Dogs may dig out of boredom or to make a cooling/heating pit.
Some approaches:
Filling in the holes: Try refilling the holes with junk. With junk, dogs can quickly lose
interest and pretty much stop digging. Fill the hole with whatever is at hand - dead leaves,
sticks, pine needles, rocks or even dog feces. Fill the top 2 inches or so with dirt. The dog
finds the stuff, gets discouraged and often quits digging. They seem to get the idea they'll
never know where they'll find junk, and it's not worth the effort to dig only to find junk so
they quit.
Surprises in the hole: you can try burying a water balloon in one of the holes which will
pop in its face when it starts digging.
A sandbox: Try to remember that digging is a natural tendency for dogs. So, if there is any
place where your dog may be allowed to dig, you should encourage it (and only in that
place). Designate an area where the dog can dig. Many people build a sand box for their
dog. Place the box in an area that is cool in summer and warm in winter.
To teach the dog to dig only in the box, place or bury toys or treats
(sliced hotdogs, for example) in the box. Encourage the dog to dig up the
toy or treat. Praise the dog. Repeat until the dog willingly jumps in and
digs. Watch the dog. When it starts to dig in any other place, quickly go
out and take your dog to its box. Show it (by digging yourself), that it
should dig in its box.
To deter boredom, place several toys/treats in the
box before you leave for work. The dog will spend its time digging in the
correct place rather than digging up your roses. You can also sprinkle
animal essence (available at hunting supplies places).
Remember that dogs like to dig in freshly turned earth. So get out that
shovel and turn the dirt over in the sand box every now and then. Toss in
some fresh dirt. Keep a close eye on freshly planted areas, as they will be
very attractive (bury some extra hotdogs in the sandbox when you are
putting down new plants).
Line the yard- for extreme cases you can line the yard with chicken wire and put a layer of
sod over that. Use paving bricks or blocks around the edge to prevent the dog from injuring
itself on the edge of the chicken wire.