Insights into the links between microstructure and Bishop's χ parameter for unsaturated soils

In recent years, Bishop's proposal for a generalized stress extending Terzaghi's stress to unsaturated states gained a large audience. Despite the complexity introduced in some aspects of modelling or stress representation, such an approach allows to model in a simple manner particular features of unsaturated soil behaviour. In this paper, an alternative choice for this parameter is proposed and validated using either shear strength or elastic stiffness experimental data from a set of soils ranging from almost granular materials to high plasticity clays. A physical interpretation in terms of microstructurally trapped water is provided. It is shown that the amount of trapped water is closely linked to the definition of χ. When the amount of non-free water increases (increasing plasticity indices), a significant deviation of χ values from the degree of saturation is observed. It is thus concluded that the hypothesis stating that Bishop's χ parameter equals the degree of saturation of water is only approximately valid for a particular class of soils, namely those having a marked granular nature.