  In our main result, we establish that any conical sandpile monoid $M = SP(G)$
of a directed sandpile graph $G$ can be realised as the $\mathcal{V}$-monoid of
a weighted Leavitt path algebra $L_K(E,w)$, and consequently, the sandpile
group as the Grothendieck group $K_0(L_K(E,w))$. We show how to explicitly
construct $(E,w)$ from $G$. Additionally, we describe the conical sandpile
monoids which arise as the $\mathcal{V}$-monoid of a standard (i.e.,
unweighted) Leavitt path algebra.
