I can't talk from experience, but I'm going to do this for my dog in a year or two when I rebuild the deck. My new design plan has a spot for a doggie digging box.
I plan to dig a large hole, drop in a large plastic container (heavy duty plastic like a feed container or something). Nothing too big, 4 to 5 feet on a side. Then I plan to line the outside of it (on two sides as the other 2 sides will be against the deck) with large paving stones.
I plan to fill the thing with regular ole dirt. He'll be able to dig holes and what not, a lot of the dirt will be contained on the pavers so it can easily be pushed back in. I also plan to bury toys in it every time I refill it.
The reason for the container is that I don't want him burrowing under my deck, or out under the yard and causing problems.