My usual commute involves a couple obstacles that can be crossed at only a few spots. I have many route options, but all of them go over the same bridge at approx. the halfway point. And if they're doing work anywhere on the road that bridge is on, they close the whole section of road, even though there is usually nothing wrong with the bridge.

My solution is to get off the bike, and to walk up to the guy manning the roadblock (assuming there is such a guy) and ask if a bicyclist (or pedestrian) can get through as far as that bridge (where I can get on the canal path if the road is not an option). So far, they've always let me. Sometimes they give specific instructions-- one time they had me walk behind a certain building where wires had blown down in front of the building.