Thermo-Mechanical Potentials for Unsaturated Soils
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.
KeywordsBulk Modulus Unsaturated Soil Solid Skeleton Complementary Energy Plastic Multiplier
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- Bowen, R.M (1976). Theory of mixtures. In: Continuum Physics, vol. 3, 1–127, A.C. Eringen eds., Academic Press, New York.Google Scholar
- Gens, A., Jouanna, P. and Schrefler, B.A. (1995). Modern issues in non-saturated soils. CISM Courses and Lectures n°. 357, Springer Verlag, Wien.Google Scholar
- Haase, R. (1990). Thermodynamics of Irreversible Processes. Dover Publications, New York.Google Scholar
- Kestin, J. (1968). A Course in Thermodynamics. Blaisdell Publishing Co., Waltham, Massachusetts.Google Scholar
- 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.Google Scholar
- 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.Google Scholar
- Khalili, N. and Loret B. (2000). An elasto-plastic model for non-isothermal analysis of flow and deformation in unsaturated porous media: formulation, submitted.Google Scholar