Answer: Dogs are pretty hard on any turf or groundcovers. In order for the lawn to recover, you will need to fence off the damaged areas for a while to keep traffic off. The only other alternative is to use a pet-friendly artificial turf in the area. There are many types to choose from and some have an amazingly natural look. For options, do a web search on synthetic turf. (Or try http://www.sprinturfsp.com/products.php)
Best wishes with your dog-friendly yard!
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