Phase transition in saturated porous media: pore-fluid segregation in consolidation

TL;DR

This paper introduces a nonlinear poromechanical model that predicts phase transitions and pore-fluid segregation during soil consolidation, extending classical Biot theory to account for multiple equilibrium states.

Contribution

It develops a nonlinear model incorporating a strain energy potential that captures phase transitions and pore-fluid segregation phenomena in saturated porous media.

Findings

Existence of two distinct equilibrium states under certain conditions.

Pore-fluid segregation can occur during consolidation, resembling a phase transition.

Model extends classical Biot theory to include nonlinear effects and multiple minima.

Abstract

Consider the consolidation process typical of soils, this phenomenon is expected not to exhibit a unique state of equilibrium, depending on the \textit{external loading} and the constitutive parameters. Beyond the standard solution, also pore-fluid segregation, which is typically associated with fluidization of the granular material, can arise. Pore-fluid segregation has been recognized as a phenomenon typical of the short time behavior of a saturated porous slab or a saturated porous sphere, during consolidation. In both circumstances Biot's three dimensional model provides time increasing values of the water pressure (and fluid mass density) at the center of the slab (or of the sphere), at early times, if the Lam\'{e} constant $\mu$ of the skeleton is different from zero. This localized pore-fluid segregation is known in the literature as Mandel--Cryer effect. In this paper a non linear poromechanical model is formulated. The model is able to describe the occurrence of two states of equilibrium and the switching from one to the other by considering a kind of \textit{phase transition}. Extending classical Biot's theory a more than quadratic strain energy potential is postulated, depending on the strain of the porous material and the variation of the fluid mass density (measured with respect to the skeleton reference volume). When the consolidating pressure is strong enough the existence of two distinct minima is proven.