From reading the novels, the impression is that Dune is like a vast ocean of sand, with the sandworms akin to gigantic sea-monsters, only in sand. I can't remember any specific mention of how deep the sands are, though. They'd certainly need to be quite deep to accommodate some of the very big worms, and it is said that the sandtrout can go deeper still.
Here on Earth, although desert depth is hard to measure, it is said that the Sahara is up to 40m deep, although deserts far into geologic history can have depths of several hundred meters. Then again, the sandworms aren't exactly physically plausible, so speculation based on the real world will only go so far.
How deep are the sands on Arrakis? Is there any direct or indirect reference in the books, or any notes?