  We compute the sandpile groups of families of planar graphs having a common
weak dual by evaluating the indeterminates of the critical ideals of the weak
dual at the lengths of the cycles bounding the interior faces. This method
allow us to determine the algebraic structure of the sandpile groups of
outerplanar graphs, and can be used to compute the sandpile groups of many
other planar graph families. Finally, we compute the identity element for the
sandpile groups of the dual graphs of many outerplane graphs.
