SOONER OR LATER THE SURFACE of almost anything will develop cracks. Often they grow into an intricate network. Although the network may appear to form randomly, in many cases it actually develops systematically according to certain rules. Applying those rules as you look at the places where cracks intersect, you can ascertain how the network formed.

It is instructive to investigate two types of crack network. One of them is the network that develops in drying mud or paint. Similar networks are found in broken pavement, tile, plaster and other materials. Do the cracks tend to intersect at any particular angle? Do the "islands" left by the cracks fend to have any particular geometric I shape? Why do the tops of the islands in drying mud sometimes separate and then curl? Are the giant crack networks found on some playas (desert basins that temporarily become shallow lakes after heavy rain) similar to mud cracks?

The other type of crack network is found in some ancient lava flows that formed pools on the surface, cooled, solidified and then cracked so as to form tall columns whose cross sections are hexagons and other polygons. When I walked over an outcropping of such columns at Giant's Causeway in Northern Ireland recently, I was surprised at the regularity of the formation. Why did cooling basalt crack in such an organized way? No one has advanced a definitive answer, but recent theories may have resolved part of the mystery.

When a solid is placed under tensile stress by stretching forces, its molecular bonds resist the elongation. The ratio of the elongation to the initial length is called strain. If the strain is less than 1 percent, the bonds can be regarded as tiny springs linking the molecules; if the stress is removed, the solid regains its initial length as the springs contract. Under a larger strain a ductile solid first is distorted and then breaks. A brittle solid breaks immediately with no distortion.

The mechanism of breaking is by means of cracks that form and then extend through the solid. Imagine a solid block under a uniform vertical stress. h Each vertical molecular bond along any horizontal line through the block shares equally in resisting the stress. The stress is said to be uniformly distributed over such a line.

Suppose a small crack appears on one side of the block because of a local weakness in the material or a scratch on the surface. The stress on the block acts to pull apart the two faces of the crack. Molecular bonds are broken; the stress they would have resisted is shifted to the bonds at the tip of the crack, increasing the stress there. It may break those bonds, extending the crack into the block.

The process can be repeated at the new tip. In this way the crack travels though the block. It may move almost as fast as the speed of sound or it may travel in spurts. Its movement tends to be straight unless it encounters points of weakness, in which case the path becomes sinuous.

Suppose the block is under both vertical and horizontal stress when a crack develops horizontally. The vertical stress in the material along the faces of the crack is relieved, but the horizontal stress is still there. It may initiate a side crack that begins to travel at right angles to the original crack. Where points opposite each other on the faces of the original crack are weak, side cracks can develop. They travel in opposite directions.

When a crack travels toward an older crack at some angle other than 90 degrees, it comes under the stress that is parallel to the sides of the old crack. The distribution of stress around the tip of the new crack becomes asymmetric. The new crack changes its direction of travel so that the angle between the cracks gradually increases to 90 degrees when the cracks join. The new crack then ends.

With these general rules you can often determine the history of a crack network. Pick out a long, more or less straight crack that has many intersections. The side cracks that extend from it but do not reach another crack must have been formed by the stress parallel to the faces of the main crack. The side cracks that intersect other cracks either began on the main crack or traveled there. In both cases the intersections with the main crack are perpendicular to it.

To make a record of how the network formed draw a map of what appear to be the oldest cracks. The islands they create are large and quite likely four-sided because of the perpendicular intersections. Add the side cracks. They create smaller islands, which are probably four-sided also. In a complex network of cracking you might be able to discern several generations of cracks.

In 1962 Arthur H. Lachenbruch of the U.S. Geological Survey classified polygonal crack networks in terms of their dominant intersection angle. One class contains all networks with nonperpendicular intersections. The networks with perpendicular intersections are grouped according to whether they are randomly formed or are oriented because of an asymmetry in the stresses producing them. The randomly formed group is further classified as having either irregular or regular polygons according to whether the sides of the polygons are sinuous or approximately straight. In some cases a network that begins as a system of irregular polygons may develop enough additional cracks to become a system of smaller regular polygons.

I surveyed many crack systems. On a tennis court I found cracks that developed when ground pressure forced the playing surface upward, putting it under tensile stress. The stress produced sinuous cracks with 90-degree intersections that created large polygons, most of them four-sided. A few of the intersections formed small triangular islands. A triangle may form when two nearby side cracks from the main crack curve toward each other, intersect and then continue as a single crack. A triangle may also form when two cracks intersect at some angle other than 90 degrees and new stress adds a short third crack.

Polygonal-crack networks were also evident in blacktop road surfaces, but the polygons were typically smaller than the ones on the tennis court and more of the intersections were at angles other than cracks were noticeably sinuous. Some of them were curved, presumably because they changed directions when they approached older cracks. (Crack e production in road surfaces is complicated by the fact that a passing automobile displaces developing islands. Water creates additional stresses when it freezes and expands in the cracks.)

Many concrete slabs display cracks and crack networks. Cracks develop where the slab buckles because of its weight or the stresses induced by a shifting support. Although many intersections are perpendicular, many are not, presumably because the stresses are complex and may be influenced by the shape of the slab, particularly if the slab is small.

Crack networks develop in drying mud as the water between grains evaporates. Forces on the grains tend to contract the mud surface, giving rise to cracks. One source of these forces is the surface tension of the water between the grains. As water is lost, the top surface of the remaining water becomes concave and pulls on the grains. If the grains have electrically charged surfaces, they may also be pulled toward one another by electrical forces between those surfaces and any molecules in the water between them that are oriented by the charged surfaces. The resulting contraction puts the top layer of mud under tensile stress. Every small region is simultaneously pulled horizontally in all directions.

The tensile stress increases until it cracks the mud surface. Many cracks may appear almost simultaneously. Then side cracks develop in the islands. When the cracks meet older cracks smaller islands are left. Theoretical calculations of the energy involved in cracking mud predict that in an ideal situation the tensile stress will produce uniformly spaced centers of contraction, each of which will pull on its surroundings in such a way that cracks intersect at 120-degree angles, creating hexagonal islands. Although photographs of such hexagonal arrays can be found in textbooks and research papers, nearly all the intersections I have seen in mud-crack networks are perpendicular.

In 1966 James T. Neal of the U.S. Air Force Cambridge Research Laboratories concluded from his studies of mud cracks that as a rule the intersections are indeed perpendicular and the islands are four-sided. Why does theory predict otherwise? Perhaps the e premise that mud dries uniformly is unrealistic. In my observations mud initially cracks in random places, relieving a stress in some complicated way. Newer cracks then travel through material that is no longer under uniform tensile stress. When they approach the older cracks, they must turn to make perpendicular intersections, creating four-sided polygons.

I think another factor may account for hexagonal networks. I have explained crack propagation as being due to pure tensile stress, a fracturing condition sometimes called Mode I. There are also modes II and III. Imagine a three-dimensional mud crack with a tip several millimeters deep. Mode II fracturing results when the two faces of the crack slide horizontally past each other. In Mode III fracturing the faces slide vertically. Both modes create shearing with no separation of the crack faces.

Mode II seems to me to be more likely in mud cracking. When an initial crack opens in the mud, it may put an adjacent region under shearing stress. The region is already under tensile stress. The combination of stresses forces the crack into the adjacent region but in a new direction, possibly at an angle of 120 degrees to the initial direction. If fracturing continued in this way, the crack pattern would be hexagonal.

Neal also studied the giant networks of sinuous cracks revealed by aerial photographs of playas and deserts. The cracks developed after decades of drought had lowered the water table in areas of clay or sandstone. Some of the polygons are 100 meters across. The fissures, which are generally V-shaped, can be more than a meter deep. Here again the dominant angle at intersections is 90 degrees.

In networks of mud cracks the top layer of each island may curl upward. In 1928 Chester R. Longwell published a study of such mud curls. As the layer dries and contracts, it separates from an underlying sandy layer. If the evaporation is rapid, the top surface of the layer shrinks faster than the bottom surface, and the resulting stresses within the layer force its perimeter to curl upward. Depending on the rate of evaporation and the type of grain, it may curl until it becomes a cylinder no wider than a pencil.

Longwell described fine clay material as being ideal for this extreme curling, presumably because it contracts so much when it is dried. Silt develops only concave plates; when sand is mixed into clay or silt, there is no curling. If there is an underlying bed of sand, a thin top layer of clay or silt may separate from it. Hence curling can be found in regions where a recent rain had washed a think layer of clay or silt over a sandy or hard bed. I find curls when a thin layer of mud dries on my stone patio.

I examined crack networks in a solution of cornstarch that I mixed by hand in a large, rectangular baking dish until all lumps were gone. After several hours a layer of water had separated from the solution. I removed it with a rolled paper towel that I dipped into the water and hung over the side of the dish.

When I examined the dish a few days later, the cornstarch looked dry, but it had not cracked. Then, within an hour, several large cracks appeared across the length of the material and smaller ones appeared at the edge. Their paths were obviously influenced by the shape of the dish. The cracks that subsequently formed in the isolated islands were independent of the dish shape. Often they curved to intersect at right angles with older cracks, which were widening continuously with further shrinkage of the material. Some of the polygons began to curl upward, but later they flattened out.

With the end of a paper clip I poked a hole in the middle of an island. The surface was brittle, as was shown by the fact that three cracks developed immediately and traveled away from the hole for several millimeters. Within minutes these new cracks lengthened until they joined older ones. One of them curved almost 90 degrees to make its intersection. Crack formation continued for another day, leaving many four-sided islands. Next, within an hour every island ruptured into fine-scale polygons outlined by shallow, sinuous cracks. The cracking then stopped. The network had begun with hI regular polygons; it ended with irregular ones.

The crack networks in the basalt fields of Giant's Causeway, Devil's Tower in Wyoming, Devil's Postpile in the Sierra Nevada, Fingal's Cave in Scotland the Boiling Pits in Hawaii, Mount Etna in Sicily and those in many other places are remarkably different from the others I have discussed. They appear to be due to lava flows that formed pools and whose top and bottom surfaces then cooled rapidly. The interior of the flows took years to cool and solidify. The stresses induced by contraction as the material cooled made the interior fracture into polygonal columns.

At Giant's Causeway weathering has exposed many horizontal and vertical faces of the crack network. In some places the fracture has left a two-tiered vertical arrangement. Near the bottom of the basalt are stately columns up to 20 meters in height. Their cross sections are distinctly polygonal, many of them appearing as hexagons. The average width is about 70 centimeters. Above this "colonnade" is an "entablature" consisting of smaller, less well formed and often chaotic columns. In other places a three-tiered arrangement is seen: above the entablature there is another colonnade made up of columns that are almost as impressive as those in the lower colonnade. The transition between adjacent tiers is abrupt, although there is no evidence of any change in material content across the transition. The transition line can run for quite a distance horizontally, implying that whatever was happening to cause the transition at one point was happening everywhere at the same level.

These formations present two enduring puzzles. Why should rupturing create splendidly shaped columns in the colonnades and irregular ones in the entablature? Why is the transition between tiers so sharp and so extensive horizontally? For hundreds of years scholars have proposed varied theories to explain these lava formations. Among the more recent ones are an idea put forward in 1978 by Michael P. Ryan and Charles G. Sammis, who were then at Pennsylvania State University, and another idea advanced by Lakshmi H. Kantha, then at Johns Hopkins University.

Ryan and Sammis considered the solidification of a pool of lava. As a pool solidifies, the upper and lower interfaces between the solid and the liquid move slowly into the interior. As the upper interface progresses, for example, a cooling solid layer is left above it. Contraction that accompanies the cooling process puts the layer under tensile stresses that build up until the layer suddenly ruptures into a network of cracks.

In 1959 the Kilauea volcano in Hawaii filled a crater with lava to a depth of more than 100 meters. Observations by means of boreholes indicate that the upper solid-liquid interface is descending at the rate of about one centimeter a month. Occasionally shock waves are recorded. They can even be felt and heard when one walks on the now solid top surface. They seem to result from the sudden fracturing of a solid layer just above the interface. The layer appears to be no more than .5 meter thick when it fractures.

In such a case the theoretical calculations that predict a trend toward hexagonal polygons may be applicable. As the solid-liquid interface continues to descend, the crack network may follow it, thereby forming columns. Ryan and Sammis worked out details of how the process might operate. They argued that the cracks propagate vertically by means of a combination of Mode I and Mode III fracturing. Indeed, there seems to be evidence of such propagation along the length of the columns they examined at Boiling Pits. Although the explanation may be correct, it fails to account for the formation of tiers or their knife-edge transitions.

Could some feature of the liquid leave its trace in the solid and thus influence rupturing and the subsequent formation of columns and tiers? Benard cells are a candidate. Under certain conditions a liquid heated at the bottom or cooled at the top can develop hexagonal convection cells with fluid rising within the cells and descending at their perimeter. Benard cells, however, are short in relation to their width-nothing like the long, thin columns in basalt.

In 1981 Kantha noticed that the tiering in basalt resembles the fluid-flow phenomenon called salt fingers. The fingers are thin columns of fluid that form at the interface between two solutions because of a difference in the diffusion rate of the molecules in the solutions.

With patient work you can demonstrate the phenomenon in your kitchen. Get a transparent container, preferably rectangular in order to avoid refraction of light by curved surface. Mix salt into water several centimeters deep. In another container wit a pouring lip mix a sugar solution about the same amount of water. Add a drop of food coloring. Pour the sugar solution slowly onto a spoon held just at the top of the salt solution. The sugary liquid mixes gradually with the salty one. The density of the sugar solution should be slightly less (specific gravity 1.1) than that of the salt solution (1.12), in which case the sugar solution should spread into a layer over the salt solution.

Although the distribution of densities is stable, the arrangement become unstable with any small disturbance of the interface. Suppose the interface bulges upward. The bulge contains saline solution. Because salt diffuses faster than sugar, salt diffuses from the bulge into the surrounding sugar solution faster than sugar diffuses into the salt. The bulge becomes lighter than the surrounding solution and moves upward. As the process continues, the bulge becomes a finger.

An hour or two after you pour the sugar solution the interface develops short columns, each a millimeter or less in width. Above and below that region the solutions are mixed by convection. With time the columns grow longer, wider and better defined and, develop polygonal cross sections. The transition between the columns and the mixing layer above it resembles the two-tier formation in basalts.

A three-tier formation can be made if the density of the salt solution decreases with height. You will observe a middle layer where the mixing is turbulent. Above and below it are columnar layers. (In both demonstrations you can see the columns better if you stand a meter or so away from the; container and move your head to the left and right so that the refraction of; light by the columns produces a weak scintillation.)

Kantha hypothesized that fingers in lava gave rise to the fracture network seen in columnar basalts. When the basalt solidified, cooled, contracted and cracked, the cracks tended to follow the edges of the polygons that were formerly the fingers. The cracks then traveled vertically as the crack net work followed the solid-liquid interface. The exciting aspect of this explanation is that it neatly explains the knife-edge transitions between tiers in the basalts. They mark the ends of fingers. Was Kantha right? Work now being done seeks to test the explanation and to show how fingers could form in molten basalt.

Bibliography

CYCLIC FRACTURE MECHANISMS IN COOLING BASALT. Michael P. Ryan and Charles G. Sammis in Geological Society of America Bulletin, Vol. 89, No. 9, pages 1295-1308; September, 1978.

"BASALT FINGERS"-ORIGIN OF COLUMNAR JOINTS? L. H. Kantha in Geological Magazine, Vol. 118, No. 3, pages 251-264; 1981.

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