Surely there is another name for the plant besides bluebeard....
I have never heard of a plant by that name.
Linda C

The scientific name is Caryopteris clandonensis. It's the same as the Blue Mist shrub (sometimes called Blue Mist Spiraea), just with slightly darker flowers.

Caryopteris is one of my faves too!!!!
I would prop up the bent branches.....but don't get your hopes up that they will live...
However it will come back from the base.....keep it watered....and next spring ( not now!!) give it some nice composted cow manure....
And let the foreman of the cement project know he has caused you a monetary loss and should reduce the bill proportionally!
Linda C

June thru Aug can be a good time to take semi-mature wood cuttings from caryopteris, you might try rooting those broken branches. Cut the stem cleanly, shorten from the tip if necessary, use rooting hormone, insert in potting medium, place in shade and keep damp.

My caryopteris Worcester Gold roots somewhat easily; close inspection of the branches will sometimes reveal little 'bumps' at nodes. I'll cut those stems to about 8" pieces that include the 'bumps', insert that part into the potting soil....presto, new plant to place in the garden or share in Spring.