Determination of the lens water content for several different configurations of elliptical particles in unsaturated soils

Until now, all of the calculations about determining of water content around the particles in unsaturated soil have done with supposing the spherical shape of particles and most of quantities such as matric suction and interparticle stress due to water meniscus were calculated by using that simple assumption.
In this paper, three packing methods of ellipsoidal particles are studied and by considering changes in meniscus geometry, matric suction and water content volume are evaluated as functions of meniscus radii for soil particles under the pore-water regime. This analysis provides a theoretical basis for describing several well-known phenomena in unsaturated soil behavior. A series of rigorous analytical equations was developed for describing the total volume of menisci between contacting ellipsoidal soil grains by treating the zero contact angle. Matric suction characteristic curves modeled using the analytical solutions displayed behavior similar to real unsaturated soils by using the ellipsoidal particles.
The results show that by increasing the filling angle, the volumetric water content of horizontal arrangement is about 2 to 5 times higher than other states, while by changing in the radius ratio of the lens, this amount is more for vertical alignment. So, the matric suction for elliptical particles is quantified with little inclination towards the water content change which achieved four times larger for double diameter ratio.