Experimental investigation of the scaling of columnar joints

Columnar jointing is a fracture pattern common in igneous rocks in which cracks self-organize into a roughly hexagonal arrangement, leaving behind an ordered colonnade. We report observations of columnar jointing in a laboratory analog system, desiccated corn starch slurries. Using measurements of moisture density, evaporation rates, and fracture advance rates as evidence, we suggest that an advective-diffusive system is responsible for the rough scaling behavior of columnar joints. This theory explains the order of magnitude difference in scales between jointing in lavas and in starches. We investigated the scaling of average columnar cross-sectional areas due to the evaporation rate, the analog of the cooling rate of igneous columnar joints. We measured column areas in experiments where the evaporation rate depended on lamp height and time, in experiments where the evaporation rate was fixed using feedback methods, and in experiments where gelatin was added to vary the rheology of the starch. Our results suggest that the column area at a particular depth is related to both the current conditions, and hysteretically to the geometry of the pattern at previous depths. We argue that there exists a range of stable column scales allowed for any particular evaporation rate.

Figure 1

(Color online) Columnar jointing in (a) basalt of the Columbia Plateau near Banks Lake ($95\mathrm{cm}$ average diameter), and (b) in desiccated corn starch.

Figure 2

(Color online) The total mass of the drying sample, vs drying time. (a) shows an uncontrolled desiccation, with the evaporation rate (b). (c) shows a feedback controlled run in which the final drying rate in (d) is made constant. The three stage feedback controlled desiccation shown in (e) and (f) was designed to initiate and develop the columnar jointing in a controllable way. Arrows point out the kink in the curves that occurs when the sample ceases to dry homogeneously. In (c)–(f) the dotted lines and boxes indicate controlled parameters.

Figure 3

Propagation of the fracture front into (a) uncontrolled, and (b) controlled starch desiccation experiments, with power law fits. Errors $(\pm 1\mathrm{mm})$ are approximately the size of the data points.

Figure 4

Fractional moisture content of a partially dried starch colonnade. The dashed line indicates the depth of columnar fracture.

Figure 5

Average areas of corn starch columns under uncontrolled drying conditions, vs depth. The gray diamonds show the scales reached at the base of 17 identical slurries dried under the same, relatively slow conditions, but with different initial thicknesses. Micro-CT x-ray observations on a $25\mathrm{mm}$ deep, more quickly dried slurry (open circles) show a nonzero average column area near the drying surface. The filled circles show measurements from the destructive sampling of a thick, rapidly dried slurry that exhibits a sudden jump in an average column area.

Figure 6

Average column areas at the base of the colonnade for $13\mathrm{mm}$ (open circles) and $6.5\mathrm{mm}$ (filled circles) deep samples. The incident power records photometer readings as the heat lamp height was varied. The line represents an inverse relationship between drying power and cross-sectional area.

Figure 7

Average cross-sectional area at the base of five $17\mathrm{mm}$ deep samples, dried slowly with a heat lamp $75\mathrm{cm}$ above. Gelatin concentrations are given relative to the initial mass of the slurry.

Figure 8

Average cross-sectional area of columns, measured through destructive sampling, for single-controlled experiments with a fixed final desiccation rate $Q$. The initial duty cycle of the desiccating lamps on the $0.7\mathrm{g}∕\mathrm{h}$ sample is half that of the other samples. Representative errors are shown on the $0.7\mathrm{g}∕\mathrm{h}$ data.

Figure 9

Average cross-sectional area of columns for two slurries under fully controlled desiccation rates, measured through destructive sampling. The filled circles have $Q_1=6\mathrm{g}∕\mathrm{h}$, $Q_2=1\mathrm{g}∕\mathrm{h}$, and $\dot{Q}=0.5$. The open triangles are identical but use $Q_1=9\mathrm{g}∕\mathrm{h}$. Representative errors are shown on one data set.

Figure 10

Dependence of the average cross-sectional area of columns for experiments with $Q_1=6\mathrm{g}∕\mathrm{h}$ and $\dot{Q}=0.5$, with a varying final evaporation rate $Q_2$.

Figure 11

Area evolution for selected individual columns in uncontrolled coarsening (a) and (b) and controlled (c) experiments. Column merger events are marked by a dark arrow pointing to discontinuities in the area. In (c), a dashed arrow points to the creation of a new column, which grew from an adjacent vertex.