A Capillary Water-Retention Framework for the Effective Stress Parameter Considering Hydraulic Hysteresis

Formulation of an effective stress equation for unsaturated soils where all relevant physical characteristics are included has challenged researchers for several decades. On one hand, the interfacial forces and the contractile skin have recently been understood to be of significant contribution to the effective stress, particularly at low degrees of saturation. On the other hand, the microstructural effects play a significant role, especially in fine-grained soils. In this study, an equation is proposed for the effective stress parameter ( $$\chi$$ ) based on the recent advances in modeling the adsorbed water, and thereby determining the capillary water retention curves. In the proposed relationship, both the microstructural effect and interfacial forces are taken into account. Additionally, in formulating effective stress, these two aforementioned aspects have been considered and formulated for both drying and wetting conditions. To this end, the interfacial forces were determined based on the capillary water content. Next, the proposed model was further simplified to reduce the number of unknown parameters to one with the rest of the parameters readily available from the soil water retention curve. The simplified formulation agrees fairly well when compared with the experimental data on soils experiencing both drying and wetting paths. Furthermore, assessing the performance of the proposed model, compared with the available equations incorporating the contribution of the interfacial forces, indicates the superiority of the proposed model for the eight soil types examined in this study.