PEPPIN, S. ... et al., 2011. Frost heave in colloidal soils. SIAM Journal on Applied Mathematics, 71 (5), pp. 1717 - 1732.
We develop a mathematical model of frost heave in colloidal soils. The theory accounts for heave and consolidation while not requiring a frozen fringe assumption. Two solidification regimes occur: a compaction regime in which the soil consolidates to accommodate the ice lenses, and a heave regime during which liquid is sucked into the consolidated soil from an external reservoir, and the added volume causes the soil to heave. The ice fraction is found to vary inversely with the freezing velocity V, while the rate of heave is independent of V, consistent with field and laboratory observations.