The paper presents a study on the stress variables for the constitutive modelling of unsaturated soils. In the last years, the scientific literature has provided some reviews on the unsaturated soil constitutive modelling but these papers have been focused mainly on the comparison between the different approaches. The aim of the present paper is slightly different and it wants to give new argumentations on the debate. The discussion will be supported by two simulations of experimental data in literature. The adopted model for the theoretical investigation is the extension of the elastoplastic modified Cam clay model to the range of negative pressure TAMAGNINI [2000]. The presented model is based on the use of an 'effective' stress that accounts for the volume fractions of the saturating fluids (Bishop's stress like formualation) in contrast with the classic constitutive assumptions (bitensorial approach) The discussion is developed within the framework of Thermodynamics. The use of the Legcndre transform in the resolution of the differential equations allows to obtain a quadratic form of the free energy of the skeleton. The resulting thermodynamically based stress is able to predict a stationary value for the rate of the free energy and for the Gibbs potential of fluids during constant volume (referring to the solid matrix) swelling tests. The obtained condition could be considered as a rational definition of the effective stress principle for unsaturated soils (i.e. for no change in the stress field there are no change in the skeleton volume). This result overcomes previous theoretical discussions about the limitation of the Bishop's stress when it is combined with an appropriate hardening law.
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