I recall from a couple of threads here on Hometalk that several people suggested artificial turf for preventing dog damage.
Here's one of those discussions:
Preventing abuse by the 4-footed friend is one of the toughest challenges a landscape faces. As @ suggested artificial turf is one of the few practical solutions, though not the least expensive. The other is to 'give over' part of your yard as an enclosed dog run. There are no sprays, or rocks or shrubs that will prevent a determined and bored canine from wreaking havoc on the yard.
Ages ago I had a Malamute and she dug holes...lot of holes my mom called it the "golf course"
Many dog "problems" have to do with them being bored...does your dog have a playmate?
allowing your dog to interact "socially" with other dogs in a natural environment is a good way to prevent some of these issues.
Pick up Temple Grandin's book "animals make us human" and lean about some of these tricks
What about putting in a water feature, fun for the dog and beautiful in your yard?
Our labs dig like yours. We tried many different ideas but none worked and finally let the dogs have their own hole. I started several hole behind shrubs in the yard and the dogs continued the digging. Now that is their space and the rest of the yard is safe.
One of our clients in Rochester NY wanted a Pondless Waterfalls out by the street to reduce noise. When I arrived, I asked if I could see the back yard and she said sure, if you don't mind dogs. She has a fenced in area made especially for them. I asked, instead of installing a Pondless Waterfall out by the street, why not install a Pond and a stream out by the deck and close to the house? You would get a lot more enjoyment? She liked the idea and we also installed some beautiful plantings that are protected from the deer. Here is a link to view the project: http://www.hometalk.com/726764/ecosystem-ponds-garden-ponds-fish-ponds-landscape-ponds-backyard-ponds-waterfall. We installed her pond and Landscape Design in Rochester NY in 2007 she recently gave us this review: http://www.houzz.com/viewReview/22422/Acorn-Landscaping-review. You can click here to learn more about Ecosystem Ponds or Backyard Ponds: https://www.facebook.com/notes/acorn-landscaping-landscape-designlightingbackyard-water-gardens/acorn-landscaping-designs-installs-aquascape-ecosystem-water-garden-fish-ponds-i/464917560212038.
You may be able to add some heavy fabric under the rocks. The underlayment (used under liner to protect it from objects pushing up from the ground) we use for waterfeatures is pretty tough & will allow water to pass through. It might frustrate the dog enough to have him/her find a new area to dig.
@Premium Aquascapes , I did lay some hog wire down on a landscape area before seeding with grass in an area where a dog insisted on digging, that did work pretty well as a deterrent, but the wire was a bit difficult to conceal. Might work with mulch or rock over it.