  We study the abelian sandpile growth model, where n particles are added at
the origin on a stable background configuration in Z^d. Any site with at least
2d particles then topples by sending one particle to each neighbor. We find
that with constant background height h <= 2d-2, the diameter of the set of
sites that topple has order n^{1/d}. This was previously known only for h<d.
Our proof uses a strong form of the least action principle for sandpiles, and a
novel method of background modification.
  We can extend this diameter bound to certain backgrounds in which an
arbitrarily high fraction of sites have height 2d-1. On the other hand, we show
that if the background height 2d-2 is augmented by 1 at an arbitrarily small
fraction of sites chosen independently at random, then adding finitely many
particles creates an explosion (a sandpile that never stabilizes).
