Question
MArc,
We have been in this house (concete foundation) for 20 years.  My husband planted a live oak in the back yard at that time.  The house forms a u-shape around the tree, with about 2 foot diameter trunk.  From the trunk, there is a 12 foot reach over to the garage, same over to the patio (with another 10 feet to the house), and same distance to the other side of the U, to the back bedroom.

We are getting a bit worried about roots messing up the house foundation---not because we have had any foundation problems, but because the little walk next to the garage has buckled a bit from roots underneath it.  My husband's idea is to make a trench and cut roots along that U-shaped area bordering the patio, edge of house, and sidewalk along the garage.  That gives the tree roots 12 feet in all directions.

What do you think of this, or what recommendations?  Is there something we should put in the trench?  I'd hate to chop down this big oak, but I'd hate to have bad foundation problems in the future, also.

Answer
I was taught, "What you see above ground is what the roots look like below ground."  Turns out this is wrong. A tree is like a wine glass (the above-ground part of the tree) on a dinner plate (the roots), according to the a UC Davis study.

That said, a "live oak" can be any of a number of oaks, as there are over one hundred species of oak world-wide, and 5 called "Live Oak" in my horticultural book, alone.

12 feet is normally lots of room for a tree, trunk, and root system of any oak, as its roots are generally not invasive.  

If you are in California and its a native Live Oak (Quercus agrifolia - Coast Live Oak), then here are some additional guidelines for rootcare -
http://www.californiaoaks.org/faq.html

While white oaks are highly sensitive to root disturbance, I think you CAN carefully prune Southern Live Oak (Q. virginiana) roots with little long-term harm.  

The Southern Live Oak is a lot tougher than it's California cousin, and it gets bigger, faster - up to 60 ft. tall and about as wide!  Unfortunately, it's roots are known to cause concrete-lifting problems:

hort.ifas.ufl.edu/trees/QUEVIRA.pdf

The Southern Live Oak is not grown out here on the west as often, which is sad, as it is supposed to grow really well in a desert climate.

Bottom line - You can trim the SURFACE roots by trenching (at our beyond hte drip-line) and I would further suggest installing a root barrier of no less than 18-inches deep.

Some root barrier links:
http://www.biobarrier.com/daveytree/index.html
http://www.ndspro.com/Products/Info.aspx?tab=Overview&cat=37&class=Landscape

~M