How to stop dogs from destroying lawn?

Last summer, we paid to have aluminum fence installation completed for our three dogs' safety. We fenced off an area of our backyard for them so they could run and play safely. They love it but they've dug holes and ran most of it down to mud.

I am going to plant grass seed next month, but is there a way to keep it grass? I don't want them destroying the lawn again. I'm not sure how to maintain the lawn and prevent the dogs from destroying it again. How do you stop a dog from digging holes?