We have used reinforced concrete pipe. It a tedious and slow
process, not to mention restricting to work in. You'll need some
type of crane to lower and raise the sections.
Garrow and Associates (1993) excavated a 18th century "Ordinary",
Maplewood, Amelia County, Virginia. This site contained cellars, a
privy, and a brick-lined well.
Holler if you need additional Info.