Flavius Josephus writes in "The War of the Jews"(5:8):
Now as to the tower of Antonia, it was situated at the corner of two cloisters of the court of the temple; of that on the west, and that on the north; it was erected upon a rock of fifty cubits in height, and was on a great precipice; it was the work of king Herod, wherein he demonstrated his natural magnanimity. In the first place, the rock itself was covered over with smooth pieces of stone, from its foundation, both for ornament, and that any one who would either try to get up or to go down it might not be able to hold his feet upon it. Next to this, and before you come to the edifice of the tower itself, there was a wall three cubits high; but within that wall all the space of the tower of Antonia itself was built upon, to the height of forty cubits. The inward parts had the largeness and form of a palace, it being parted into all kinds of rooms and other conveniences, such as courts, and places for bathing, and broad spaces for camps; insomuch that, by having all conveniences that cities wanted, it might seem to be composed of several cities, but by its magnificence it seemed a palace. And as the entire structure resembled that of a tower, it contained also four other distinct towers at its four corners; whereof the others were but fifty cubits high; whereas that which lay upon the southeast corner was seventy cubits high, that from thence the whole temple might be viewed; but on the corner where it joined to the two cloisters of the temple, it had passages down to them both, through which the guard (for there always lay in this tower a Roman legion) went several ways among the cloisters, with their arms, on the Jewish festivals, in order to watch the people, that they might not there attempt to make any innovations; for the temple was a fortress that guarded the city, as was the tower of Antonia a guard to the temple; and in that tower were the guards of those three.
Fort Antonia was huge, like a city, big enough to house a Roman legion. It seems to me that it must be that it was built around the rock that is now under the Dome. Thus it was in between two deep valleys, one to the East and one to the West. On the northern side was an artificial ditch. I would guess that the part of the Antonian rock that was made smooth was the southern side of the ditch. Flavius Josephus relates to the ditch when he describes "The War of the Jews"(5:2) the Betseda hill:
It [Betseda] lies over against the tower Antonia, but is divided from it by a deep valley, which was dug on purpose, and that in order to hinder the foundations of the tower of Antonia from joining to this hill, and thereby affording an opportunity for getting to it with ease, and hindering the security that arose from its superior elevation; for which reason also that depth of the ditch made the elevation of the towers more remarkable.