The river level is projected to reach 8 feet above the flood stage, or around 1 foot shy of the record, at Morris by noon Thursday.
The river is already more than 8 feet above flood stage at St. Louis and expected to rise another 4 feet by Monday.
The Davenport breach came as communities in Iowa, Illinois and Minnesota have prepared for record or near-record crests along the river.
"We do have a few problem ares around the city especially near the Conservation Clubhouse and on the south side", the mayor said Thursday evening. Davenport has no permanent levee or floodwall.
Further downstream, Mississippi River levels are expected to reach rare heights in Missouri.
The latest round of flooding in the Midwest has claimed at least four lives, closed hundreds of roads and forced residents of threatened towns to shore up threatened levees with sandbags.
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Heavy rain in MI swamped homes and closed a stretch of a freeway near Detroit, where sandbags were stacked to curb flooding near canals off the Detroit River.
The Memorial Bridge connecting Quincy, Illinois, and West Quincy, Missouri, closed Wednesday, forcing all traffic to take the only other bridge in Quincy. City officials say moderate riverfront flooding begins at 22 feet.
"We're going to have a full-fledged flood fight", Hark said. "There is not a lot we can do with water filling the buildings". He and his colleagues set up a temporary kitchen outdoors so they can cook for flood victims and volunteers working in the area.
Parts of the Ozarks region of Missouri received up to 6 inches (15 centimeters) of rain Wednesday night and Thursday morning, prompting flash flooding that forced hasty evacuations in some areas.
Along the Osage River, high waters are inundating campsites at the Mari-Osa Campground.