In the Southeast we have used, and modern day well diggers use, reinforced
concrete pipe sections (2.5-3 feet in diameter and approx. 2 feet high) to
dig wells.  After you have excavated 3 or 4 feet, you need to place a
platform with a wench over the hole and begin placing pipe sections.  As you
dig, the pipe sections slide downwards, providing an iron reinforced concrete
well lining as you go.  The sections interlock, come in a variety of
diameters, are a lot cheaper than heavy equipment, and allow you to go to at
least 45 feet (which is what we did in one well).  A 45 foot vertical column
would be next to impossible for a backhoe.
 
Tom Wheaton