Application of a Thermodynamically Based Shrinkage Equation to Freezing Induced Bulk Soil Volume Changes.

Bulk soil volume increases do not always accompany freezing. Only when the soil pore system cannot accommodate the volumetric expansion associated with the freezing induced phase change of pore water does bulk soil volume expansion occur. Pore water migration towards zones of ice nucleation in larger pore spaces, and the concomitant localized desiccation within smaller pores, is thought to be responsible for the freezing induced bulk soil shrinkage that can occur in non-rigid soils. A constitutive shrinkage equation developed from basic equilibrium thermodynamics, and fitted to freezing induced volume change data using an unbiased least-squares curve fitting procedure, was applied to freezing induced shrinkage data for seven soils of differing clay contents. The resulting equations defining void ratio as a function of moisture ratio are differentiable thus allowing precise estimation of the different regions of the unsaturated shrinkage curves.  The range of water contents associated with these different regions may be related to characteristic soil properties including Atterberg limits. Air entry void ratio from the fitted curves was found to be similar when comparing frozen and non-frozen shrinkage curves. Structural shrinkage, that begins immediately following air entry, was typically not noted as samples were frozen at progressively drier water contents. The Atterberg plastic limit, thought to be the transition between structural and proportional shrinkage on the drying curves, was therefore not found to be useful in characterizing freezing induced shrinkage. The fitted void ratio at the dry end of the freezing shrinkage curve was typically found to be less than the corresponding value for non-freezing shrinkage although neither value corresponded well with the Atterberg shrinkage limits. The data suggests that a more vigorous shrinkage process occurs during freezing than during air drying.