Years ago in Elk Grove California, I learned that and oak tree or any tree can be saved when building a house in the drip line of the tree. You don't have to cut it down, as a matter of fact it might cost you less to save the tree. Big oaks cost a lot of money to cut down and remove.
Contact an arborist and he will tell you how you can design a drip system under your slab so the tree can get the water it needs to live. Also the drainage!
In my case I only had to put 4" abs pipe 1' under the ground on 2' centers for about 38'. The cost was only about 800.00 and it did not hurt the structural integrity of the house at all. The cost of removing the tree would have been about 2500.00
I not only saved money, but the tree is still standing today almost twenty years later. That's a good thing!