Starch columns: Analog model for basalt columns

Desiccation of starch-water mixtures produces tensile-crack patterns which appear to be interesting, but largely unknown study objects for fracture mechanics, structural geology, and volcanology. This paper concentrates on columnar jointing and on columns in starch. Starch columns have polygonal cross sections and are very similar to basalt columns. They are produced by lamp drying starch specimens with dimensions of several centimeters and have diameters in the millimeter range. The columns develop behind a crack front which propagates from the surface into the interior. The experiments, supported by X ray tomograms; show that polygonal regularity of the crack pattern is not present at the surface but develops during penetration. This transition is steered by a minimum-fracture-energy principle. The analogy between basalt cooling and starch desiccation is far reaching: water concentration in starch is analogous to temperature in basalt, both quantities obey diffusion equations, water loss is equivalent to heat loss, the resulting contraction stresses have similar dependences on depth and time, and in both cases the material strength is exceeded. The starch experiments show that column diameters are controlled by the depth gradient of water concentration at the crack front. High (low) gradients are connected with thin (thick) columns. By analogy, a similar relation with the temperature gradient exists for basalt columns. The (normalized) starch gradients are about 3 orders of magnitude larger than the (normalized) gradients in basalt. This explains why starch columns are much thinner than basalt columns. The gradients are so different, because the crack front speeds differ by a factor of about 10: after 3 days the speed is about 10 mm/d in starch but about 100 mm/d in basalt [Peck, 1978]. The speed difference; in turn, results from the difference of the diffusion constants: the hydraulic diffusivity of starch is 2 orders of magnitude lower than the thermal diffusivity of basalt.