MODELING THE EVOLUTION OF COLUMNAR JOINTS

Cooling cracks, developing from the margins of solidifying lava flows or intrusive dykes or sills, often propagate inward and divide the roc k into prismatic columns. It has been shown that: (1) the initial crac k pattern that forms at the surface of the body is not as regular as t he pseudo-hexagonal pattern which evolves later; (2) columnar structur es develop by repeated, step-wise crack advances, forming cm to dm tra nsverse bands on the column faces; (3) even within well-developed colo nnades, the polygonal outlines continue to shift slightly from one cra ck advance to the next. We propose that each new crack should propagat e parallel to the highest thermal gradient ahead of the current crack tip. When adjacent columns are of unequal size, the local asymmetry of the isotherms drives the new crack toward the biggest and hottest col umn. We present a geometrical model and algorithm that follows this ru le and mimics the successive crack advances as the cooling front migra tes into the lava sheet, or dyke. The model polygonal pattern obtained consists of convex, irregular polygons with a variable number of side s, but in which pentagons and hexagons predominate. The algorithm succ essfully reproduces the rapid evolution from an initial, immature crac k pattern to a pseudo-hexagonal, mature one in which the average numbe r of sides approaches six. It predicts also the predominance of Y-type crack junctions, the rapid evolution toward columns of approximately equal sizes, and the persistent changes in length and diverging orient ation of growth steps observed along the sides of columns. The model p olygonal patterns exhibit geometrical properties which are very simila r to those observed in well-developed columnar jointed flows such as t he Giant's Causeway.