Answer: Changing the soil depth over tree roots can cause problems with rot but a few inches of organic mulch such as bark nuggets shouldn't cause any damage. Don't use weed barrier in the area, simply spread bark over the site to cover the roots. You might also consider planting groundcover in small pockets, avoiding the roots of the tree. Fragaria (ornamental strawberry) is drought tolerant so it won't require lots of watering, and it will scramble over the bark nuggets, eventually rooting in the soil beneath. Best wishes with your garden!
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