It might be wise to reconsider your plan for turfgrass and think of shade tolerant groundcovers instead. Since southern lawns require a minimum of 5-6 hours of full sun daily, adding turf to this shady location would likely be a waste of money. Instead, select from Asiatic jasmine, bromeliads, cast-iron plants, English ivy, Algerian ivy, ferns and mondo grass. You also can add color from begonias, caladiums, eucharis lilies and impatiens. Save the turf for the sunny areas with much less tree root competition. If you decide to add a layer of topsoil, the limit is 1-2 inches over the surface roots of trees

Additional Resource

http://edis.ifas.ufl.edu/ep072