We present a mathematical model for the breakdown of porous rock by the growth of ice within cracks. The model is founded upon well-established principles of fracture mechanics and recent advances in soil physics, along with the assumption that progressive crack growth results from water migrating to ice bodies in cracks, much as water migrates to ice lenses in freezing soil.
Our model predicts crack-growth rates compatible with empirical data. Calculations for a granite and a marble indicate that sustained freezing is most effective in producing crack growth when temperatures range from ∼ −4 °C to −15 °C. At higher temperatures, thermodynamic limitations prevent ice pressure from building up sufficiently to produce significant crack growth; at lower temperatures, the migration of water necessary for sustaining crack growth is strongly inhibited. In hydraulically “open” systems, in which pore-water pressure remains near atmospheric pressure during the freezing process, crack-growth rates during continuous cooling will generally be greatest at low rates of cooling, less than ∼0.1–0.5 °C/h. At higher rates of cooling, the influx of water to growing cracks is significantly inhibited.
The model delineates clearly the role of material parameters (elastic moduli, fracture-mechanical properties, grain size and shape, and crack size), environmental conditions (temperature, temperature gradient, water pressure), and time in frost damage to rocks. Our calculations, along with recent experimental work on water migration in freezing rocks (Fukuda, 1983), lead us to question the widely accepted importance of two phenomena—freezing of water in sealed cracks and freeze-thaw cycling—in the fracture of rock exposed to natural freezing conditions.