Well, a DIGGING DOG ESCAPE ARTIST probably means he's an UNSUPERVISED Dog. Straight up.
There have been very helpful suggestions here already, so I've not much to add except this concept to consider.
Contrary to popular belief, Dogs don't necessarily WANT to be out in their yards alone. The concept of "getting some fresh air...go out and play" is a HUMAN one. (echos of Mom).
If you gave your Dog the option, chances are he would choose to hang out in the house with you if that is where you were. That's because they are Pack Animals and feel safe & secure with their family.
Leaving your Dog out in the yard alone can be misinterpreted by him that he is being SHUNNED. As a Dog Trainer, I often use Shunning to teach a Dog the difference between unacceptable behavior and acceptable behavior. What this means is that when a Dog is "acting up" or "acting out" in a host of many ways, I quietly remove him from the group. No words, no anger, just remove the dog and usually put him in another room. I wait a few minutes so he feels the separation and if he is calm & quiet (if not, I'll wait until he is), I invite him back in without any fanfare. If he resorts to the previous behavior, I do it again. Over and over until he makes the connection. And believe it or not, they do and rather quickly.
Why? is this so effective? Because a Dog wants to be with his Pack. That is more important to him than the behavior he is doing. So removing him is a very strong signal and it's a wonderful technique if it's done properly and without irritation or anger. (that can be very distracting and cloud the point). You are not punishing the behavior, you are Teaching him what you expect. Big difference.
So when you place your Dog out in the yard, shut your door and he feels separated from his safety and home, he sometimes will act out and become anxious. YOU might think you are doing him a fun favor giving him fresh air, but he might perceive that as being punished. Dogs don't think like humans.
Dogs are happiest when they are safely snug in their beds or crates in the home around familiar scents when you are gone. If it is for long periods of time, then you need to come home and give them some potty relief or if this is impossible, hire someone to do that.
A Dog left alone in a Yard is inadvertently shaping his behavior in a very negative way. In addition to digging, there are a host of other problems that can develop. Aggression being one of them. Increased Territorialness. Less connection to you so they listen and respond less. Boredom. Anxiety. Loneliness. Since they are unsupervised, there is no Leadership present so they often get some cockamamie notions about who they are out there.
So please consider the possibility that maybe your Yard isn't the optimum place to leave your dog unsupervised. Go out and play with him there or just chill and hang out with him. (it's a very relaxing thing to do after a long day not to mention you get to just observe your Dog and connect with him more). After awhile, you will begin to recognize the signals of what he is about to do (dig). And instead of reprimanding him, REDIRECT him to do something else. There's something to be said about Nipping Things In The Bud, particularly from a Behavior point of view.
I'm not sure what Breed or type of Dog you have, but chances are he's got some Terrier in there. Those guys are genius escape artists! Terriers also have been bred to ferret out vermin in mines, aboard ships, etc. so they're natural at it. I've done lots of Rehabilitation with Shelter Dogs (have 4 of my own) and the best way to deter your Dog from escaping is to:
a. Establish a strong bond and Leadership with him so he won't really want to leave you and,
b. Give him lots of long walks out in the world where he can be stimulated and satisfied from a sensory & mental point of view. Dogs need more than just physical exercise. Keeping his mind engaged and challenged is equally important. A good Dog Walk is more than just a time for potty relief. It's a bonding time and reinforces your connection to one another. The Leash, if used properly, is a very powerful connecting tool & signal to your Dog. (use a cotton/nylon one and forget the Zipline Flexi's. They were designed for Field Dogs to retrieve and are not only unsafe & non secure, letting your Dog zoom all over at a distance is NOT bonding with him).
Hope these thoughts are helpful and give you perhaps a fresh perspective.
All the Best! (and YEAH! for you adopting a Shelter Dog!!)
Justine Blair Carroll
Saratoga Springs, NY http://web.mac.com/justineblaircarroll (I've got more yard advice on my website)