Dogs dig for various reasons which include boredom, seeking prey, and comfort and attention. Your dog may be doing it for various reasons. Moles and ground dwelling critters tend to live under plants and tree roots and their burrows tend to run through a yard. A dog can smell them and will dig to try and get to them and thus plants and bushes are sometimes dug up and around the roots of trees. Dogs digging as part of prey drive is hard to correct as prey drive is an instinct. None of my dogs have ever tried eating grub worms and we do get them, the dogs just don't like them at all. If your yard has lots of grub worms, I imagine it has other critters that feed on grub worms.
The best way of stopping this behavior if it is indeed prey driven digging is to rid your yard of the prey. There are mole repellers that are relatively cheap and safe for use around animals as they do not use pesticides. They basically use sound to keep the critters out. If you eliminate the pests, the dog should stop trying to dig them out.
A method I’ve used with great success for escape diggers (digging at bottom of fence) is to bury chicken wire along the edge of the fence and cover it with a layer of dirt. Dogs don’t like the feel of it on their nails and stop digging. This would work if you want to stop the digging in specific places.
Of course, the digging could be related to boredom, in that case stimulating toys can be added to your yard such as balls or kongs. Some dogs dig because they like the cool feel of the earth that is a few inches down. For these diggers it helps to provide them with a nice cool shaded grassy shelter where they can still see their whole yard. Sometimes giving them their own area in the yard to dig in helps but they will need to be trained to use that specific area for digging by watching them closely and encouraging digging only in the one area.
These are some suggestions that may help with your problem.
Here is also a few links to sites that have excellent information on this subject..
I hope this information is helpful to you.