special references to the mechanism and prediction of squeezing-swelling rock pressure, Bulletin of the National Research Institute of Agricultural Engineering, Ministry of Agriculture and Forestry (Japan), No. 12, 89–142, 1974.Google Scholar
  6. [6]
    Ghaboussi J. and G. Gioda, On the time dependent effects in advancing tunnels, Int. J.Numer.Anal.Methods in Geomech., Vol. 1, 1977.Google Scholar
  7. [7]
    Sakurai S., Approximate time-dependent analysis of tunnel support structure considering progress of tunnel face. Int.J.Num.Anal.Meth. Geomech., Vol. 2, 159–175, 1978.Google Scholar
  8. [8]
    Terzaghi K., Soft ground tunneling, in From Theory to Practice in Soil Mechanics, J. Wiley & Sons, 338–357, 1960.Google Scholar
  9. [9]
    Peck R.B., Deep excavation and tunneling in soft ground„ Proc.7th ICSMFE, Mexico City, State-of-the-art volume, 225–284, 1969.Google Scholar
  10. [10]
    Mitchell J.K., Fundamentals of soil behavior, J.Wiley & Sons, 1976.Google Scholar
  11. [11]
    Einstein H.H. and N. Bishoff, Design of tunnels in swelling rock, Proc.l6th Symp.on Rock Mechanics, Minneapolis, 120–130, 1975.Google Scholar
  12. [12]
    Bishop A.W. and H.T. Lowenburg, Creep characteristics of two undisturbed clays, Proc.7th ICSMFE, Vol.1, Mexico City, 1969.Google Scholar
  13. [13]
    Cividini A., Constitutive behaviour and numerical modeling, in Comprehensive Rock Engineering (Hudson J.A. et al. edts.), Pergamon Press, Oxford, Vol.1, 395–426, 1993.Google Scholar
  14. [14]
    Christiansen R.W. and T.H. Wu, Analysis of clay deformation as a rate process, J.Soil Mech.Found.Div., ASCE, Vol.90, No.SM6, 125–157, 1964.Google Scholar
  15. [15]
    Singh A. and J.K. Mitchell, General stress-strain-time function for soils, J.Soil Mech.Found.Div., ASCE Vol.94, No.SM1, 21–46, 1968.Google Scholar
  16. [16]
    Semple R.M., A.J. Hendron and G. Mesri, The effects of time-dependent properties of altered rock on tunnel support requirements, U.S. Department of Transportation, Federal Railroad Administration, Rep. No. FRA-OR & D 74–30, December, 1973.Google Scholar
  17. [17]
    Nair K. and A.P. Boresi, Stress analysis for time-dependent problems in rock mechanics, Proc.2nd ICRM, Beograd„ Vol. 2 531–536, 1970.Google Scholar
  18. [18]
    Gioda G., A finite element solution of non-linear creep problems in rocks, Int.J.Rock Mech.Min.Sci. & Geomech.Abst., Vol. 18, 35–46, 1981.CrossRefGoogle Scholar
  19. [19]
    Zienkiewicz O.C., I.C. Cormeau, Viscoplasticity-plasticity and creep in elastic solids, Int.J.Numer.Meth.Engng., Vol. 8, 821–845, 1974.CrossRefGoogle Scholar
  20. [20]
    Cividini A., G. Gioda and A. Carini, A finite element analysis of the time dependent behaviour of underground openings, Proc.7th Int. Conf.on Computer Methods and Advances in Geomech., Cairns, 1991.Google Scholar
  21. [21]
    Landanyi B., Time dependent response of rock around tunnels, In: Comprehensive Rock Engineering (Hudson J.A. et al. eds.), Pergamon Press, Oxford, Vol. 2, 77–112, 1993.Google Scholar
  22. [22]
    Christian J.T. and B.J. Watt, Undrained visco-elastic analysis of soil deformation, Proc.Symp.on Application of Finite Elem.Method in Geotechnical Engineering, Waterways Experiment Station, Vicksburg, Missisipi, 1972.Google Scholar
  23. [23]
    Cristescu N., Viscoplastic creep of rocks around horizontal tunnels, Int.J.Rock Mech.Min.Sci. & Geomech.Abstr, Vol. 22, No. 6, 453–459, 1985CrossRefGoogle Scholar
  24. [24]
    Gioda G., On the non linear squeezing effects around circular tunnels, Int.J.Numer.Anal.Methods in Geomech., Vol. 6, 1982.Google Scholar
  25. [25]
    Gioda G. and A. Cividini, Viscous behaviour around an underground opening in a two-phase medium, Int.J.Rock Mech.Min.Sci. & Geomech. Abstract, Vol. 18, 1981.Google Scholar

Copyright information

© Springer-Verlag Wien 1994

Authors and Affiliations

  • G. Gioda
    • 1
  • A. Cividini
    • 1
  1. 1.Polytechnic of MilanMilanItaly

Personalised recommendations