Prediction of drying shrinkage beyond the pore isodeformation assumption
Résumé
The paper aims at assessing how, for a porous material whose pore size distribution is experimentally known, the variation in pore deformation with pore size might affect predictions of drying shrinkage. Unsaturated poroelasticity is first revisited in a general macroscopic thermodynamic framework irrespective of any morphology of the porous space. Saturation is shown to be a state function of capillary pressure governing the change in the solid-fluid interface energy; it can be experimentally obtained from a knowledge of pore size distribution only. Unsaturated poroelastic properties are then determined under three homogenization schemes: the standard Mori-Tanaka scheme, the self-consistent scheme, and the differential homogenization scheme extended to unsaturated conditions. Except for the Mori-Tanaka scheme, the function weighting the fluid pore pressure in the poroelastic constitutive equations is found to depart from the pore volume fraction the liquid occupies. As a result the pores do not deform uniformly. This departure roughly accounts for the difference in deformation between pores of different sizes and subjected to the same pressure, and it is found to significantly affect predictions of drying shrinkage, in particular for cement paste.