Thermodynamically consistent effective stress formulation for unsaturated soils across a wide range of soil saturation

We outline an extension of Biot's theory of dynamic wave propagation in fluid-saturated media, which can be used to model dynamic soil-structure interaction in frictionless conditions across a wide range of soil saturation levels. In this regard, we present a comprehensive analysis of experimental evidence, the thermodynamic, and the theoretical basis of using the degree of saturation as Bishop's parameter in unsaturated soils. The analysis highlights the limitations of using this parameter to accurately model unsaturated soil behaviour, particularly as the soil approaches dryness. Based on the analysis, a new definition of effective stress is proposed, and the associated work-conjugate pairs are identified. Recommendations are made for constitutive modelling using the new definition of effective stress. Finally, we introduce a fully coupled finite element contact model that utilises the new effective stress definition. Through numerical examples, we demonstrate the model's capability to control the vanishing capillary effect on soil-structure interaction as the soil dries.