Yes, Typar BioBarrier will prevent tree roots from growing under driveways or sidewalks depending on how far down you are willing to install them. All trees have different root systems and some are very pervasive. Some plant roots can penetrate through bricks, pavers, and even hard stone given enough time. Some Hardwood trees and Bamboos are especially troublesome to concrete upheaval. So much so that right in Typar’s website they say “BioBarrier has been successful against certain varieties of Bamboo, but due to the unique growing characteristics of Bamboo, TYPAR Geosynthetics does not extend the product warranty to include the use of BioBarrier as a barrier against Bamboo or Bamboo Rhizomes.”
Your local reputable concrete contractor should know what types of trees are a problem in the area you live, and what products and systems are successful at limiting future damage.