The plan is to till the soil, add compost, add a french drain, regrade the slope and then reseed the lawn.
After killing off the existing lawn, I found that under the surface it is crisscrossed with tree roots up to 2-inch in diameter. They appear to come from a birch tree in the corner. I yanked out some of those roots and have some more to go. Other than cutting down the tree, is there a way to prevent the roots from invading the lawn in the future?
Also, the soil seems very clay-like. In fact, when it rains some puddles would form and drain away very slowly. Should I do something about this, like add sand?
Some books suggest the french drain be put near the foundation wall. I fear that losening the soil near the foundation would weaken the support of the foundation, so I'm inclined to put the french drain on the perimeter of the lawn, i.e. the lowest point after it is regraded. Would this work?