OP
get business cards made at through the online business card maker that offers 500 cards for $10USD
then bring a card to the trailer, office, architect, engineer in charge. tell them you would like to photograph their site
and that you will stay out of harm's way ( long lens ) . also tell them you will give them copies of the good photographs...
maybe for a small fee or maybe as a thanks.
when you do it enough you will have a stack of construction photographs, you will have a better business card
and you will be able to ask for more $$ for the photographs you took.
i hate to suggest you bring an electronic camera as well, so the photographs you bring, send, have a cd of email &c
don't take a long time to develop and print, but it might help ...
I would emphasize "historical documentation" as a reason and hope the construction firm would resonate with that. Most construction projects are photographed by the company/client or their insurers for such purposes since they often need it for contractual compliance and liability purposes.
you can say THAT again !
but those photographs are usually
taken months, even years before
the construction begins...