Abstract
The behaviour of unsaturated soils is known to depend strongly and in a nonlinear way of suction. Usual elastic formulations store energy during arbitrary paths in the stress and strain spaces. To avoid polluting the interpretation of the energy balance when thermal effects are accounted for, a hyperelastic formulation is systematically developed, first in a purely mechanical analysis, and in a second step, in a thermo-mechanical analysis where each of the three phases is endowed with its own temperature. The secant constitutive matrices are shown to lack symmetry, in contrast with the tangent matrices. For the mechanical analysis, the potentials are obtained in explicit form for the stress-based formulation and for a mixed formulation. The thermo-mechanical potential accounting for the menisci effect is also provided for the formulation where the solid strain, the two fluid pressures and the three phase temperatures are the primary variables.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Biot, M.A. (1973). Nonlinear and semilinear rheology of porous solids. J. of Geophysical Research, 78 (23), 4924–4937.
Bowen, R.M (1976). Theory of mixtures. In: Continuum Physics, vol. 3, 1–127, A.C. Eringen eds., Academic Press, New York.
Eringen, A.C. and Ingram, J.D. (1965). A continuum theory for chemically reacting media -I. Int. J. Eng. Science, 3, 197–212.
Fleureau, J.M., Kheirbek-Saoud, S., Soemitro, R. and Taibi, S. (1993). Behavior of clayey soils on drying-wetting paths. Canadian Geotechnical J., 30, 287–296.
Gens, A., Jouanna, P. and Schrefler, B.A. (1995). Modern issues in non-saturated soils. CISM Courses and Lectures n°. 357, Springer Verlag, Wien.
Haase, R. (1990). Thermodynamics of Irreversible Processes. Dover Publications, New York.
Hassanizadeh, S.M. and Gray, W.G. (1993). Thermodynamic basis of capillarity pressure in porous media. Water Resources Research, 29 (10), 3389–3405.
Kestin, J. (1968). A Course in Thermodynamics. Blaisdell Publishing Co., Waltham, Massachusetts.
Khalili, N. and Khabbaz, M.H. (1995). On the theory of three-dimensional consolidation in unsaturated soils. In: Unsaturated Soils/Sols non saturés, E.E. Alonso and P. Delage eds, Presses de l’Ecole Nationale des Ponts et Chaussées, Paris, 1995, 745–750.
Khalili, N. and Khabbaz, M.H. (1998). A unique relationship for x for the determination of the shear strength of unsaturated soils. Géotechnique, 48 (2), 1–7.
Khalili, N. and Loret B. (2000). An elasto-plastic model for non-isothermal analysis of flow and deformation in unsaturated porous media: formulation, submitted.
Loret B. (1985). On the choice of elastic parameters for sand. Int. J. Num. Anal. Meth. Geomechanics, 9, 285–292.
Loret B. and Khalili (2000). A three-phase model for unsaturated soils. Int. J. Num. Anal. Meth. Geomechanics, 24, 893–927.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Wien
About this chapter
Cite this chapter
Loret, B., Khalili, N. (2001). Thermo-Mechanical Potentials for Unsaturated Soils. In: Griffiths, V.D., Gioda, G. (eds) Advanced Numerical Applications and Plasticity in Geomechanics. International Centre for Mechanical Sciences, vol 426. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2578-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2578-6_7
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-83337-7
Online ISBN: 978-3-7091-2578-6
eBook Packages: Springer Book Archive