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 consumption2.

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 example3,4,5,6,7,8. For sandcastles, the only estimate in the literature9, 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.

To account for the (in)stability of sandcastles, we show here that it is sufficient to consider that the limit of instability is reached when a column of sand undergoes a buckling transition under its own weight. An elastic rod becomes elastically unstable and buckles under its own weight when exceeding a critical height h crit 10. We present here the analytical solution for h crit for a cylindrical column:

where G is the elastic modulus, R the column radius, ρ is density, g the gravitational acceleration and J ≈ 1.8663 is the smallest positive root of the Bessel function of the first kind of order −1/311. A similar expression is used in civil engineering to calculate the stability of buildings12 and we therefore expect that this also gives the maximum height for which a sandcastle falls apart as the buckling instability will cause the sandcastle to fracture.