Summary: Our aim is to introduce and study a new partial integrodifferential equation (PIDE) associated with the dynamics of some physical granular structure with arbitrary component sizes, like a sandpile or sea dyke. Our PIDE is closely related to the nonlocal evolution problem introduced in [F. Andreu et al., Calc. Var. Partial Differ. Equ. 35, No. 3, 279–316 (2009; Zbl 1173.35022)] by studying the limit, as \(p\to\infty\), of the nonlocal \(p\)-Laplacian equation. We also show the connection between our PIDE and the stochastic model introduced by L. C. Evans and F. Rezakhanlou [Commun. Math. Phys. 197, No. 2, 325–345 (1998; Zbl 0924.60099)] for modeling the sandpile problem.