  We study the effect of strong disorder in a 3-dimensional topological
insulators with time-reversal symmetry and broken inversion symmetry. Firstly,
using level statistics analysis, we demonstrate the persistence of delocalized
bulk states even at large disorder. The delocalized spectrum is seen to display
the levitation and pair annihilation effect, indicating that the delocalized
states continue to carry the Z2 invariant after the onset of disorder.
Secondly, the Z2 invariant is computed via twisted boundary conditions using an
efficient numerical algorithm. We demonstrate that the Z2 invariant remains
quantized and non-fluctuating even after the spectral gap becomes filled with
dense localized states. In fact, our results indicate that the Z2 invariant
remains quantized until the mobility gap closes or until the Fermi level
touches the mobility edges. Based on such data, we compute the phase diagram of
the Bi2Se3 topological material as function of disorder strength and position
of the Fermi level.
