Abstract
We present a mathematical model of the fracturing of water-saturated rocks and other porous materials in cold climates. Ice growing inside porous rocks causes large pressures to develop that can significantly damage the rock. We study the growth of ice inside a penny-shaped cavity in a water-saturated porous rock and the consequent fracturing of the medium. Premelting of the ice against the rock, which results in thin films of unfrozen water forming between the ice and the rock, is one of the dominant processes of rock fracturing. We find that the fracture toughness of the rock, the size of pre-existing faults and the undercooling of the environment are the main parameters determining the susceptibility of a medium to fracturing. We also explore the dependence of the growth rates on the permeability and elasticity of the medium. Thin and fast-fracturing cracks are found for many types of rocks. We consider how the growth rate can be limited by the existence of pore ice, which decreases the permeability of a medium, and propose an expression for the effective 'frozen' permeability.
Highlights
Large pressures can develop inside water-saturated porous media at sub-zero temperatures
This study of a penny-shaped cavity has provided us with a mathematical model capable of explaining the physical processes governing fracturing, and establishing the relevance of different parameters
Phase planes of the different types of solutions were discussed in §3, and general patterns of dependence of the cavity growth curves on the different parameters of the problem were established
Summary
Large pressures can develop inside water-saturated porous media at sub-zero temperatures These pressures occur owing to the solidification of water inside the pores and can cause fracturing of pre-existing faults, leading to the degradation of the rock. A similar process, called frost heave, occurs in soils, where segregated ice lenses form devoid of soil particles, causing upward movement of the ground above. This frost-induced deformation of material can destroy building foundations, damage roads and statues, and deform cooled gas pipelines laid. Phenomena such as patterned ground, potholes, needle ice and pingos play an important role in the development of landscapes [1]
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