Forecasting Frost Damage: Follow the Water

Abstract:

Frost damage takes place when the pressure exerted against pore walls exceeds the cohesive strength of water-infiltrated rock and causes cracks to extend. Elegant theoretical treatments supported by meticulous field and laboratory observations have combined to unravel the basic mechanical and thermodynamic controls in idealized systems. Frost damage is most vigorous when conditions are cold enough that the net pressure exerted against the pore walls can cause crack extension, yet warm enough to enable the flow that supplies further ice growth in the newly opened space. This insight is applied here to develop practical geomorphic process laws for the effects of frost damage at the larger scales that are relevant for describing the evolution of landscapes. To this end, a direct connection is made between the intensity of frost damage and the porosity increase that results from gradients in water flux under conditions that are cold enough for ice–rock interactions to propagate cracks. This implies that the annual temperature variation at the ground surface can be combined with considerations of heat and mass transport to derive rigorous forecasts of the potential for frost damage that are tied to the increases in water mass that accompany solidification in porous rock.

As an example, the image shows the depth-integrated porosity change λ promoted by crack growth at temperatures colder than –ΔT_c over an annual cycle for different choices of mean annual temperature MAT and surface amplitude A (assuming a thermal diffusivity of 1 mm²/s and a power-law relationship between permeability and undercooling with exponent α=4, such that a base value of 10^-14m² is reached at a reference undercooling of 0.1 ºC). The abrupt onset in cracking once MAT decreases below a threshold is produced by the requirement that undercooling surpass ΔT_c in order to generate sufficient pressures to propagate cracks. The eventual reduction and gradual tail in λ at colder MAT is produced by the clogging of the permeable pathways needed to supply additional water to propmote crack growth.