You are already recieving conflicting answers. This is NOT a good forum to ask this question. Most of the people here do not own Great Pyrenees, and do not understand how these dogs think and act differently than most.
Great Pyrenees are FANTASTIC diggers (actually well known for this trait). You may need to bury fencing several feet down (expensive) to stop this boy. You could also try an electric wire about 6 inches off the ground, to see if that keeps him away.
Those are a pain to keep free of brush, so the electric does not short out, and your Pyr may be smart enough to just move farther back and tunnel longer. Who did you adopt this rescue Pyr from? Was it a Pyr rescue group?
They should be able to recommend an obedience trainer you can go to with this dog. This Pyr needs obedience training in the worst way. Unfortunately, it is EXTREMELY difficult to find an obedience trainer who can actually handle Pyrenees and understands how they work mentally.
They simply ARE different from other breeds. Pyrenees THINK and ACT for themselves. They do NOT wait for input or approval from a human.
Until this Pyr thinks of you as not only a member of his pack, but the leader of his pack, he's not going to become trustworthy. Do you have prior dog experience? Are you afraid of dogs?
This dog may not be the one for you. However if you are willing to put in the time and money this Pyr is going to need you will have a loyal companion for life. Neutering him was the first step, and a very good thing.
The hormones should be starting to calm down in his body about now (it takes a couple of months for adults to start to loose the testosterone). PLEASE, join this Yahoo group. It's completely free, and there are WONDERFUL people on there who own Pyrenees and even some who own rescue Pyrenees.
Decades of experience with this group, and endless knowledge for you to call upon. They are friendly people, always willing to help you out. Here's the link: http://pets.groups.yahoo.com/group/PyrTa... Garnet Permaculture homesteading/farming over 20 years Owner of three working Great Pyrenees (they guard the goat herd 24/7).
You need to do what his previous owners failed to do: GET HIM IN A TRAINING CLASS NOW. This is NOT normal gp behavior. They are defenders, not attackers.
Digging is completely uncharacteristic and is probably a result of improper keeping in his former home--most likely he was left in a small backyard all day and was expected to be a good dog by some miracle of God. When that didn't happen, the owner probably got frustrated--most likely for the same behavior he is exhibiting now--and dumped him at a shelter, failing to realize their circumstance was their own fault, not the dog's. Unless you have experience with training aggressive dogs, don't try to do this on your own.
(I'm assuming you don't have experience or you wouldn't be asking this question. :P) Get a certified dog trainer who has had experience socializing dogs like your's. You should probably look into an electric fence as well.
I'm always the last person to suggest any kind of shock collar, but I believe in this instance, COUPLED WITH PROFESSIONAL TRAINING, it seems appropriate. You should talk to your trainer about this first. I highly suggest browsing dogtime.com for info on various aspects of dog keeping.
Even if you've had dogs before, this is still an excellent resource. Start with the articles on training and the great Pyrenees breed, and go from there. There are also tons of forums out there for breed specific dogs as well as for shelter dogs.
You could probably get some good advice from people there as well. Good luck. :).
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