Evolution of polygonal crack patterns in mud when subjected to repeated wetting–drying cycles

Three-Dimensional Modeling of Polygonal Ridges in Salt Playas

“…Desiccation traction can cause the crack lines to change their orientation. These processes have been reported in experiments. ,, But the end of every wetting cycle sees the crack channel filled with water of equilibrium salinity c 0 . As water evaporates the advection-diffusion flow commences in the channel, the value of salinity increases in the top layers that facilitates supersaturation and finally crystallization.…”

“…The angles created at the junctions where two or more crack lines meet, evolve from 90 to 120° . The crack pattern and therefore the salt ridge pattern becomes Voronoi-like . The shifting salt ridges are taken as a transient that stabilizes to a steady state once the crack mosaic reaches maturation.…”

“…If the centroids of the polygons coincide with the seeds, then the Voronoi diagram is known as the Centroidal Voronoi diagram. Many Voronoi-like patterns exist in nature and are often found to be associated with the optimization of material or energy. − Images of salt ridges tessellating salt playas visually appear to resemble Voronoi mosaics Figure d. The Voronoi-ness of a real mosaic can be measured by comparing it with the Voronoi diagram generated using the centroids of the polygons as seeds .…”

“…Many Voronoi-like patterns exist in nature and are often found to be associated with the optimization of material or energy. − Images of salt ridges tessellating salt playas visually appear to resemble Voronoi mosaics Figure d. The Voronoi-ness of a real mosaic can be measured by comparing it with the Voronoi diagram generated using the centroids of the polygons as seeds . The Hausdorff metric is used to measure the deviation of the simulated salt ridge patterns from the corresponding Voronoi diagram generated from the centroids.…”

“…The random points represent points of surface inhomogeneity that act as crack seeds. With desiccation, the lower layers of clay develop stress due to evaporation of water from the interstitial pores and the cracks extend vertically downward with every drying step . These vertically extended cracks act as conduits that eventually connect with the subsurface water table.…”