It is speculated that the Mound Builder culture occupied nearly the whole basin of the Mississippi and its tributaries, with the fertile plains along the Gulf, and their settlements were continued across the Rio Grande into Mexico. Toward their eastern, northern, and western limit the population was evidently smaller, and their occupation of the territory less complete than in the Valley of the Ohio, and from that point down to the Gulf. As the culture extended itself from the Mississippi basin, the need for defensive works seems to have evolved, of which the Fortified Hill Works here described are but one example.
Fortified Hill Works is a registered historic site near Hamilton, Ohio, listed in the National Register on July 12, 1974.
The site was surveyed in 1847 by Ephraim George Squier and Edwin Hamilton Davis. The works would be documented in their 1848 book, Ancient Monuments of the Mississippi Valley. They noted that the ditch around the earthworks was on the outside, instead of inside of the wall. As of 1847, they described the ditch as being "equal" at the steepest points of the hill, and "almost obliterated" in other areas. The wall is noted as being eight to ten feet high, and following the shape of the hill it was built on. There are three entrances into the earthwork.
The top part of the earthwork is described as enclosing a small circle, one hundred feet in diameter, with two small mounds inside of it. A third mound, which has been "truncated" was just north of the small circle. Both the small mounds had altars found in them after excavation.
Other examples of fortified Mounds settlements:
The Works at Liberty, Ohio.
The Works at Brownsville, Ohio.
The circular enclosures are perfect circles, and the square enclosures perfect squares. They were constructed with a geometrical precision which implies a knowledge of mathematics, engineering and astronomy. Relics of art have been dug from some of the mounds, consisting of a considerable variety of ornaments and implements, made of copper, silver, obsidian, porphyry, and greenstone, finely wrought. There are axes, single and double; adzes, chisels, drills or gravers, lance-heads, knives, bracelets, pendants, beads, and the like, made of copper. There are articles of pottery, elegantly designed and finished; ornaments made of silver, bone, mica from the Alleghenies, and shells from the Gulf of Mexico.
In the context of first contact with Europeans, this culture had become extinct and none of the natives in the areas in question lived in settled fortified towns of the type described here.
National Parks Service (https://npgallery.nps.gov/AssetDetail/NRIS/74001403)
John D. Baldwin, Ancient America, in Notes on American Archaeology