On the scaling and ordering of columnar joints

On the scaling and ordering
of columnar joints

Ph.D. thesis, Unpublished, Nov. 2007.

Lucas Goehring

Department of Physics, University of Toronto,
60 St. George St., Toronto, Ontario, Canada M5S 1A7.

Columnar jointing is a fracture pattern, best known from locations such as the Giant's Causeway, or Fingal's Cave, in which cracks self-organize into a nearly hexagonal arrangement, leaving behind an ordered colonnade. In this thesis observations of columnar jointing are reported from both a controlled laboratory setting, and in cooled lava flows. Experiments were performed in slurries of corn starch and water, which form columnar joints when dried. This drying process is examined in detail, and it is shown how desiccation leads to the propagation of a sharp shrinkage front. In general, but with some signi cant exceptions, the size of columnar joints is inversely dependent on the speed of this shrinkage front during their formation. The exceptions, which include sudden jumps in column scale, show that hysteresis is also important in choosing the column scale. Novel observations of the 3D structure of joints in starch show that columnar joints do not settle down to a perfect hexagonal pattern, but rather mature into a continuously evolving dynamic pattern. This pattern is scale invariant, and the same statistical distribution of column shapes applies equally to joints in both starch and lava. Field work was performed to study columnar jointing in the basalts of the Columbia River Basalt Group and the island of Staff a, and the more heterogeneous lava flows of Southwestern British Columbia. The widths of columns and the heights of striae (chisel-like markings that record details of cooling) were examined in detail, and these length scales are shown to be inversely proportional to each other. An additional length scale, that of wavy columns, is also first reported here. Based on these measurements, empirical advective-diff usive models are developed to describe the transport of water in a drying starch-cake, and the transport of heat in a cooling lava flow. These models have only a single scaling parameter, the Péclet number, which relates the fracture front velocity times the column size to the (thermal or hydraulic) di usivity. In both cases, the formation of columnar joints occurs at a Péclet number of about 0.2. This model explains the hundred-fold di fferences in scale between columnar joints in starches and lavas, and can be used as a tool for the interpretation of joint patterns in the field.


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