Putting a tough groundcover or plants native to your area in the inhospitable conditions directly under a mature tree is one thing, but what if you want to plant something else there?
It can be done - I've been doing it for more than twenty years in my USDA zone 7 garden. Simply put, you need to add soil over the existing grade. But, it's not really that simple. Before you rush out and start dumping dirt, you need to seriously consider the welfare of the tree you're contemplating planting beneath.
As I pointed out last week, tree feeder roots are not far beneath the surface of the soil and they extend a long way beyond its canopy. If you raise the grade too much all around a tree, you will cut off the air and water that those roots need to survive and your tree will eventually die. The same result is obtained if you lower the grade substantially around a tree - particularly a mature tree. Mature trees are not as adaptable to changes in their environment, sorta like mature humans. The older we get, the more set in our ways we become.
Some trees are more sensitive to changes in grade than others, which is why you need to know your tree and learn a bit about it. Many experts advocate no changes in grade at all around mature trees. This, in my opinion, is a bit drastic, but probably the safest advice to give so that people don't dump two feet of soggy clay around a tree and then, when the tree dies, complain to their lawyers that they received bad advice and sue the advisor.
So how do you add soil without raising the grade? Again, simply, you don't. Whatever you add will change the grade somewhat. The secret is not to add actual soil, but a light mix of organic material in which your chosen plants can establish their roots, but which is loose, open and free draining so it doesn't cut off vital supplies to the tree roots.
You also have to use some common sense. I prefer to make my changes to one, or at most two sides of a tree instead of encircling it completely. This leaves the bulk of the root system as it was. If I need to lower the grade, I also keep this to only one side of the tree. Trees get roots cut during construction operations all the time. While many large trees left on construction sites linger and die over a period of years; many others survive. Cutting some roots on one side of a tree does not make the tree happy, but if the balance of the root system is undisturbed and the soil on top of it is not compacted by heavy equipment or foot traffic, a healthy tree will grow more roots and continue on its way. Obviously, when you need to do major work around trees, you have got to keep your wits about you and think about the consequences of your activity before you act.