That all sounds like good advise. My problem is being on a hill. Erosion has taken dirt from under the trees and we have roots above ground under the canopy. I would like to bring in dirt to cover the roots and plant something to hold the dirt in place, either a grass or ground cover. I am at a total loss because we moved here from a yard of full sun and all grass with only one mature pine tree on the property. It was alot of mowing, but no headaches.
Also consider other ways to control the erosion. Such as terracing, using timbers, rocks/boulders, diversions, etc.
I had good luck with a Bluegrass/ creeping red fescue grass mix underneath a large elm tree (in heavy clay soil) when I lived in central Oklahoma. Bermuda in the remainder of the lawn. Bermuda absolutely will not grow (satisfactorily) in heavy shade. The soil beneath a canopy never benefits much from rainfall so you have to be prepared to keep the area irrigated. At least the clay soil helps you out some with that!
You might also look into some of the liriopes ('Monkey grasses' as they're sometimes called.) They are quite hardy in zone 6 (Oklahoma), drought tolerant, semi-evergreen, will hold the soil well when they're established and do well in shade. Another plus is that you can set the mower to a high setting & mow them off to make fall leaf collection easier.
“My problem is being on a hill. Erosion has taken dirt from under the trees”
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My last post before going to bed.( I am now in Asia)
Be careful on adding dirt to any long exposed roots.
You may invite disease that could kill the tree.
It might be better to just block the erosion path and add
fast growing ground covers.
Consult an arborist before covering any exposed roots.