Nonlinear Poro-Elastic Model for Unsaturated Porous Solids

Abstract

A nonlinear poroelastic constitutive model for unsaturated porous materials is formulated based on a higher order formulation of free energy including mechanical and moisture contributions and the coupling between moisture and mechanics. This orthotropic model leads to the explicit formulation of the dependence of the compliance, moisture capacity, and coupling coefficient on stress and liquid pressure. The nonlinear poroelastic material properties can be easily determined from mechanical testing at different moisture content and free swelling/sorption tests. An academic example illustrates the capacity of the proposed model to describe nonlinear moisture dependent elasticity, stress dependent sorption, and swelling, also called mechano-sorption and moisture expel during mechanical loading. Two materials are analyzed in detail: wood and Berea sandstone. The poroelastic model shows a good agreement with measurements. Different moisture dependence of the elastic properties is found, with wood showing a more complex moisture/mechanical interaction. Berea sandstone is found to show an important nonlinear elastic behavior dependent on stress, similar in dry and wet conditions.