Question
Our live oak is approx. 20+ yrs old and for as long as we've lived here (10 yrs), the grass dies in a perfect circle under the tree.  We have one on the other side of the sidewalk, and that does not happen.  We have put new sod and even put new top soil and eventually the grass dies again in a circle all the way around the tree.  The circle is approx. 12 ft from the trunk.  We have never had anyone that is able to solve this problem.  Thanks, Jami

Answer
Hi Jami;
Could it be that the one where the grass grows well is situated where sungets to the grass longer, and the other has more shade?
If that is the case. maybe you could strategecly remove a few limbs that would alow more sun on the grass, without ruining the shape of the tree.
If the tree roots are up close to the surface of the ground, they could be robbing the grass of nutrients.
Adding topsil to it, a couple ( 4 if possible) and starting a dep watering program especially under tht tre, would help.
If you add soil, be sure to not bank the soil up around the tree trunk.
Build a little brick ( or something) wall around the trunk, leaving enough room for it to expand as it grows, and you can dump soil as dep as you want around the tre then, so you could build up the soil, deep enough to give the grass room to grow. the feeder roots of the tree, if they are very thick, and very close to the surface, could be chocking the grass roots .
I am, betting the no sun is the problem though.
The only other thing I can suggest is to build a raised bed all around that tree, making the well at the trunk, and planting shade loving plants and flowers.
Like ferns, maybe.
Charlotte