They usually have a 3x3 ft ft opening for the dirt. When it rains it goes there, but how do the roots continue to grow? Does water flow through the concrete and asphalt so the the roots can expand in diameter?
Don't know. But this has crossed my mind plenty of times. Sometimes concrete is all that surround a tree like in downtown Chicago. Maybe they plant a certain kind of tree in the area that has a specific root structure designed for this kind of irrigation limitation.
Well, how deep is the concrete surrounding the trees? Tree roots can grow pretty far to find water. May be this is why the new plants are watered (by sprinklers) and the bigger trees are not (except in desert states).
The concrete is only 3-4 inches thick. Underneath that is dirt. The roots will grown down. And yes, the water seeps into the cracks and down. Plus the area around the tree and down. And often there is irrigation in that area as well. I had trees planted in my easement (the area between the street and the sidewalk) and ran an irrigation line under the sidewalk and then down the easement to water each tree. I have rose bushes there now. The remaining tree was moved to the yard and likes it much better. Pedestrians no longer break branches off and step on them and cars don't drive up onto the easement and drive over them, breaking them off. (Yes, I replaced the tree on the end three times. After the fourth death I said enough and the rose bushes went in. )
Moisture in the soil will rise up under structure. Lay a sheet of plastic on bare ground and it will be wet under it even if the weather is dry.