I don't think you can plug up more than the entrance portion of the hole. Not only do the burrows go fairly deep, but they twist and wind around, and are made with ups and downs so that rain, snow-melt, etc won't wet the living areas. Nature will gradually fill in unused burrows. I have a family of chippies living in the azaleas, and although I once found a tunnel opening near the house, that's been years ago.

You can try using Pine-sol, diluted 1 part to 5 of water, poured in a line around the perimeter of the house. I've long used Pine-sol [in a bowl in a locked cupboard] to keep mice and squirrels out of the attic, and it seems to be a long-term deterrent for rodents when poured on the ground around the house. My house has a crawl-space and we live near fields, and I used to think the field mice owned the house until I tried the pine-sol as a barrier. Humans can't seem to smell it after an hour or so, but apparently it's awful to the rodent-nose.