That sounds like a groundhog or a skunk. If you not smelling the tell-tale ammoniated smell of a skunk and seeing the holes left in your yard from them digging grubs, then I'd think it was a groundhog and not a skunks. Once you've gotten rid of the offender (small-caliber rifle works well for groundhogs), I think I'd try they skirting idea I've heard people mention on here. Lay a horizontal course of welded wire fence on the ground 2-3 feet out and cover it with rocks and dirt. Most animals, they say, will not back up to begin their digging. There is a lot of information on here about it, look up skirts or aprons.
If it's a groundhog, the easy way to get rid of it is to shoot it. I do know of folks who've lived trapped them, but, believe or not, they can be quite nasty in a cage. I also know people who live trap skunks and they tell me so long as the can't lift their tail in the cage they can't spray. I really don't want to try it though.