Have these 2 holes far in the back yard, the only holes I see anywhere at all. They are pretty big, maybe 3 inches in diameter. Any guesses on what did this.
In the photo the digging at the bright is the dog's work. Talking about the holes at the top.
We are a couple miles east of Atlanta.
Those look like a rodent of some kind, though they don't look like gopher holes. Usually, gophers block their holes and push dirt to the surface. On the other hand, sometimes they don't do that.
If they're gophers, they're the southeastern pocket gopher (named for the pockets on its cheeks).
We have LOTS of gophers here in California, and they can be a real problem to get rid of completely. The first thing I'd try is to light a safety flare, stuff it down the suspected gopher hole, and watch and wait. The burning flare will consume the oxygen in the tunnels and (you hope) asphyxiate the gopher(s) living there. You want to watch, especially if the tunnels are near a house or other structure, as the smoke may go in there, too. Also, if you notice smoke coming out of a hole, you'll want to block it with a rock or some dirt.
They sell "gopher gassers" but they don't have nearly the amount of combustible that a flare does; flares are a better deal.
Gophers usually pop up from their tunnels at around dawn or dusk. Cats and dogs will sometimes learn to wait and grab them, particularly if there's lots of them to practice on. (Most dogs eventually learn that digging is futile.)
If you're a bit sadistic, you can sit and wait till the vile little rodent pops up and bash it with something hard and heavy, or, even better, plug it with an air gun. (Pop-squeak! Mua ha ha ha.)
I'd avoid the poisons; if something other than a gopher eats them, they can die, too. Accidentally poisoned some birds 35 years ago, not fun.
Don't fiddle around with "vibrators" or repellants. Death of the gopher solves that problem, though, be warned, if you're near an area that has a lot of them, you may have a continued problem. Also, if you have neighbors with gophers and they don't control them, you'll have trouble, too.
If all else fails, you can hire services that will come monthly and kill them.
Hope this helps, let us know what happens and if you have any further questions.