Differential frost heave is often implicated in the formation of patterned ground in regions subject to recurrent freezing and thawing. A linear stability analy-sis (LSA) indicates that a continuum model of frost heave is linearly unstable under typical natural freezing conditions of silty-clay soils. A two-dimensional non-linear numerical analysis corroborates the frozen time LSA results, and also indicates the importance of non-linear and time-dependent terms that ultimately lead to a preferred mode, which the LSA fails to predict. Instability of the one-dimensional solution oc-curs at shallow freezing depths and near-zero surface loads when positive perturba-tions in the ice content at the freezing front lead to a concomitant increase in thermo-molecular pressure and upward ice velocity. Differential frost heave can then occur because of the increased heat flux from the perturbed surfaces. A three-dimensional model using random initial surface perturbations indicates that regular surface pat-terns will evolve with a length scale in the order of 2-4 meters, which corresponds quite closely with naturally-occurring non-sorted patterned ground.
展开▼
