Thermodynamics of unsaturated soils

The paper deals with a thermomechanically based analysis of three-phase porous materials with two-phase flow. The thermomechanical analysis is based on the framework of hyperplasticity in which the free energy decoupling offers some insights on the mathematical formulation. The strains decomposition is mathematically discussed; it is shown as the resulting third term of the adopted constitutive equations is coupled with the water flows into the porous matrix. Total strains can be decomposed into one part coupled with the Bishop's stress and another depending on the energy of the capillaries. At the same time, the strains coupled with the Bishop's stress can be hierarchically divided into plastic and elastic parts, recovering the saturated formulation for constant degree of saturation (this includes the fully saturated case, in which the degree of saturation is constant and equal to one). The need of this analysis is explained by some paradoxes that naturally emerge in the bitensorial formulation. Some previous work in this area is discussed, and some proposed formulations of recent years are reviewed and improved.