If you are building a garage under the tree, its not just that you will cutting into the tree for your pit, but presumably for the foundations for the garage as well. cutting any root will create an instablity of the tree and open a wound for infection. also compression of the ground will affect the tree. reducing air pockets in the ground and starving it.....sycamore are not the most valued of trees. if you are going to keep the tree perhaps you could reduce the size of the tree before you build. this would reduce the risk of instability.