Mechanics of Thermal Contraction Cracks and Ice-Wedge Polygons in Permafrost

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Abstract
Leffingwell’s contraction-crack theory of ice-wedge polygons in permafrost has been examined from the point of view of mechanics. A nonlinear viscoelastic model of thermal stress in permafrost leads to results consistent with the theory within the limits of existing information on polygon dimensions, crack depths, temperature, and mechanical properties of ice and permafrost. Stresses that cause cracking are evidently generated not only by low temperature but also by rapid cooling. The size of the polygons can be explained in terms of the stress-perturbation due to a single crack and the distribution of mechanical flaws. The polygonal patterns can be classified according to whether or not the intersections are predominantly orthogonal. It is proposed that orthogonal polygons evolve by progressive subdivision, nonorthogonal ones by successive branching of cracks attaining high propagation velocities. Much of the discussion is general and applies directly to other types of contraction-crack polygons such as columnar basalt joints and mud cracks.

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