Evolution of Tiling-like Crack Patterns in Maturing Columnar Joints

Fracture or cracking essentially involves the formationof new interfaces. These patterns are usually studied as two-dimensional mosaics. The new surface that opens up is in the thirddimension, along the thickness of the sample. The thickness is usuallyvery small compared to the lateral dimensions of the pattern. Aspectacular and distinctive departure from these everyday examples ofcracks are columnar joints. Here, molten volcanic lava, by the sea,cools and cracks under appropriate thermal and elastic conditions,causing the crack system to grow downward, creating long, verticalcolumns with polygonal cross-section. The focus of this paper is thestudy of the elongated interfaces of these columns: how the cross-section of their outlines gradually undergoes a metamorphosis from a disordered-looking Gilbert tessellation to a well-orderedhexagonal Voronoi pattern. As the columns grow downward to lengths of several meters (in natural systems), their outlinecontinuously changes, the center may shift, causing the column to twist. For thefirst time, the evolution of these crack mosaics hasbeen simulated and mapped as a trajectory of a 4-vector tuple in a geometry-topology domain. The trajectory of the columnar jointsystems is found to depend on the crack seed distribution and crack orientation. An empirical relationship between the systemenergy and the crack mosaic shape parameter lambda has been proposed on the basis of principles of fracture mechanics. The total systemenergy shows a power-law dependence on lambda with the exponent beta similar to 0.3 and lambda approximate to 0.75 at crack maturation. The parameter values arevalidated by matching the proposed relation with energy estimates existing in the literature. The relation not only matches the visiblechanges in geometry but also provides a feasible measure of the energy of the system. The geometric energy for the polygonalmosaics in the transverse section has also been estimated as a function of time. The geometric energy moves toward a minimum asthe mosaic becomes more Voronoi-like at maturation.

Automated summary

This paper presents a detailed study on columnar joints, including simulation of crack evolution trajectories, the relationship between energy and crack shape parameters, and the trend of system energy changes.