When engineers began poking and prodding at the Utah Capitol a few years ago, sounding the structure for how it might fare in the earthquake that seismologists say will surely strike here one day, they grew increasingly scared as they moved higher toward the dome.

The quality of the concrete varied — solid at the foundation, crumbling near the top — and that finding could mean only one thing: There had been only so much building material, and construction crews, in finishing the dome in 1916, had added more and more water to stretch out what they had.

“It was frightening: we got up there and said, ‘There’s nothing here,’ ” recalled David H. Hart, an architect and the executive director of the Capitol Preservation Board, which led the $200 million project, completed just this month, to assess and retrofit the Capitol. “We did core samples and came up with rubble.”

Every grand old public building has its back story, and as often as not, it comes around to just such a mix as this one, where grandiose ambition and real-world execution meet, where a skyward reach toward some higher purpose or statement — the spirit of democracy, faith, you name it — is bound up with human imperfection, as well as a yearning for acceptance.