That sounds more like deep bedding not deep litter (often confused). You don't want DE in deep litter. Also, the lower layers need moisture for composting to occur. The key is making sure that waste and moisture stay down near the bottom by flipping the top and keeping it nice and deep, and not disturbing the deep layers. Keeping it too dry or turning it all over lets the poop dry out, which is great as far as smell goes, but it will not decompose and you will just keep building up poop. That is deep bedding.
I add leaves, lawn clippings, pine needles, dirt, weeds, etc to my deep litter. Keep adding organic stuff with low nitrogen to balance out the poo and you are good to go.
Some people do really like sand. To me, it seems like it would be too cold in winter if you live anywhere cold (like Maine).