I've dealt with groundhogs/woodchucks for years, and the only thing that worked for me was to remove them from the property like the previous poster stated, then I made sure where they were living was covered with chicken wire, so no new ones could move back in.
They usually eat within a short distance of where they are living, so I'd suggest figuring out where that is, then set up a live trap in front of the hole they have dug. Generally they are living under a shed, garage, porch, deck, something like that where they can dig under it pretty easily.
Once you are sure that you've caught them all, staple chicken wire to the base of each outbuilding on your property, lift the sod in front of it, about a foot, then lay the chicken wire under the sod. This will prevent them from digging close to the building.
I have never found peppers or repellants to work, and you have to be careful what you use around food crops.
Fencing your garden would work, if you can prevent them from digging under the fence. Good luck!
Okay, as a vetern of many groundhog invasions I can offer some advice. However, I am sorry to say that the best way to stop a gourndhog is to remopve it from your property, either humanely or not. These animals do not share or stop feeding.
That said, here are some tips that work for awhile at least;
1. Fence the garden, dig down about a foot to bury the fence to discourage the citter. You may also consider electric fence, a string about 2 inches above the ground gives a shock to the nose that won't wound, but still trains them to stay away.
2. Black pepper, ground up and sprinkled liberally. The smell can make some animals sneeze which they dislike. Red pepper flakes work for more persistent animals, but this must be reapplied after rain.
3. Have your dog or a friend's dog wander round the garden at least once a week. The smell of a predator will often discourage the groundhog.
These are techniques that I've used successfully in the past, sadly though some groundhogs will go to great lengths to eat your garden.
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