Too many nuts, too little lawn
 

There is a stand of mixed hardwoods, including mostly mature and extremely
prolific (hickory?) nut trees, beginning about 20 feet south from my back
porch. I would like to have a strip of lawn between my porch and the
trees, but the yearly onslaught of nuts combined with lots of shade from the
trees has made it impossible. I am in AL zone 7b and have burmuda lawn out
front.

Is there any type of lawn that can take this abuse or should I resign myself
to just paving in as much patio as I can afford? A garden supply suggested
sodding zoysia, but they had pallets of the stuff to sell ;-)