Large areas of the Arctic are covered by ice-wedge polygons. Shallow troughs, spaced 10 to 100 feet apart (3–30 m.), form a conspicuous network on the ground surface. Beneath the troughs, buried in the permafrost, are generally found wedge-shaped masses of fairly clear ice, commonly some tens of feet deep and several feet wide at the top; I remember my surprise when Dr. Lachenbruch first showed them to me in an exposure near Point Barrow, Alaska.
In 1915, Leffingwell put forward a theory of the origin of ice-wedges that is now widely, but not universally, accepted. During the winter thermal contraction cracks the ground, and in early spring melt water refreezes in the new cracks. In the next winter thermal tension cracks the ground again at the same place, because the ice vein now situated there is a place of weakness. Again spring melt water refreezes in the crack, and so the process continues; an ice wedge begins to grow. Dr. Lachenbruch has set himself the task of seeing whether this idea of the origin of ice wedges is reasonable from the point of view of mechanics, having regard to what is known about the mechanical behaviour of ice and permafrost and temperature changes in the ground. He concludes that it is. Any such investigation is inevitably limited by the fact that not much is known about the mechanical properties of permafrost and dirty ice, and what is known about brittle fracture shows that its details can be rather complex. Nevertheless, a great deal can be done, as Dr. Lachenbruch's very thorough and carefully argued study shows.
He deduces from qualitative observations a set of rather stringent conditions that must be satisfied if Leffingwell's theory is to work. They relate the maximum thermal tension (which varies with depth) to the strength of the material at two definite levels: at the ground surface, that is, at the top of the seasonally thawed layer, and, a foot or so lower down, at the top of the permafrost itself, where the ice wedges are. He is at once able to rule out the simple idea that the frozen soil behaves purely elastically—the tensions would be far too high. More remarkably he is also able to rule out a linear visco-elastic behaviour of the frozen soil. But, with a model that combines elasticity with a non-linear viscous behaviour (strain-rate proportional to the third power of the stress), he succeeds in satisfying all the conditions. It appears that it is not the change of temperature, or mere low temperature, that cracks the ground; it is high rates of temperature change that do it. This is the implication of visco-elastic rather than purely elastic behaviour.
Dr. Lachenbruch goes on to consider the fracture process itself in detail. The area of stress relief due to a crack is an important factor in determining the spacing of the polygonal pattern. Here the latest developments in the elastic theory of brittle fracture are called in. To explain the details of the polygonal pattern, the angles at which the cracks meet and so on, is a general problem in the mechanics of contraction cracks; mud cracks, columnar jointing in cooling basalt, shrinkage cracks in concrete, and cracks in the glaze of ceramics are all aspects of the same problem. The theory of contraction crack patterns seems to be still in a fairly crude state, but, as this study illustrates, some principles are beginning to emerge.
This notable paper is a good example of the power of judiciously chosen simplified models to give insight into natural processes.
