I have a raised flower bed made from stone and mortar on a cement base. It's about ten inches tall, and I get tree roots.
The host of a radio garden program said to trench down one foot around the raised bed and place an impermeable barrier to keep the roots out.
I did that and still get roots.
This year, I'm going to dig all the dirt out and find where the roots are getting in and just for fun, and to make myself feel good. I'm going to pour much bleach all over the area.
Then I will lay down a plastic barrier before replacing the fill.