Nothing will effectively stand up to that kind of traffic and use - even stepable type, low-growing groundcovers will rapidly be churned into mud, given nearly constant use and weather. Taller growing, more woody material will stand up better but is far less suited to this type of use. Dog parks here (and there are a lot of them) use a combination of wood chips, asphalt and turf grass, depending on the type of area and its use. Asphalt for primary access paths, wood chips for most of the rest and lawn for some more natural play areas. FWIW, the lawn areas are periodically closed off for rehabilitation on a cyclical schedule at least once a season.

Why are wood chips not desirable? Easy and cheap to replenish and easy to clean up. Also tends to neutralize odors as well.

I am also looking for a hardy ground cover for our garden. Doesnt need to be totally rough and rugged, as our dog is fairly light on his feet, and does most of his heavy duty outdoor play in the park. We have a small area to cover, and get full sun for most of the day in the spring and summer, and very little sun in the winter.....

We use wood chips in ours at work and it is a smelly mess in the summer. The urine stays in the chips. We are also looking for an alternative covering.

Try stepables.com for hardy ground covers. Nancy