Acta Geotechnica

, 1:137 | Cite as

On constitutive modelling of unsaturated soils

  • Antonio GensEmail author
  • Marcelo Sánchez
  • Daichao Sheng
Review Paper


The paper presents a review of constitutive modelling of unsaturated soils. After a brief historical perspective, a number of existing constitutive models are classified and discussed according to the type of stress variables adopted in their formulation. Afterwards, attention is given to recent developments in the proposal of coupled hydraulic-mechanical models and the possibility of casting them in a sound thermodynamical framework. Finally, a double structure model for expansive soils is described. The incorporation of microstructural considerations and its use as a platform for incorporating the influence of new variables are highlighted.


Unsaturated soils Constitutive models Expansive soils Elastoplasticity Thermodynamics 


  1. 1.
    Alonso EE, Gens A (1994) Keynote lecture: on the mechanical behaviour of arid soils. In: Conference on engineering characteristics of arid soils, London, pp 173–205Google Scholar
  2. 2.
    Alonso EE, Gens A, Hight DW (1997) Special problem soils. General Report. In: 9th European conference on soil mechanics, Dublin, vol 3, pp 1087–1146Google Scholar
  3. 3.
    Alonso EE, Gens A, Josa A (1990) A constitutive model for partially saturated soils. Géotechnique 40:405–430Google Scholar
  4. 4.
    Alonso EE, Vaunat J, Gens A (1999) Modelling the mechanical behaviour of expansive clays. Eng Geol 54:173–183CrossRefGoogle Scholar
  5. 5.
    Bishop AW, Alpan I, Blight GE, Donald IB (1960) Factors controlling the strength of partly saturated cohesive soils. In: Research conference on shear strength of cohesive soils, Boulder, ASCE, pp 503–532Google Scholar
  6. 6.
    Bishop AW, Blight GE (1963) Some aspects of effective stress in saturated and partly saturated soils. Géotechnique 13:177–197Google Scholar
  7. 7.
    Bolzon G, Schrefler BA, Zienkiewicz OC (1996) Elasto-plastic soil constitutive laws generalised to partially saturated states. Géotechnique 46:279–289Google Scholar
  8. 8.
    Brackley IJ (1973) Swell pressure and free swell in compacted clay. In: Proceedings, 3rd international conference on expansive soils, Haifa, vol 1, pp 169–176Google Scholar
  9. 9.
    Brackley IJ (1975) Swell under load. In: Proceedings, 6th regional conference for Africa on soil mechanics and foundation engineering, Durban, vol 1, pp 65–70Google Scholar
  10. 10.
    Buisson MSR, Wheeler SJ (2000) Inclusion of hydraulic hysteresis in a new elasto-plastic framework for unsaturated soils. Experimental evidence and theoretical approaches in unsaturated soils. Balkema, Rotterdam, pp 109–119Google Scholar
  11. 11.
    Chu TY, Mou CH (1973) Volume change characteristics of expansive soils determined by controlled suction test. In: Proceedings, 3rd international conference on expansive soils, Haifa, vol 1, pp 177–185Google Scholar
  12. 12.
    Coleman JD (1962) Stress strain relations for partly saturated soil. Correspondence. Géotechnique 12:348–350Google Scholar
  13. 13.
    Collins IF, Hilder T (2002) A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests. Int J Numer Anal Meth Geomech 26:1313–1347CrossRefGoogle Scholar
  14. 14.
    Collins IF, Houlsby GT (1997) Application of thermomechanical principles to the modelling of geotechnical materials. Proc R Soc Lond A 453:1975–2001CrossRefGoogle Scholar
  15. 15.
    Croney D (1952) The movement and distribution of water in soils. Géotechnique 3:1–16Google Scholar
  16. 16.
    Cui YJ, Delage P, Sultan N (1995) An elasto-plastic model for compacted soils. Unsaturated soils, vol 2. Balkema, Rotterdam, pp 703–709Google Scholar
  17. 17.
    Dangla OL, Malinsky L, Coussy, O (1997) Plasticity and imbibition-drainage curves for unsaturated soils: a unified approach. In: 6th international conference on numerical models in geomechanics, Montreal. Balkema, Rotterdam, pp 141–146Google Scholar
  18. 18.
    De Gennaro V, Delage P, Priol G, Collin F, Cui YF (2004) On the collapse behaviour of oil reservoir chalk. Géotechnique 54:415–420Google Scholar
  19. 19.
    Fredlund DG, Morgenstern NR (1977) Stress state variables and unsaturated soils. J Geotech Eng Div ASCE 103:447–466Google Scholar
  20. 20.
    Fredlund DG, Rahardjo H (1993) Soil mechanics for unsaturated soils. Wiley, New YorkGoogle Scholar
  21. 21.
    Gajo A, Loret B, Hueckel T (2002) Electro-chemo-mechanical couplings in saturated porous media: elastic-plastic behaviour of heteroionic expansive clays. Int J Solids Struct 39:4327–4362CrossRefGoogle Scholar
  22. 22.
    Gallipoli D, Gens A, Sharma R, Vaunat J (2003) An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Géotechnique 53:123–135Google Scholar
  23. 23.
    Gawin D, Baggio P, Schrefler BA (1995) Coupled heat, water and gas flow in deformable porous media. Int J Numer Meth Fluids 20:969–987CrossRefGoogle Scholar
  24. 24.
    Geiser F, Laloui L, Vulliet L (2000) Modelling the behaviour of unsaturated silt. Experimental evidence and theoretical approaches in unsaturated soils. Balkema, Rotterdam, pp 155–175Google Scholar
  25. 25.
    Gens A (1995) Constitutive laws. Modern issues in non-saturated soils. Springer, Berlin Heidelberg New York, pp 129–158Google Scholar
  26. 26.
    Gens A (1996) Constitutive modelling: application to compacted soil. Unsaturated soils, vol 3. Balkema, Rotterdam, pp 1179–1200Google Scholar
  27. 27.
    Gens A, Alonso E (1992) A framework for the behaviour of unsaturated expansive clays. Can Geotech J 29:1013–1032Google Scholar
  28. 28.
    Gens A, Alonso EE, Josa A (1989) Elasto-plastic modelling of partially saturated soils Numerical models in geomechanics III. Elsevier, London, pp 163–170Google Scholar
  29. 29.
    Gens A, Olivella S (2001) THM phenomena in saturated and unsaturated porous media. Revue française de génie civil 5:693–717Google Scholar
  30. 30.
    Guimarães L, Gens A, Sánchez M, Olivella S (2006) A chemo-mechanical model for expansive clays (submitted for publication)Google Scholar
  31. 31.
    Hassanizadeh SM, Gray WG (1980) General conservation equations for multiphase systems: 3 Constitutive theory for porous media flow. Adv Water Resour 3:25–40CrossRefGoogle Scholar
  32. 32.
    Houlsby GT (1997) The work input to an unsaturated granular material. Géotechnique 47:193–196Google Scholar
  33. 33.
    Hueckel T, Borsetto M (1990) Thermoplasticity of saturated soils and shales. Constitutive equations. J Geotech Eng ASCE 116:1765–1777Google Scholar
  34. 34.
    Hutter K, Laloui L, Vulliet L (1999) Thermodynamically based mixture models for saturated and unsaturated soils. Mech Cohes Frict Mat 4:295–338CrossRefGoogle Scholar
  35. 35.
    Jennings JEB, Burland JB (1962) Limitations to the use of effective stresses in partly saturated soils. Géotechnique 12:125–144CrossRefGoogle Scholar
  36. 36.
    Jommi C (2000) Remarks on the constitutive modelling of unsaturated soils. Experimental evidence and theoretical approaches in unsaturated soils. Balkema, Rotterdam, pp 139–153Google Scholar
  37. 37.
    Jommi C, Di Prisco C (1994) A simple theoretical approach for modelling the mechanical behaviour of unsaturated granular soils (in Italian) Il ruolo dei fluidi in ingegneria geotecnica. In: Proceedings of Italian conference Mondovi, 1 (II), pp 167–188Google Scholar
  38. 38.
    Josa A, Balmaceda A, Gens A, Alonso EE (1992) An elasto-plastic model for partially saturated soil exhibiting a maximum of collapse. In: 3rd international conference on computational plasticity, Barcelona, vol 1, pp 815–826Google Scholar
  39. 39.
    Justo JL, Delgado A, Ruiz J (1984) The influence of stress-path in the collapse-swelling of soils at the laboratory. In: 5th international conference on expansive soils, Haifa, vol 1, pp 201–208Google Scholar
  40. 40.
    Khalili N, Loret B (2001) An elasto-plastic model for non-isothermal analysis of flow and deformation in unsaturated porous media: formulation. Int J Solids Struct 38:8305–8330CrossRefGoogle Scholar
  41. 41.
    Kohgo Y, Nakano M, Miyazaki T (1993) Theoretical aspects of constitutive modelling for unsaturated soils. Soils Found 33 (4):681–687Google Scholar
  42. 42.
    Leroueil S, de Barbosa PSA (2000) Combined effect of fabric bonding and partial saturation on yielding of soils. Unsaturated soils for Asia. Balkema, Rotterdam, pp 527–532Google Scholar
  43. 43.
    Lewis RW, Schrefler BA (1987) The finite element method in the deformation and consolidation of porous media. Wiley, ChichesterGoogle Scholar
  44. 44.
    Li XS (2003) Effective stress in unsaturated soil: a microstructural analysis. Géotechnique 53:273–277Google Scholar
  45. 45.
    Loret B, Hueckel T, Gajo A (2002) Chemo-mechanical coupling in saturated porous media: elastic-plastic behaviour of homoionic expansive clays. Int J Solids Struct 39:2773–2806CrossRefGoogle Scholar
  46. 46.
    Loret B, Khalili N (2002) An effective stress elastic–plastic model for unsaturated porous media. Mech Mater 34:97–116CrossRefGoogle Scholar
  47. 47.
    Matyas EL, Radhakrishna HS (1968) Volume change characteristics of partially saturated soils. Géotechnique 18:432–448Google Scholar
  48. 48.
    Modaressi A, Abou-Bekr N (1994) A unified approach to model the behaviour of saturated and unsaturated soils. In: 8th international conference on computer methods and advances in geomechanics. Balkema, Rotterdam, pp 1507–1513Google Scholar
  49. 49.
    Olivella S, Carrera J, Gens A, Alonso EE (1994) Nonisothermal multiphase flow of brine and gas through saline media. Transp Porous Media 15:271–293CrossRefGoogle Scholar
  50. 50.
    Pakzad M (1995) Modélisation du comportement hydro-mécanique des argiles gonflantes a faible porosité. Ph.D. Thesis, Université d’OrléansGoogle Scholar
  51. 51.
    Russell AR, Khalili N (2006) A unified bounding surface plasticity model for unsaturated soils. Int J Numer Anal Meth Geomech 30:181–212CrossRefGoogle Scholar
  52. 52.
    Sánchez M, Gens A (2005) Final report on thermo-hydro-mechanical modelling. Deliverable D19-3, Febex II Project, EC Contract FIKW-CT-2000-00016Google Scholar
  53. 53.
    Sánchez M, Gens A, Guimarães L do N, Olivella S (2005) A double structure generalized plasticity model for expansive materials. Int J Numer Anal Meth Geomech 29:751–787Google Scholar
  54. 54.
    Sharma RS (1998) Mechanical behaviour of unsaturated highly expansive clays. DPhil. Thesis, University of OxfordGoogle Scholar
  55. 55.
    Sheng D, Sloan SW, Gens A, Smith DW (2003a) Finite element formulation and algorithms for unsaturated soils. Part I: theory. Int J Numer Anal Meth Geomech 27:745–765CrossRefGoogle Scholar
  56. 56.
    Sheng D, Smith DW, Sloan SW, Gens A (2003b) Finite element formulation and algorithms for unsaturated soils. Part II: verification and application. Int J Numer Anal Meth Geomech 27:767–790CrossRefGoogle Scholar
  57. 57.
    Sheng D, Sloan SW, Gens A (2004) A constitutive model for unsaturated soils: thermomechanical and computational aspects. Comput Mech 33:453–465CrossRefGoogle Scholar
  58. 58.
    Sivakumar V (1993) A critical state framework for unsaturated soil. Ph.D. Thesis, University of OxfordGoogle Scholar
  59. 59.
    Tamagnini R (2004) An extended Cam-clay model for unsaturated soils with hydraulic hysteresis. Géotechnique 54:223–228Google Scholar
  60. 60.
    Tamagnini R, Pastor M (2005) A thermodynamically based model for unsaturated soil: a new framework for generalized plasticity. In: Mancuso C, Tarantino A (eds) Unsaturated soils. Advances in testing, modelling and engineering applications. Balkema, Leiden, pp 121–134Google Scholar
  61. 61.
    Tarantino A, Mongiovi L, Bosco G (2000) An experimental investigation on the isotropic stress variables for unsaturated soils. Géotechnique 50:275–282Google Scholar
  62. 62.
    Thomas HR, He Y (1995) An analysis of coupled heat, moisture and air transfer in a deformable unsaturated soil. Géotechnique 45:667–689Google Scholar
  63. 63.
    Vaunat J, Jommi C, Gens A (1997) A strategy for numerical analysis of the transition between saturated and unsaturated flow conditions. In: 6th international conference on numerical models in geomechanics, Montreal. Balkema, Rotterdam, pp 297–302Google Scholar
  64. 64.
    Vaunat J, Romero E, Jommi C (2000) An elastoplastic hydro-mechanical model for unsaturated soils. Experimental evidence and theoretical approaches in unsaturated soils. Balkema, Rotterdam, pp 121–138Google Scholar
  65. 65.
    Wheeler SJ (1996) Inclusion of specific water volume within an elastoplastic model for unsaturated soil. Can Geotech J 33:42–57Google Scholar
  66. 66.
    Wheeler SJ, Sharma RS, Buisson MSR (2003) Coupling of hydraulic hysteresis and stress–strain behaviour in unsaturated soils. Géotechnique 53:41–54CrossRefGoogle Scholar
  67. 67.
    Wheeler SJ, Sivakumar V (1995) An elasto-plastic critical state framework for unsaturated soils. Géotechnique 45:35–53CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Geotechnical Engineering and GeosciencesTechnical University of Catalonia BarcelonaSpain
  2. 2.Department of Civil EngineeringUniversity of StrathclydeGlasgowUK
  3. 3.Discipline of Civil, Surveying and Environmental EngineeringThe University of NewcastleCallaghanAustralia

Personalised recommendations