Thank you for posting such nice photos of the base of your plant as opposed to just the photo of one twig.
You're might be dealing with Botryosphaeria although it could be another canker fungus. Botryosphaeria is one of those opportunistic nasties that attacks stressed plants (usually drought stressed from subsequent years) and plants that have been injured. My husband is NOT allowed to mow anywhere near my trees or shrubs any longer. Weed wackers are a big no no for him to even think about touching ever again as he was getting overzealous and was repeatedly damaging the bark on me trees and shrubs. My poor trees and shrubs were getting hit with crap like this all the time when he was wacking away with wild abandon. One thing to be hit with a canker fungus because a tree or shrub is stressed as a result of droughts in prior years or because rabbits have stripped bark but another to be hit with this because one's own husband is into wacking weeds and ramming trees with the front of the lawn mower while listening to tunes on his iPod.
Botryosphaeria is a fungus. It enters through a wound or opening created as a result of bark splitting. Once in, it kills off the cambium layer and moves on to destroy the sapwood. This generally girdles the affected branch over time. The blunt of your damage is toward the base of the shrub which admittedly isn't the greatest location.
What I'm seeing doesn't look all that encouraging but we've all seen worse survive and that shrub is multi stemmed. You could start by pruning out all infected branches. Definitely burn the branches as suggested by opabinia51. Don't apply any type of a product to seal the area where you prune. From there mulch heavily around the base of your shrub. Over the course of this growing season, make sure the plant is deep watered if you go for a period of say 10 days or so without rain.
Botryosphaeria is present in the environment however healthy plants simply wall off the pathogen. In other words, don't worry about this attacking healthy plants.
Although I don't think your odds of being able to save this shrub are all that great (please don't reach out and choke me for those comments but that damage is low to the ground and has already created some sunken dead areas that are disproportionately large in relationship to the branches) I don't think you've got much to lose trying to save it. Remember, a canker fungus doesn't exactly attack healthy plants.
If you aren't able to save it, don't feel bad. I couldn't save most of mine. One I lost in particular made me see red so I ended up putting that one under the covers on my husband's side of the bed that night.
There are quite a few viburnums out there that are considerably more drought tolerant than V. carlesii. There are also viburnums that are equally as shade tolerant although the ones coming to mind for me aren't evergreens. They're equally beautiful if you'd like another viburnum for that location but just not evergreen.