Answer: Your blackhaw viburnum is actually behaving in a natural way. It is not a formal shrub but rather forms a thicket by extending its roots and sending up suckers. It really wants to colonize an area rather than be a single shrub. There's no way to kill the invading roots without also killing the shrub so you may want to consider removing it and replacing it with a better-behaved viburnum. You can do some extensive root pruning but the roots will continue to extend themselves and invade your perennials. To root prune, simply cut through the soil and the roots with a shovel to sever the roots, then dig up the roots that you just severed from the parent plant. You may have to do this kind of root pruning every spring to keep the roots under control. Best wishes with your project!
Q&A Library Searching Tips