Coupled Analyses in Geomechanics

  • D. V. Griffiths
Part of the International Centre for Mechanical Sciences book series (CISM, volume 350)


This paper presents a thorough review of the implementation of the Biot equations of equilibrium for a saturated elastic porous medium into a finite element code. The generation of the matrix equations via a Galerkin formulation is described in detail and an incremental form of the equations is presented suitable for nonlinear analysis. Simple elasto-plastic models for geoniaterials are described including a survey of different failure criteria and the Viscoplastic algorithm for stress redistribution is reviewed. Full listings of computer code in modular form are included for both elastic and elasto-plastic examples and attention is drawn to certain programming features which lead to improved efficiency and verstility. The paper concludes with several examples of finite element analysis of transient collapse problems of relevance to geotechnical engineering.


Pore Pressure Effective Stress Friction Angle Failure Criterion Read Time 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M.A. Biot. General theory of three-dimensional consolidation. J Appl Phys, 12: 155–164, 1941.CrossRefGoogle Scholar
  2. [2]
    O.C. Zienkiewicz. The finite element method. McGraw Hill, London, New York, 3rd edition, 1977.Google Scholar
  3. [3]
    M.A. Hicks. Numerically modelling the stress-strain behaviour of soils. PhD thesis, Department of Engineering, University of Manchester, 1990.Google Scholar
  4. [4]
    R.S. Sandhu. Finite element analysis of coupled deformation and fluid flow in porous media. In: J.B. Martins, Eds, Numerical Methods in Geomechanics, pages 203–228. D. Reidel. Publishing Company, Dordrecht, Holland, 1981.Google Scholar
  5. [5]
    D.V. Griffiths, M.A. Hicks, and C.O.U. Transient passive earth pressure analyses. Géotechnique, 41(4): 615–620, 1991.Google Scholar
  6. [6]
    R.L. Schiffman. Field applications of soil consolidation, time-dependent loading and variable permeability. Technical Report 248, Highway Research Board, Washington, U.S.A., 1960.Google Scholar
  7. [7]
    I.M. Smith and D.V. Griffiths. Programming the Finite Element Method. John Wiley and Sons, Chichester, New York, 2nd edition, 1988.Google Scholar
  8. [8]
    D.C. Drucker and W. Prager. Soil mechanics and plastic analysis in limit design. Q Appl Mech., 10: 157–165, 1952.Google Scholar
  9. [9]
    D.C. Drucker, R.E. Gibson, and D.J. Henkel. Soil mechanics and work-hardening theories of plasticity. Trans ASCE, 122: 338–346, 1957.Google Scholar
  10. [10]
    C. Humpheson. Finite element analysis of elasto/viscoplastic soils. PhD thesis, Department of Civil Engineering, University of Wales at Swansea, 1976.Google Scholar
  11. [11]
    O.C. Zienkiewicz, V.A. Norris, L.A. Winnicki, D.J. Naylor, and R.W. Lewis. A unified approach to the soil mechanics of offshore foundations. In: Numerical methods in offshore engineering, pages 361–412. John Wiley and Sons, Chichester, New York, 1978.Google Scholar
  12. [12]
    D.V. Griffiths. Some theoretical observations on conical failure criteria in principal stress space. Int J Solids Struct, 22 (5): 553–565, 1986.CrossRefGoogle Scholar
  13. [13]
    A.W. Bishop. The strength of soils as engineering materials: 6th Rankine Lecture. Géotechnique, 16 (2): 91–130, 1966.CrossRefGoogle Scholar
  14. [14]
    P.V. Lade and J.M. Duncan. Elasto-plastic stress-strain theory for cohesionless soils. J Geotech Eng, ASCE, 101 (10): 1037–1053, 1975.Google Scholar
  15. [15]
    H. Matsuoka and T. Nakai. Stress-deformation and strength characteristics of soil under three different principal stresses. Proc Jap Soc Civ Eng, 232: 59–70, 1974.CrossRefGoogle Scholar
  16. [16]
    T.W. Lambe and R.V. Whitman. Soil Mechanics, page 206. John Wiley and Sons, New York, 1969.Google Scholar
  17. [17]
    O.C. Zienkiewicz and I.C. Cormeau. Viscoplasticity, plasticity and creep in elastic solids. a unified approach. Int. I Numer Methods Eng, 8: 821–845, 1974.CrossRefGoogle Scholar
  18. [18]
    I.C. Cormeau. Numerical stability in quasi-static elasto-viscoplasticity. Int. J Numer Methods Eng, 9 (1): 109–127, 1975.CrossRefGoogle Scholar
  19. [19]
    D.V. Griffiths. Finite element analyses of walls, footings and slopes. PhD thesis, Department of Engineering, University of Manchester, 1980.Google Scholar
  20. [20]
    D.V. Griffiths. The effect of pore fluid compressibility on failure loads in elasto-plastic soils. Int J Numer Anal Methods Geomech, 9: 253–259, 1985.CrossRefGoogle Scholar
  21. [21]
    J.C. Small, J.R. Booker, and E.H. Davis. Elasto-plastic consolidation of soil. Int J Solids Struct, 12: 431–448, 1976.CrossRefGoogle Scholar
  22. [22]
    W. Prager and P.G. Hodge. Theory of perfectly plastic solids. Dover Publications Inc., 1968.Google Scholar
  23. [23]
    C.O. Li. Finite element analyses of seepage and stability problems in geomechanics. PhD thesis, Department of Engineering, University of Manchester, 1988.Google Scholar
  24. [24]
    H.B. Seed and K.L. Lee. Undrained strength characteristics of cohesionless soils. J Soil Mech Found Div, ASCE, 93 (6): 333–360, 1967.Google Scholar
  25. [25]
    J. Ghaboussi and D.A. Pecknold. Incremental finite element analysis of geometrically altered structures. Int. I Numer Methods Eng, 20: 2151–2164, 1984.CrossRefGoogle Scholar
  26. [26]
    D.A. Holt. Transient analysis of excavations in soil. Master’s thesis, Department of Engineering, University of Manchester, 1991.Google Scholar
  27. [27]
    D.W. Taylor. Fundamentals of soil mechanics. John Wiley and Sons, Chichester, New York, 1948.Google Scholar
  28. [28]
    M.A. Hicks and S.W. Wong. Static liquefaction of loose slopes. In: G. Swoboda, editor, Proc 6th Int Conf Methods Ceomech, pages 1361–1368. A.A. Balkema, R.otterdam, 1988.Google Scholar

Copyright information

© Springer-Verlag Wien 1994

Authors and Affiliations

  • D. V. Griffiths
    • 1
  1. 1.Colorado School of MinesGoldenUSA

Personalised recommendations