How Sandcastles Fall
Exxon Research and Engineering, Route 22 East, Annandale, N.J. 08801(February 1, 2008)Capillary forces signiﬁcantly aﬀect the stability of sandpiles. We analyze the stability of sandpileswith such forces, and ﬁnd that the critical angle is unchanged in the limit of an inﬁnitely largesystem; however, this angle is increased for ﬁnite-sized systems. The failure occurs in the bulk ofthe sandpile rather than at the surface. This is related to a standard result in soil mechanics. Theincrease in the critical angle is determined by the surface roughness of the particles, and exhibitsthree regimes as a function of the added-ﬂuid volume. Our theory is in qualitative agreement withthe recent experimental results of Hornbaker et al., although not with the interpretation they makeof these results.81.05.Rm, 68.45.Gd, 91.50.Jc