Abstract
Fractal dimension fd, was used as one of the parameters to describe dessicationcracking pattern of a remolded Black Cotton soil (Eutric Vertisol). The fractal dimension computed from filtered, thinned and skeletonized binary images of soil cracks using the Fractal3 software provided an insight into temporal variability of fd as well as its relationship with the Crack Intensity Factor (CIF) and Soil Moisture Content (SMC). The results showed that even for single crack, the fd prior to filtering and thinning were higher than after. Cracking patterns were observedfroma chosen soil sample during dessication and the corresponding relationship between fd and CIF compared and monitored. As the critical SMC decreased during drying (45% to 27%), the CIF soil increased (0.023% - 5.75%), so did the fd (1.233 to 1.7193). The fd showed a positive linear correlation with CIF at r2 = 0.247 (P fd with SMC was best described using a polynomial function at r2 = 0.969 (P fd was sensitive to dessication cracking and therefore on SMC changes. Visual observation of dessication cracking showed that CIF increased and attained stability after day 4 while the computed and logarithmic transformed crack area attained stability between days 7 to 10 gradually decreasing to values below 2%. The estimated crack Cover or Brightness of the digitized binary images also gave better approximation of the CIF though this was slightly higher. Our results showed that dessication cracking of the Eutric Vertisol was independent of antecedent critical SMC and was time-constrained. Further soil cracking therefore stopped once maximum CIF was attained and only widening and deepening of pre-existing cracks continued.
Highlights
Dessication cracking may be perceived as a two-fold process that entails the gradual loss of moisture from an initially saturated porous body, in this case a soil and after surpassing a threshold tensile strength, culminates into germination, propagation and widening of cracks with subsequent reduction in soil volume. [1] [2] describe this as a three-stage process: initial, primary and steady states
The results indicated that the MVP and so the f(W) as well as the fd increased with dessication time to day 8 - 10 especially within the primary cracks, whereas this was between day 28 - 30 in the secondary cracks
The cracks that developed during dessication of a remolded Eutric Vertisol clearly showed fractal properties between 2 ≥ fd ≥ 1 During the initial and the subsequent stages, the crack length and number increased and showed that, the fd was not a constant but rather a spatio-temporal variable characterizing a type of cracking behavior that was conditioned by soil water loss during drying
Summary
Dessication cracking may be perceived as a two-fold process that entails the gradual loss of moisture from an initially saturated porous body, in this case a soil and after surpassing a threshold tensile strength, culminates into germination, propagation and widening of cracks with subsequent reduction in soil volume. [1] [2] describe this as a three-stage process: initial, primary and steady states. Dessication cracking may be perceived as a two-fold process that entails the gradual loss of moisture from an initially saturated porous body, in this case a soil and after surpassing a threshold tensile strength, culminates into germination, propagation and widening of cracks with subsequent reduction in soil volume. The complexity of dessication cracking in soils can better be understood through the Fractal Dimension. This approach seeks to characterize complex patterns at the Representative Elementary Volume (REV) and quantifying them as ratios of change from the micro-to mega-scale. It is based on the premise that dessication cracks do not exhibit typically Euclidean or topological dimensions in space and so fractal indices may only be expressed as non-integer values. Cracks are more or less curvi-linear and would necessarily have a dimension greater than 1 and less than a 2-dimensional square and this is the in-between Hausdorff-Besicovitch dimension
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