The Ascent by Adam Plantinga

When a high security prison fails, a down-on-his luck cop and the governor's daughter are going to have to team up if they're going to escape in this "jaw-dropping, authentic, and absolutely gripping" (Harlan Coben, #1 New York Times bestselling author) debut thriller from Adam Plantinga, whose first nonfiction book Lee Child praised as "truly excellent."
Kurt Argento, an ex-Detroit street cop who can't let injustice go-and who has the fighting skills to back up his idealism.
If he sees a young girl being dragged into an alley, he's going to rescue her and cause some damage.
When he does just that in a small corrupt Missouri town, he's brutally beaten and thrown into a maximum-security prison.
Julie Wakefield, a grad student who happens to be the governor's daughter, is about to take a tour of the prison. But when a malfunction in the security system releases a horde of prisoners, a fierce struggle for survival ensues.
Argento must help a small band of staff and civilians, including Julie and her two state trooper handlers, make their way from the bottom floor to the roof to safety.
All that stands in their way are six floors of the most dangerous convicts in Missouri.