Interactions between two rough spheres, water bridge and water vapour

Micromechanical considerations of the interactions between the granular skeleton of an unsaturated granular soil and the contained moisture involve the classical interaction model consisting of a water bridge in contact with two rigid smooth spheres of equal radius, at a separation determined by their actual surface roughness, and surrounded by a gas with a vapour pressure at equilibrium with the water. In this paper the water volume and the interparticle contact force are related to the water suction, the water–solid surface contact angle, and the size and roughness of the spheres in dimensionless terms. The dimensionless water suction is also related to the corresponding relative humidity of the water vapour. The calculated equilibrium relations are shown to possess non-uniqueness, which is interpreted in terms of soil mechanical properties while recognising that for low saturations in natural processes the humidity of the pore air is the independent parameter. The developed analytical solutions show the classical toroidal approximation to be reasonable. These solutions are applied in a companion paper to clarify the concept of an intergranular stress induced by both pore suction and related surface tension.