A theoretical determination of the characteristic equation of snow in the pendular regime

Recent mathematical models treat a natural snow-pack as a mixture body consisting of solid ice grains, liquid water, and a gas made up of air and water vapour. Such a model requires two independent constitutive equations for the two independent volume fractions. However, so far only one equation, a power law relating the liquid-water content to capillary pressure, has been suggested, by analogy with the so-called “characteristic” equation for liquid water in soils. Experimental data from drainage tests on snow columns may be used to determine the characteristic equation for snow for relatively high water contents. However, the experimental method is not valid when water exists in isolated inclusions in the snow, i.e. in the pendular regime. In this paper a theoretical method is used to derive two independent volume-fraction laws for snow in the pendular regime.