Modeling relative frost weathering rates at geomorphic scales

Abstract

Frost damage is a powerful agent of geomorphic change. Cracks can grow when the ice pressure in pores reaches a threshold that depends on matrix properties and crack geometry. Mineral surfaces that are preferentially wetted by liquid water rather than ice are coated by premelted liquid at a pressure that is lower than the ice pressure. Because this pressure difference increases as the temperature cools, when the ice pressure is effectively pinned at the cracking threshold, temperature gradients induce gradients in liquid pressure that draw water towards colder temperatures. Porosity increases and frost damage accumulates in regions where water supplies crack growth. To apply this understanding over the large spatial and temporal scales that are relevant to evolving landscapes, we develop a simple model that tracks porosity changes. Our central assumption is that frost damage is correlated with porosity increases under conditions where frost cracking takes place. Accordingly, we account for the permeability reductions with decreased temperature that accompany ice growth along porous pathways and derive general expressions for the porosity change through time at particular depths, as well as the total porosity increase through all depths beneath a point at the ground surface over the time during which cracking occurs each year. To illustrate the resulting patterns of frost weathering, we consider a general case in which the permeability has a power law dependence on temperature and the annual surface-temperature variation is sinusoidal. We find that the degree of frost damage generally decreases with depth, except at localized depths where damage is elevated because the rock spends longer times near the threshold for cracking, leading to enhanced water supply in comparison with neighboring regions. The magnitude of the net expansion that results from porosity changes at all depths beneath the ground surface is increased for seasonal thermal cycles with larger amplitudes, with a broad maximum centered on a mean annual temperature near the threshold required for crack growth. Warmer mean annual temperatures lead to less damage because of the reduction in time during which it is cold enough for cracking, whereas colder mean annual temperatures are accompanied by reduced water supply due to the temperature dependence of permeability. All of the controlling parameters in our model are tied explicitly to physical properties that can in principle be measured independently, which suggests promise for informing geomorphic interpretations of the role of frost weathering in evolving landforms and determining erosion rates.