They will continue to breed, expanding territory unless there are predators. When they come across a culvert (or bridge), they will block it, eventually overtopping roads and washing them out.

Is there no more demand for beaver pelt and/or meat?

I've heard the tail is particularly tasty and easy to skin and cook.

Thanks for the good faith reply. I can see that this would require regular maintenance.

It is interesting that we see our infrastructure as 'valid' or correct, but the work these engineers (beavers) put in as a nuisance. In an ideal world, the benefits to local biodiversity and ecosystem health should be balanced with the cost of relocating roads when necessary.