-I'm faced with a similar scenario with the Wife's DD-vehicle.
Which leads me to highly suggest:
You really need to wash your vehicle.
-I believe that once you have assessed what type of construction is the cause of this dust,
and how it's going to (hopefully not undesirously) affect your vehicle's paint and other surfaces:
"When all the dust has settled"...You, in turn, may just agree.
Is this
'dust' laden with contaminates from:
-Tearing-down existing structures/jackhammering concrete
-New cement pours
-Diesel-fuel-equipped: trucks'/cranes'/lift-trucks'...exhausts wafting through the air
-Welding smoke contaminates
-Metal-
"shavings" from grinding operations
-Disturbance of soil/dirt
-etc.
IMHO...
-When this construction project is completed...
You'll need to apply a total paint-decontamination-system to thoroughly rid your vehicle
from all of the contaminates it has accumulated that a
'normal-wash' will not remove.
Just a few of my thoughts.
Bob