  The tenfold classification of topological phases enumerates all strong
topological phases for both clean and disordered systems. These strong
topological phases are connected to the existence of robust edge states.
However, in addition to the strong topological phases in the tenfold
classification, there exist weak topological phases whose properties under
disorder are less well understood. It is unknown if the weak topological
indices can be generalized for arbitrary disorder, and the physical signatures
of these indices is not known. In this paper, we study disordered models of the
two dimensional weak AIII insulator. We demonstrate that the weak invariants
can be defined at arbitrary disorder, and that these invariants are connected
to the presence or absence of bound charge at dislocation sites.
