If you want to build him a potty area IMO the better option would be to use mulch or sand rather than something like AstroTurf. Here's a site that explains how to go about it --
LinkAn easier option may be to do as PapPappy suggests.
I have to ask -- are you leaving him outside alone for periods of time? Because it seems rather unusual to me that a small dog could do significant damage just from the amount of pawing/digging they typically exhibit after doing their business. For most dogs that's more of a quick wiping of the feet than actual digging. OTOH it's very common for dogs to dig from boredom/stress if left outside alone.