Cracking mud, freezing dirt, and breaking rocks

1. What they did

Two physicists explain, for a general science readership, why cracks in nature so often form tidy patterns. They start with the basic theory of how a single crack grows: a crack advances when the energy released by growing just balances the energy needed to make new surfaces, and it grows along the path that releases the most stored strain energy at its tip. This is a local rule, worked out at the point and moment a crack grows, not a rule for the whole pattern at once.

They then use this rule to explain three kinds of crack networks:

• Cracking mud: the familiar cracks in mud that has dried once.
• Freezing dirt: permafrost that cracks every winter and closes every summer, forming polygonal terrain on Earth and Mars.
• Breaking rocks: the columns of cooling lava flows, and similar millimetre-wide columns in drying cornstarch in the laboratory.

They end with wavy and branching cracks, and include two simple paper-tearing experiments that readers can try.

2. What they found

Cracking mud

• As mud dries, the shrinking mud builds up stress if it is stuck to what lies below it. A first crack starts at a weak spot, such as a bubble, and runs across the layer in a roughly straight line.
• A later crack is guided by the earlier one and turns to meet it at a right angle. So the T-shaped junction records which crack came first.
• Cracking goes on until the pieces reach a size proportional to the depth of the mud layer. After that, more stress simply widens the existing cracks.
• Mud that has dried once has junctions mostly near 90° and 180°, and the pieces (called peds) are mostly four-sided, roughly square or rectangular.

Freezing dirt

• Permafrost cracks in deep winter as it shrinks with the cold, and the cracks can reach a few metres into the ground. As in mud, the polygon size is proportional to the depth of cracking.
• The cracks close and partly heal each summer, and new cracks follow the old weak lines the next winter, but not always in the same order. Over many cycles the T-junctions turn into Y-junctions with angles near 120°, and the polygons become mostly six-sided. Today’s polygons usually represent many thousands of years of this.
• A laboratory experiment with mud cracked, rewetted and cracked again shows the same change: the angles between cracks start at 90° and 180° and move towards 120°.
• The polygon centres are often raised, possibly because material such as ice fills the open cracks and pushes the centres up as they close.
• An undisturbed mud puddle that is wetted and dried many times can also form a mostly six-sided crack pattern with raised centres, as in mud near Death Valley.
• Something similar shapes the scales on the snouts of Nile crocodiles: during embryonic development, the snout scales (but not the body scales) form where a brittle skin fails, rather than being laid out directly by genes.

Breaking rocks

• A thick lava flow cools from the outside in. Cracks start at the surface and move down through the flow in steps, carving out columns. Boiling and condensing groundwater in the cracks carries the heat away and sets a steady speed for the cracking front. Cooling a large flow can take decades.
• Near the surface the pattern is mostly T-junctions, but within a few metres it becomes mostly Y-junctions, and the columns settle to a common width.
• Column width depends on how fast the cracking front moves: slowly cooled flows have wider columns, and quickly cooled flows narrower ones, even in the same material. The data from many lava flows fit a single rule (Péclet number about 0.35), and drying cornstarch follows the same kind of rule (about 0.1).
• The old idea, often given in tourist guidebooks, that the six-sided columns form all at once in a “best possible” arrangement is wrong. The pattern grows over time from local rules.

Wavy cracks

• A notched hot glass plate dipped into cooler water can grow a straight, wavy or branching crack, depending on the speed and temperature difference. Why the crack tip wavers is still not fully understood.
• Lava columns can also be wavy, as at Frenchman Coulee in Washington State. This has not been seen in cornstarch, and how it forms is not understood.

3. What they concluded

• Reading crack networks is still something of an art. Crack patterns partly record their whole history of formation, but they also reflect subtle internal dynamics.
• Simple tabletop experiments can give new insights and help to interpret large patterns in the landscape.
• Energy and symmetry only go so far; a fuller understanding needs to ask whether a crack network settles down, starts to oscillate, or becomes more complex.
• “From the snouts of Nile crocodiles to the surface of Mars, crack networks can tell us much about the hidden mechanisms at work during their evolution, if we can learn to read them. Ordinary mud is not a bad place to start.”