Root barriers can inhibit the growth of the root system, the effectiveness of root barriers is perhaps worth investigating- for example, you may fing that in ten years you would need to repeat the process.
material will affect the tree; it will endeavour to replace the loss of energy (roots in this instance) as this loss will have a corresponding affect upon the crown of the tree -there will be crown die back. The die back will result in dead wood (many oaks tend to decline and die slowly) in the crown. Dead wood is more susceptible to fail under duress- such as high winds, especially gusts- the falling dead wood poses a hazard.
The reverse is also true- if you remove live material from the crown there will be resulting root loss.
The removal of some of the tree's root system may weaken the stability of the tree, then it is more susceptible to fail under duress/ extreme weather conditions. Or, it may put forth so much root material that you find you problem is increased.
Either way, many times people undertake work upon a tree and unwittingly end up with the very trouble they attempted to avoid.
I work with trees, I have seen it many times, many a tree person has had a hand in such an outcome, unwittingly too, perhaps.
If you like the tree, take a good look at it, if you decide to keep the tree, the best course of action is to help the tree to maintain optimum health, then the tree can respond, to the best of its natural ability, to its environment- a healthy limb accounts for the necessity of movement, as in a storm. This suppleness is the tree's natural resistance to falling apart. If the wind of a storm is gusty, lifting the limbs in many directions, the healthiest limb may fail; it is such wind that accounts for many a fallen limb or tree.
Keeping it free of dead or diseased branches or limbs will help to discourage pathogens interested in dead or diseased material for lunch. Feed it every so often- a bit of mulch do not run over it with a lawnmower or vehicles as the abrasiveness will have a detrimental affect to the whole tree, eventually.
Tree the tree well, it will treat you well.
Nothing can fully accomodate the perils of Nature acting unusual. Things happen- roofs are torn off houses, a tree smashes a roof. That is what insurance companies are for, to cover eventualities.
Will the roots damage your foundations? Perhaps. Enough to worry about? Perhaps. Do massive trees live snug to houses and the houses survive intact? Yes, perhaps more than modern day cover every eventuality deemed negative or undesirable living mention.
I love Oak trees, there are many where I live, young and old. They are quite magnificent to look at; they are beautifully shaped trees, that are eye catching in leaf or bare, they may live for a hundred, or three years. The dead wood makes wonderful firewood, too. Oak burns hot and long with a lovely smell of tannin.
Of course, it is possible to remove the tree, plant something small, ornamental, unobtrusive.... A driveway can be repaired or relaid in a day or two, costly perhaps. Drains can be cleaned.
Change the driveway; build a shelter for the roots over which vehicles may pass... Tie a swing to a suitable limb.... do not be a tree butcher- all or nothing. The bigger the loss, the bigger the threat.