Modelling the evolution of columnar joints

Budkewitsch, P; Robin, Pierre-Yves F.

doi:10.1016/0377-0273(94)90092-2

Cited by 142 publications

(129 citation statements)

References 32 publications

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“…Similar considerations apply to the lava cooling case, with the poroelastic diffusivity D P replaced by the thermal diffusivity D T = k/ρC p . In the case of cooling lava, coarsening has been observed near the flow margin (23), whereas the nonequilibrium steady state is maintained far away from the flow margin by the heat transport due to the reflux of water in the cracks (24)(25)(26). In this regime, a very regular column scale is observed as in Fig.…”

Section: Scaling Theorymentioning

confidence: 89%

“…Striae are chisel-like marks (see Fig. 1E), which are left by the individual, sequential fracture advances of a growing crack as it intrudes into the slowly cooling lava (23,24,33). These features, which are also called joint increments (23), are related to the commonly seen striations characteristic of metal fatigue (33), and always form perpendicular to the direction of crack motion (33).…”

Section: Field Observations On Lavamentioning

confidence: 98%

“…1, reduces to a linear diffusion equation with a diffusivity D T = k/ρC p . Then, we transpose the result for drying starch to the case of cooling lava by reinterpreting D as the thermal diffusivity D T and J 0 as the heat flux that is strongly influenced by the continuous reflux of water in the cracks (24,25), although this effect does not significantly influence the water transport in the case of drying starch (21). Because the thermal diffusivity of basalt (25) is approximately D T = 6.5 × 10 −7 m 2 /s, and the fracture front velocities are comparable to those in the starch experiments, columnar jointing in lava should be 10-100 times larger than in starch.…”

Section: Dynamic Similarity Of Starch and Lava Columnsmentioning

confidence: 99%

“…1, which only occur in relatively thick layers, the similarity between crack patterns induced by drying (16)(17)(18)(19)(20)(21) and cooling (16,(22)(23)(24)(25) can be traced to the fact that the transport of water in a drying slurry and the extraction of heat from a hot solid are mathematically analogous (1)(2)(3). In a poroelastic medium, fluid flow is coupled to the elastic deformation of a porous solid, whereas in a thermoelastic medium, heat conduction is coupled to elastic deformation of a conducting solid; pressure in one case is analogous to temperature in the other.…”

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confidence: 99%

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Nonequilibrium scale selection mechanism for columnar jointing

Goehring

Mahadevan²,

Morris³

2009

Proc. Natl. Acad. Sci. U.S.A.

110

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Crack patterns in laboratory experiments on thick samples of drying cornstarch are geometrically similar to columnar joints in cooling lava found at geological sites such as the Giant's Causeway. We present measurements of the crack spacing from both laboratory and geological investigations of columnar jointing, and show how these data can be collapsed onto a single master scaling curve. This is due to the underlying mathematical similarity between theories for the cracking of solids induced by differential drying or by cooling. We use this theory to give a simple quantitative explanation of how these geometrically similar crack patterns arise from a single dynamical law rooted in the nonequilibrium nature of the phenomena. We also give scaling relations for the characteristic crack spacing in other limits consistent with our experiments and observations, and discuss the implications of our results for the control of crack patterns in thin and thick solid films.pattern formation | fracture | geomorphology | volcanology | faulting D rying solids lose moisture from their exposed surfaces and shrink as a consequence. Similarly, cooling solids lose heat from their exposed surfaces and shrink as a consequence. In either case, this differential shrinkage of one part of the solid relative to another leads to stresses that can eventually lead to cracking (1-3). Although much is known about the nucleation, growth, dynamics, and stability of a single crack in an elastic solid, most questions associated with the patterns of multiple cracks due to stresses that arise from nonequilibrium processes such as drying and cooling (4-7) remain wide open. The resulting polygonal planform patterns can arise in a variety of situations, from the mundane cracks in drying mud, to the deliberately artistic cracks in ceramics and pottery, to the spectacular columnar joint formations of the Giant's Causeway in Northern Ireland, Fingal's Cave on Staffa, in Scotland, and the Devil's Postpile in California. The latter formations have fascinated casual observers, artists, and scientists for centuries (8-10), but no comprehensive physical theory for their form or scale exists. Indeed, it is only in the past decade or so that careful laboratory experiments have started to address the dependence of any of these crack patterns on such quantities as the rate of drying or cooling, the thickness of the layers, and their mechanical properties (4-7, 11-13). For example, recent experiments show that crack formation and propagation in drying thin films leads to length scales and patterns that can be strongly timedependent; cracks in directionally drying films grow diffusively at short times, and can advance intermittently via stick-slip-like motion over longer times (11,12). The patterns formed by these cracks depend in detail on the spatiotemporal dynamics of drying, substrate adhesion, and thickness variations (4,6,13,14). This immediately suggests a nonequilibrium origin to these crack patterns, one that couples the heterogeneous elastic stresses in th...

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Section: Scaling Theorymentioning

confidence: 89%

Section: Field Observations On Lavamentioning

confidence: 98%

Section: Dynamic Similarity Of Starch and Lava Columnsmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Nonequilibrium scale selection mechanism for columnar jointing

Goehring

Mahadevan²,

Morris³

2009

Proc. Natl. Acad. Sci. U.S.A.

110

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“…The occurrence frequency of the polygon order N in columnar jointed rocks worldwide has been summarized in Ref. [50]. Attention should be paid to the fact that the hexagon is not necessarily preferred in columnar joint formation.…”

Section: B Predominance Of Pentagonal Cellsmentioning

confidence: 99%

Morphometric analysis of polygonal cracking patterns in desiccated starch slurries

et al. 2017

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We investigate the geometry of two-dimensional polygonal cracking that forms on the air-exposed surface of dried starch slurries. Two different kinds of starches, made from potato and corn, exhibited distinguished crack evolution, and there were contrasting effects of slurry thickness on the probability distribution of the polygonal cell area. The experimental findings are believed to result from the difference in the shape and size of starch grains, which strongly influence the capillary transport of water and tensile stress field that drives the polygonal cracking.

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Cooling fractures in impact melt deposits on the Moon and Mercury: Implications for cooling solely by thermal radiation

Xiao

Zeng

et al. 2014

J. Geophys. Res. Planets

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We study the distribution, morphology, and geometrical properties of fractures in several young impact melt deposits on the Moon and Mercury, and the ways that these fractures may form from cooling by thermal radiation. In each impact melt complex, the topography of the underlying terrain determines the orientation of cooling fractures, such that interior fractures that formed in the relatively thick interior areas of the melt unit are wider and have a larger spacing than marginal fractures that formed in the relatively thin areas near the unit's margins. Solid debris entrained in molten deposits provides prefracture flaws that can seed cooling fractures, but too much solid debris prevents cooling fractures from growing to macroscopic sizes. The appearance of subparallel fractures is mainly caused by subsidence of the deposits during the process of cooling and solidification. Tensile stresses caused by thermal radiation are large enough to initiate cooling fractures on both the Moon and Mercury, which may represent the initial stage of columnar joints formation, but the cooling rate caused solely by thermal radiation is not large enough to form well-organized columnar joints that feature polygonal colonnades. We therefore propose that thermal conduction and convection are the major contributors in the formation of columnar joints on planetary bodies.

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Modelling the evolution of columnar joints

Cited by 142 publications

References 32 publications

Nonequilibrium scale selection mechanism for columnar jointing

Nonequilibrium scale selection mechanism for columnar jointing

Morphometric analysis of polygonal cracking patterns in desiccated starch slurries

Cooling fractures in impact melt deposits on the Moon and Mercury: Implications for cooling solely by thermal radiation

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