This particular stretch of road isn't particularly comfortable for cyclists, anyway, what with Jersey barriers on one side and heavy, 35-mph traffic on the other. It gets downright heady when some Bozo comes riding his bike in the opposite direction, and trying to occupy that same space. (That happens to me with unsettling regularity.)
Perhaps the ACHD folks (or contractors... whoever) haven't perceived that the barrels are narrowing down the lane by 60% or so.
I'm assuming some big project must be forthcoming along that stretch. But when? And can't they find a lower-impact place to store the barrels in the meantime? I'd suggest the right motor-vehicle lane. After all, they have two lanes to work with.