11. A method of constructing aggregate piers, the method comprising the steps of:a) providing a mandrel, the mandrel comprising an upper feed tube portion, a tamper head, at least one hydrojet nozzle on the lower edge of the tamper head, wherein each hydrojet nozzle is entirely disposed at an angle ranging between 10 and 80 degrees from horizontal and a passage extending therethrough for feeding aggregate through the feed tube to the tamper head, wherein the tamper head comprises a plurality of unbiased cutting teeth on a lower edge of the tamper head opposite the feed tube and surrounding a perimeter of the tamper head edge, and wherein the cutting teeth have a flat bottom that ranges in width from 0.5 inches (1.2 cm) to 6 inches (15.2 cm) and ranges in depth from 0.25 inches (0.6 cm) to 6 inches (15.2 cm);
b) driving the mandrel in a vertical motion into free-field soils to a specified depth;
c) lifting the mandrel a specified distance;
d) repeating the driving and lifting of the mandrel; and
e) adding aggregate to form the pier.