If your nails are splitting in layers, it sounds more like they aren't healthy to start with. Talk with your doctor. Maybe you aren't getting enough calcium? Please don't start taking calcium without talking to a doctor because most people need less as they age. You could be deficient in other nutrients, as well.
They sell nail strengtheners that you apply like a clear nail polish that help. They are found at most drugstores with the nail polish.
In the meantime, slather them with lotion every time you walk by a bottle. It can't hurt.