What is the maximum depth below grade for termite activity?
According to this paper from the University of Nebraska, they can go up to 20 feet in the ground:


  Subterranean termites are ground-dwelling social insects living in colonies. The two species found in
  Nebraska have similar habitats. These termites have the ability to adjust the depth of their colony (nest) in soil
  depending on temperature and moisture requirements. The colony may be 18-20 feet deep in the ground.
  
  http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=2159&amp;context=extensionhist (PDF Link)


The paper goes on to say that the species they observed are local to Nebraska, however I think it demonstrates these things can dig deep, probably deeper than you can make a barrier. Other less-reliable sources cite depths up to 40 feet.