Formation of ice lenses and frost heave

[1] I examine the morphology of ice growth in porous media. Intermolecular forces cause premelted fluid to migrate and supply segregated ice growth (e.g., lenses) and frost heave. I account for the net effect of these microscopic interactions in a homogenized model formulated in terms of fundamental physical properties and characteristics of the porous medium that can be measured; no ad hoc parameterizations are required. Force equilibrium constraints yield the rate of fluid migration toward the ice lens boundary and predict the conditions under which new lenses are initiated. By combining this analysis with considerations of the heat flow problem in a step-freezing (Stefan) configuration, I elucidate the boundaries between different regimes of freezing behavior. At higher overburden pressures and relatively warm surface temperatures, ice lenses cannot form, and freezing of the available liquid occurs within the pore space, with no accompanying deformation. When conditions allow a lens to form, water is drawn toward it. If the fluid supply is sufficiently rapid, the lens grows faster than the latent heat of fusion can be carried away, and its boundary temperature warms until it reaches a stable steady state configuration. At lower fluid supply rates, the lens boundary temperature cools until a new lens can form at a warmer temperature beneath. With subsequent freezing this lens grows until yet another lens forms and the process repeats. An approximate treatment leads to estimates of the evolving lens thickness and spacing, as well as the accumulated total heave.