(Adjective)

Definition:of or relating to the end of the world

Source: http://www.merriam-webster.com/dictionary/apocalyptic?show=0&t=1387310339

From Philip Lopate’s Waterfront:A Walk Around Manhattan:
“compared the structure to a dinosaur, one of thous’huge giant lizards’ from which future geologists could re-create out world, and whose bones alone would survive the apocalyptic twentieth century.”

I understand the author want to say that the structure of Brooklyn Bridge is strong, huge and will be last forever, to the end of the twentieth century