  The existing estimation of the upper critical dimension of the Abelian
Sandpile Model is based on a qualitative consideration of avalanches as
self-avoiding branching processes. We find an exact representation of an
avalanche as a sequence of spanning sub-trees of two-component spanning trees.
Using equivalence between chemical paths on the spanning tree and loop-erased
random walks, we reduce the problem to determination of the fractal dimension
of spanning sub-trees. Then, the upper critical dimension $d_u=4$ follows from
Lawler's theorems for intersection probabilities of random walks and
loop-erased random walks.
