  A semiclassical formulation of the spin Hall effect for physical systems
satisfying Dirac-like equation is introduced. We demonstrated that the main
contribution to the spin Hall conductivity is given by the spin Chern number
whether the spin is conserved or not at the quantum level. We illustrated the
formulation within the Kane-Mele model of graphene in the absence and in the
presence of the Rashba spin-orbit coupling term.
