• • Particle size distributions of the sand used as the substrates in the experiments. To prepare the experimental sample, 1 kg of sand was placed, spread out and flattened in the glass plate, and then slowly saturated with water so as not to disturb the layer. Clay slurry was then prepared by mixing kaolinite clay with water in a 1:1.35 ratio adding enough water to ensure a homogeneous slurry. The slurry was then poured from a corner of the plate, which wholly covered the sand layer. The kaolinite-water mixture can be classified as a suspension due to the relatively large particle size (>1 µm) of the clay, and one day was sufficient for full sedimentation, ultimately forming three distinct layers between the water, clay, and sand.

In earth science, erosion is the action of surface processes that removes soil, rock, or dissolved material from one location on the Earth's crust, and then transport it away to another location. The particulate breakdown of rock or soil into clastic sediment is referred to as physical or mechanical erosion; this contrasts with.

This excess water layer, which rested on top of the sand and clay layers, was then decanted immediately prior to each experiment. During each experiment, the glass container was mounted on a digital balance, which recorded evaporative water losses at 5 min intervals. To ensure consistency across all samples, the start of experiments was set as the time when each sample contained 650 g of water, determined from measuring the weight of the fully desiccated clay layer at the end of each experiment. Lil Wayne 3 Peat Instrumental Mp3 Download.

Evaporation rate is expressed in units of length/time by calculating the amount of evaporating mass/time, and then dividing it by the density of water and the surface area of the entire clay surface, as fluid evaporation can still occur from partially saturated zones of porous media [e.g., Shokri and Sahimi, ]. All the systems studied had a final clay thickness of 4 mm. Digital images of the samples were taken every 5 s with an automatic camera (140 µm/pixel resolution). These images were then segmented into binary images to delineate the morphology, connectivity, and scaling characteristics of the formed desiccation cracks. The following methodology was used for image segmentation: all images taken were compared to a reference image taken at the beginning of the experiment, and any pixels that exhibited a change in gray value above a threshold were designated as “crack” pixels. Due to inherent limitations in the camera, image quality was sharper in some and not others, causing a number of crack pixels (less than 2%) to appear and disappear in each image. While this difference between images is insignificant for crack width analysis, in order to ensure accurate topological and morphological analysis, a second set of images was generated, where the originally segmented image I n −1 was superimposed onto the following segmented image I n in order to preserve all cracks that could be seen in the n − 1 images prior to I n, so that each new image J n = ∑ i = 1 n I i.

This procedure generated accurately connected crack network images. In order to analyze the underlying structure and connectivity of the crack network, the segmented images were processed using a standard skeletonization algorithm in MATLAB.

A comparison of the original image recorded by the camera with a corresponding segmented and skeletonized image is shown in Figure. • • The segmentation and skeletonization process for our cracking analysis. The images on the right are the original image recorded by the camera, segmented black and white, and skeletonized image, from top to bottom. Crack dynamics was characterized with the following: (i) velocity of the initial crack tip, (ii) minimum distance from the saturation front (see section ) to initial crack tip, (iii) crack angle, determined by measuring the angle between the projection of the crack tip and the tangent of the saturation front, and (iv) cracking duration, defined as the length of time during which all cracks with velocities over 10% of maximum velocity have formed.

Crack morphology was characterized with the following: (i) crack width, which was calculated for each pixel in the skeletonized image and calculated by doubling the minimum length from the skeletonized pixel to the edge of the crack in the segmented image, (ii) crack length density, defined as the fraction of pixels covering the clay surface in the skeletonized image, and (iii) crack length, defined as L / N with L being the length of the image (217 mm), and N being the crack ped number, defined as the total number of clay regions made topologically distinct by cracks. All the above computations were done using standard algorithms in MATLAB. One artifact was the occurrence of two drying fronts observed at the beginning and end of our experiments, which was unexpected due to the fact that the digital balance was ensured to be level; this phenomenon may be due to slight heterogeneities in the chamber and that our samples happened to be particularly sensitive to them. However, aside from the individual propagation of the initial cracks, it appeared to have no detrimental consequences in our investigation, and so no effort was made to mitigate or remove it. 3 Results and Discussion 3.1 Crack Dynamics After decantation of the ponding water from the packed glass container, a thin film of water was left on the solidified clay surface, which dried out as the evaporation process proceeded. This film of water receded horizontally in a single direction, hereafter referred to as the saturation front. The first cracks in the clay formed on the exposed clay surface at a given distance from the saturation front (210–270 mm).

These cracks—which we label as primary cracks—share some general characteristics. In one sample (0.2 mm), no saturation front was formed, and cracks initiated and propagated in all directions. A visual and dynamic schematic of the process is shown in Figure, showing time-lapse images of the two samples with manually overlaid lines.

The first primary cracks accelerate toward the edge of the saturation front at a rate much higher than that of the front's recession, and later-forming cracks propagate even faster than the first, reaching the same location as the first-formed cracks. Once these cracks are in proximity of the saturation front, they decelerate and maintain a stable distance from the crack tip to the saturation front.

Though the stabilized distance varied with each sample, this phenomenon appeared consistent with all the cracks within each configuration. • • Dynamics of crack development from two desiccating clay samples, where Figure a corresponds to the sample packed with a sand substrate with an average particle size of 2.9 mm and Figure b is the reference sample (pure clay). The cracks and saturation fronts colored by red correspond to the conditions after 2 h, 40 min from the onset of the experiment, indicated by t min. Blue and green indicate the positions of the saturation fronts and cracks after 5 and 10 min, respectively. 3.1.1 Crack Velocity Crack velocities in all samples show an initial spike as the tip approaches the boundary of the saturation front (Figure a), with the minimum distance showing a respective drop (Figure b). Both crack tip velocity and minimum distance appear to stabilize with time, with cracking velocities exponentially decreasing as its minimum distance from the front decreases (Figure a, inset). There appear to be no trends in crack velocity with increasing substrate particle size.

• • (a) Velocity profiles of the first primary crack and (b) the minimum distance from the crack to the edge of the saturation front. The substrates with average particle sizes of 0.2 and 0.6 mm were omitted due to lack of a saturation front and the crack formation along the plate boundary, respectively.

The inset shows crack velocity as a function of minimum distance to the saturation front. An anomalous, but solitary, spike in velocity is observed in the 2.9 mm sample after a period of little to no crack tip movement. This is likely due to heterogeneities in strength of the clay material, which temporarily halted the propagation of the crack. The eventual release of built-up stress caused a transient spike in acceleration, returning the crack tip to the position it would have been at had it not been stopped; the minimum distance before and after the halted crack follow a similar trajectory. 3.1.2 Crack Angle Due to the 2-D nature of the experimental system, the saturation front did not recede along a single direction, and the first cracks that formed did not always initially form directly facing the front. In the cases where the cracks formed in an orientation that is not perpendicular to the front, the crack tips rapidly realigned themselves with respect to the front within the first 5 min, where the fastest velocities also occurred.

In all cases, crack angles approach an angle range between 70 and 100°, with a mean of 83° across all samples (Figure ). Once aligned, the cracks approached the front at a velocity roughly proportional to its distance from the receding saturation front. We can then analyze the latter portion of cracking behavior as a localized directional propagation, and the saturation front as a directional instability, in this case caused by a moisture gradient.

Similar results have been reported previously in an experiment reported in Pauchard et al. [], where the crack slowed down to a nonzero velocity near the drying front and maintained a constant distance, and in theoretical work [ Jagla, ], where the stabilization of the crack tip front from the drying front was explained as a function of the stress field induced by drying. The saturation front in our experiments thus can serve as an indicator of the stress isolines in the vicinity of the saturation front. The cracks that form would follow a path that is perpendicular to such lines. • • Dynamic profile of angle value between the primary crack tip and the tangent of the saturation front nearest the tip.

As the clay surface is exposed, a pressure gradient forms due to the formation of a liquid-vapor meniscus, which enters the drying surface (the chemically induced forces which may contribute to shrinkage, like osmotic pressure, are likely insignificant due to the pure water we used in these experiments). These capillary forces contribute to the shrinkage, and thus cracking of the exposed clay [ Scherer, ]. Other experiments [ Peron et al.,; Tang et al., ] indicated that the degree of saturation was about 0.93–0.98 at the time of clay cracking, which suggests that our cracks form in desaturated clay zones.

Thus, the saturation front serves as the limiting position at which crack velocities approach zero, and where the underlying clay surface is still wet and the generated stresses are at a minimum. 3.1.3 Cracking Duration The extent and duration of cracking behavior is shown to be closely related to different phases of evaporation behavior (Figure ). A period of nearly constant water evaporation is observed during the first 20 h of all experiments.

The saturation front recedes in the first 1–2 h of this period. During this period, the surface is partially wet, and liquid vaporization at the surface maintains the evaporation rate close to what would be observed if the surface were completely saturated [ Scherer,; Shokri et al.,; Shokri and Salvucci,; Shokri and Or, ]. Figure illustrates that the evaporation rate in the system studied here was independent of the substrate particle size and the cracking morphology.

• • Various stages of desiccation cracking in a sample packed with sand with an average particle size of 1 mm underlying a kaolinite clay layer. The images on the left correspond to the crack patterns at the times indicated on the drying curve measured during the desiccation experiment. Primary cracks began their propagation immediately after the recession of the saturation front, beginning and ending their propagation within the first 2 and 3 h of experiments, respectively. All primary cracks and a majority of smaller cracks that joined the primary cracks—henceforth referred to as secondary cracks—nucleated and completed their formation entirely within the first period of evaporation, with a minimum onset and maximum completion interval of 2.6 and 14 h, respectively (Figure a). • • (a) Evaporation rates during desiccation of eight samples used in the experiment, and the earliest crack propagation and latest cessation of major cracks observed in the experiments. (b) Individual cracking duration as a function of particle size of the underlying sand substrate in each sample.

The horizontal dashed line corresponds to the cracking duration of the reference sample. The first period of evaporation ends when a part of the evaporation surface becomes fully dry, with the fully dry area increasing over time and resulting in a decreasing vaporization plane area.

This fully dry region is visible as a bright white region in the top section and top half of Figures e and f, respectively. This phenomenon can be verified experimentally in our samples with the formation and propagation of a second drying front—which we label the desiccation front—which changes the color of the clay from a dark yellow to bright white immediately following the first period of evaporation in all samples. The fraction of the clay surface that is covered by the desiccation front at any given time t directly coincides with the ratio of the evaporation rate at time t and the constant rate of evaporation, with evaporation ceasing when the desiccation front fully recedes. All samples ceased evaporation after 45–50 h elapsed time of experiments (Figure a). A downward trend in cracking duration was observed with increased substrate particle size (Figure b). The sand substrate, which has an increased roughness as particle size increases, will likely induce small variations in the thickness of the clay layer, and once the saturation front recedes and a sufficiently strong stress field was present on the clay surface, these variations in the clay thickness may serve as an aid to new crack nucleation points. Experimental and theoretical studies [ Groisman and Kaplan,; Colina and Roux,; Kitsunezaki, ] have shown that the cracking extent is proportional to the material thickness, with thinner layers experiencing a larger degree of cracking.

Greenville Ms Drivers License Office on this page. The thinner regions created by a rougher substrate will more likely reach a critical stress level for initiating fractures, thus allowing the configurations with rougher substrates and larger particle size to generate a majority of their cracks faster. The absence of clear proportionality between the cracking duration and particle size may be due to the stochastic nature of the roughness on the particle scale.

3.2 Crack Morphology A visual schematic of the segmented clay configurations as related to mean substrate particle size is shown in Figure. A lower extent of cracking can be observed with increased particle size.

The reference sample has the lowest cracking extent. • • Typical crack networks on the surface of overlying clay layer, obtained at the end of the desiccation experiments, as influenced by the mean particle size of the substrate. 3.2.1 Crack Width Distribution Figure shows various parameters of the crack width distribution with increasing substrate particle size.

The smaller substrate particle size samples all have a small range of crack widths, shown their low standard deviations, while the larger substrate particle size samples have a much wider range of crack widths, as well as a higher maximum crack width. All parameters have an upward trend with increased substrate particle size, though the larger particle size samples show an increased degree of variability between samples, suggested by the increased standard deviation. • • (a) Crack width mean and crack width standard deviation at the end of desiccation experiments and (b) maximum crack width as a function of mean substrate particle size. The horizontal dashed lines correspond to the reference sample. 3.2.2 Crack Length and Density A linearly decreasing trend in crack length density and ped number, and an upward trend in crack length, is observed with increasing particle size (Figure ). The reference values have extreme values in each case, having the highest crack length and the lowest crack length density and ped number.

• • (a) Crack length density on the desiccating clay surface and (b) crack length at the end of the desiccation experiments as a function of the sand substrate mean particle size. Right inset shows the number of peds as a function of particle size.

Dashed lines correspond to the values for the reference sample. One of the primary assumptions made in our experiments is that the sand layer acts as a frictional substrate that partially inhibits desiccation-induced shrinkage, with its extent decreasing with increased particle size. Akiba [] reported an increase in the adhesive force and the coefficient of friction with decreasing grain size when moisture was present, and additionally reported the opposite tendency under dry conditions.

Rowe [] performed a modified shear box experiment in which a discrete mass of quartz particles with varying size was slid across a solid block of the same material, with both particles and block being immersed in water. The angle of repose (i.e., friction) was shown to decrease with increased particle size. In our experiments, we assume that the frictional substrate interface is immersed in water, or at the very least, in satisfactorily wet conditions, at the onset of cracking. Thus, the decreasing particle sizes result in a higher friction coefficient and stress in the material. Furthermore, our experimental results are consistent with the physical models of cracking that predict increased crack density and cracking width variability, as well as crack duration, with increased coefficient of friction [ Vogel et al.,; Sadhukhan et al., ].

3.3 Scanning Electron Microscopy An important difference between desiccation cracks in our samples and cracks in composite materials, such as cracks that are developed in composite solids, is that unlike bulk composites, our desiccation cracks are all at the macroscopic scale. To demonstrate this, we used scanning electron microscopy to image the surface of the cracked clay at different length scales, down to a few hundred nanometers. The results are shown in Figure, where an area on the original clay surface (Figure a) was enlarged with magnification factors of 150, 1500, 5000, 10,000, and 20,000. Even at the nanometer scale (shown in Figure f), we do not see evidence of cracking. This is in contrast to bulk composite materials, which typically develop [ Sahimi, 2003] one (or very few) large macroscopic crack as well as side branches at all length scales. • • Fractal dimensions of the crack networks at the end of the desiccation experiments as a function of the average particle size of the substrates.

The bottom inset shows typical results for estimating the fractal dimension of the crack pattern on the surface of the clay overlying a sand substrate with an average particle size of 1 mm. The top inset is the image of the cracks pattern, whose fractal dimension is computed in the bottom inset. 3.4 Fractal and Scaling Characteristics The final crack morphologies developed on the clay surface exhibit a hierarchical network structure that is suggestive of fractal properties.

While macropore networks like the one observed here cannot be considered truly self-similar fractal systems, and only fractal at a statistical level [e.g., Tyler and Wheatcraft, ], which is also demonstrated due to the lack of microscale cracks in our system, fractal scaling may possibly be observed at the macroscopic level. Thus, in order to quantify the possible fractal property, the fractal dimension D f of the crack patterns was calculated using the box counting method.

As explained by many [e.g., Sahimi,; Sahimi, ], in the box-counting method the fractal object is covered by boxes of side length r. The number N ( r) of such boxes required to cover the entire object is counted and plotted versus r. An example of the use of the methodology for calculating the fractal dimension, corresponding to the sample packed with the sand substrate with the average particle size of 1 mm overlying the clay layer, is presented in the inset of Figure.

The fractal dimension D f was estimated as the (negative) slope of the linear part of the plot on the log-log scale. The box sizes varied from eight pixels to the size of the image. The fractal dimensions of the final crack patterns in all samples were then calculated, with the results plotted in Figure. The errors in all cases were less than 1%. The fractal dimension is fairly constant, with a slight decreasing trend as the average particle size of the substrate increased.

Fractal dimensions of crack networks have been shown to be tied to the development of the crack area [ Velde, ]. This is consistent with our results, as the fraction of the crack area decreases with coarser substrates. The average D f of all the samples was 1.47, with maximum and minimum values of 1.32 and 1.58, where the minimum corresponds to the reference sample (pure clay).

This value is within the range of the fractal dimensions of fracture patterns in clay reported in the literature [ Colina and Roux,; Velde,; Preston et al.,; Mal et al., ]. One may also characterize the morphology of the desiccation cracks by computing the density correlation function of the crack area C ( r), defined by Clement et al. [] and Shokri and Sahimi [].

C ( r ) = 〈 ∑ i n 0 n i ( r ) N ( r ) 〉 0 (1) where n 0 = 1(0) if site 0 is cracked (uncracked), and similarly for n i ( r) if site i at a distance r is cracked (uncracked). Here N ( r) is the total number of cracked sites located at a distance r from a cracked site 0, and 〈. 〉 0 indicates an average over all the origins of cracking sites 0 for which all the points at a distance r remain within the field of view. For final pattern of the cracks influenced by the substrate's particle size distribution, C ( r) was calculated for one trial per each type of substrate.

The results are presented in Figure, illustrating two distinct regimes separated around a cross-over distance ξ (for a detailed discussion on the significance of the cross-over distance, see Sahimi [2003]). For length scales r ξ, the density correlation functions in all samples attain an asymptotic value C ∞.

A constant C ( r) corresponds to a uniform distribution of cracks, irrespective of the length scale, and represents the crack density at the surface of the clay. The inset of Figure presents the asymptotic values of C ∞ versus the measured crack length density, delineated by image analysis. The results are represented by a straight line at 45°, indicating the equality of C ∞ and the crack density at the surface. • • (a) The density correlation function C ( r) of the crack patterns in various samples. (b) This figure shows the asymptotic values C ∞ of C ( r) versus the crack density on the surface of each sample, determined by image analysis. The numbers in the legend indicate the mean particle sizes of the sand substrates. 4 Summary and Conclusions Virtually all soil systems will experience some degree of constrained shrinkage when drying.

The resulting cracks that may form, in addition to physicochemical shifts in the structural strength and stability of the shrinking material itself, are influenced by the mechanical boundary conditions imposed on the shrinking unit of soil, and the extent of friction between the adjacent units of soil is a significant factor. While these experiments are still idealized cases of a two-dimensional shrinking layer as affected by a homogeneous substrate layer, our work is a first step to investigating experimental observations indicating how the increased friction between shrinking and nonshrinking porous layers influence morphological features that are known to have a significant influence on preferential flow behavior. This study investigated the effect of particle size of granular materials (i.e., sand) on the dynamics and morphology of cracking behavior in overlying drying slurry (i.e., kaolinite clay). The initial cracks that are formed on the clay surface follow a water saturation gradient (directional cracking) and exhibit a generally consistent behavior that is characterized by an initial spike in the velocity of the propagating crack, followed by decay to a nonzero constant velocity. The duration of time required to develop the final crack network decreased with decreased frictional constraints, characterized by a larger substrate particle size.

The extent of cracking, characterized by cracking length and density, also decreased with increased substrate particle size, and a more variable and wider crack width distribution can be observed as well. The results indicated that the evaporation rates in our systems were independent of the substrate particle size and the cracking morphology.

Besides, details of the fractal and scaling characteristics of the final crack networks at the surface of the desiccating clay are influenced by the substrate's particle size distribution, with an average fractal dimension of 1.47 and a slightly decreasing trend with larger substrate particle sizes, due to the lesser extent of cracking. Density correlation functions of the surface crack patterns at the end of experiments indicate the existence of a crossover length scale from fractal to constant-density structures with the crack density correlation function approaching asymptotic values that are equal to the final density of the surface crack. Differences between desiccating cracks and the fracture pattern in bulk materials were demonstrated and emphasized. Acknowledgments We express our gratitude to Peng Zhou, a student at Ecole des Ponts, France who visited our laboratory and conducted the SEM imaging. We are grateful to Boston University Photonics Center where the SEM imaging was conducted. We would like to thank Jonathan D.

Woodruff and his graduate student Christine Brandon from University of Massachusetts, Amherst for enabling us to use their CAMSIZER Digital Image Processing Particle Size (from Horiba). Partial funding by the Undergraduate Research Opportunities Program (UROP) at Boston University is acknowledged. Ancillary Article Information.