A Thermodynamic Treatment\\ of Partially Saturated Soils \\ Revealing the Structure of Effective Stress

Abstract: A rigorous thermodynamic treatment of partially saturated soils is developed using a minimal number of assumptions. The derivation is carried out in a way that does not require to explicitly track the complex shapes of interfaces between the solid, fluid and gas domains. Instead, suction is the property being recovered explicitly through the minimisation of energy around an ideal `suctionless limit', while considering the different compressibilities of the three domains. In interpreting experimental data the derivation ensures the thermodynamic equilibrium between the chemical potentials of the soil and measurement cells, while carefully distinguishing intrinsic from measured pressures and suctions. A most general expression for the effective stress of partially saturated soils is then derived that is strictly linked to the soil-water retention curve (SWRC). The structure of the effective stress broadly depends on the three thermodynamic densities characterising the solid, fluid and gas domains. Special cases of SWRC are explored, which reveals conditions for which the structure of the effective stress may agree with previously proposed empirical relationships.