“The dam really worries me. The idea that it could spill over and spread chemicals is really concerning,” said Charles Holliday, 27, who was clearing out debris from his family’s yard in the small town of Navassa, the nearest residential area to the plant. “This whole area has a lot of industrial plants and chemicals and that kind of thing. So you add it all up and, yes, it’s something we are all going to get a little panicked about.”

The river has already spread hundreds of yards beyond its banks, turning the piney flats west of Wilmington into a muddy lagoon punctured by tilting trees and half-submerged railroad bridges.

The plant itself, cordoned off by security but visible from a highway overpass, was covered by a thin pool of water, with the area closest to the lake appearing to be the most inundated.

Peter Harrison, a lawyer with Earthjustice, an environmental nonprofit, took a boat on the river to see the site himself. He said that there were multiple places where the dam around the lake had breached, and that the lake water was pouring into the river. From what he could see, he added, the lake water appeared full of coal ash.

“You can just see that swirling down the river for like miles and miles,” Mr. Harrison said.

Avner Vengosh, a professor of earth and ocean sciences at Duke University, said, “We’ll probably never know how much has spilled into the river.” Because the spill stems from large-scale flooding over a wide area, it’s difficult to calculate how much ash is entering the river.

The breach of the dam imperils two unlined coal ash ponds on site, which contain a combined 2.1 million cubic yards of coal ash, according to a report prepared for Duke Energy this year. That amount of coal ash would fill a large sports stadium.

Scrutiny of coal ash has increased since 2008, when the Kingston Fossil Plant in Harriman, Tenn., spilled 5.4 million cubic yards of coal ash into the environment. The cleanup cost more than $1 billion.