Pore‐scale analytic model to calculate the suction stress in partially saturated soils

The expression of effective stress in unsaturated conditions has remained controversial ever since the concept was first proposed in the 1950s by Bishop. In this paper, based on the first law of thermodynamics, a novel approach is proposed to calculate the effective stress in unsaturated soil systems by applying the improved bundled cylindrical capillary model and the probability density function of soil particles. The proposed model provided an expression for Bishop's effective stress model and Bishop's coefficient χ. The basic assumptions of the model are (a) the water in the unsaturated pores can be divided into capillary water and adsorbed water, and (b) the soil pore network is considered as a rigid body, and the particle structure is unchanged with saturation variation. Published experimental data are compared with Lu's effective stress model and our model results. The findings show that the proposed model performs well over a wide range of saturation conditions for nonexpansive soils, such as sand, and the capillary stage for expansive soils, such as silt, and clay materials. Core Ideas We derived an analytic solution to calculate effective stress in vadose zone based on microscopic force balance. Based on the probability density function, the force balance in micro is upscaled to macro. The influence from free water and capillary water are considered into the solution.