How to construct the perfect sandcastle

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How to construct the perfect sandcastle


02 August 2012

Read More: http://www.nature.com/srep/2012/1208...srep00549.html

Just a bit of water enables one to turn a pile of dry sand into a spectacular sandcastle. Too much water however will destabilize the material, as is seen in landslides. Here we investigated the stability of wet sand columns to account for the maximum height of sandcastles. We find that the columns become unstable to elastic buckling under their own weight. This allows to account for the maximum height of the sand column; it is found to increase as the 2/3 power of the base radius of the column. Measuring the elastic modulus of the wet sand, we find that the optimum strength is achieved at a very low liquid volume fraction of about 1%. Knowing the modulus we can quantitatively account for the measured sandcastle heights.

The formation of capillary bridges between sand grains are the cause of the stiffness of sculptured wet sand in a sandcastle, as opposed to dry sand which can hardly or not support its own weight1. Qualitatively, the liquid leads to the formation of capillary bridges between the sand grains, and the curvature of the liquid interface leads to a capillary pressure causing a force of attraction between the grains. This then creates a network of grains connected by pendular bridges, and allows, for example, creating complex structures such as sandcastles. Not many quantitative studies on the mechanical properties of wet sand exist, in spite of the fact that the handling and flow of granular materials is responsible for roughly 10% of the world energy consumption.

Since in many cases the humidity in the air is sufficient for liquid bridges to form between sand grains, one would expect the mechanical behavior to be well known. This is not the case, in spite of the fact that the stability of wet granular packings is of paramount importance for civil engineering purposes and that the adhesive forces due to the presence of liquid bridges are also extremely important in geophysical applications (i.e., soil stability), of which sandcastles are merely an unusual. For sandcastles, the only estimate in the literature, argues that the stability is related to the capillary rise in the granular medium, and arrives at a maximum sandcastle height of roughly 20 cm. This is in stark disagreement with the observation of sandcastles of several meters high, and the common observation that the stability depends on the base radius of the sand structure.

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Experimental data points and theoretical prediction of the maximum height of sandcastle as a function of its radius.






The elastic shear modulus vs. volume fraction of water (circles: experimental measurements, dashed line: theoretical prediction for the optimal strength from Eq. 3).






An underwater sandcastle.