Roots emerge from the trunk/root flare and rapidly taper away from the trunk; this area of taper is known as the root plate or zone of rapid taper. I have seen area estimates of five to six feet or one to two meters around the trunk. Both the trunk flare and zone of root taper (ZRT) are critical to the stability and health of the tree. (Also important is the critical root zone/tree protection zone which extends beyond the ZRT and is calculated as the distance from the trunk equal to the dbh multiplied by 12 inches.)
The trunk flare and ZRT of the two street trees on Prince Street, pictured above, have been covered with fake grass.
Deep Root blogged about different strategies for protecting the ZRT in The Space Between the Pavement and the Tree. And, if you have access to Arboriculture & Urban Forestry, read the article, Effect of Pit Design and Soil Composition on Performance of Pyrus calleryana Street Trees, by Rahman, Stringer, and Ennos in the November 2013 issue of the journal.