Question
I have a southern live oak in coastal NC. The specimen is about 30' tall with a 45' canopy; a 2' x 2'trench affecting about 25' of root system was dug about 18' from the trunk. No roots bigger than a carrot were cut, can I expect any long term damage?

Answer
As long as you did not cut more than 30% of the root system the tree should be ok. The root system will spread about 1 1/2 times the width of the branches so if you draw a circle around the tree at this point and then mark the trench through the circle you can estimate the percent roots cut. Even with 30% cut you would get only some die back of a few limbs but the tree would survive. And it should recover over time.