A process for constructing a jet grouted subterranean column provided with reinforcement. A hole is drilled in the ground to the desired depth using a drill bit carried in a hollow drill rod to which a drill casing is detachably coupled. As the drilling proceeds, grout is applied through the drill rod and is injected sidewardly at high pressure to cut into and mix with the bore wall. The casing is detached from the drill rod and lowered to the bottom of the bore, with the grout filling the annular space between the casing and enlarged bore wall. After the drill rod has been withdrawn from the casing, the casing may be left in place and filled with grout such that the casing provides reinforcement for the resulting grout column. Additional reinforcing material may be inserted through the casing. In an alternative process carried out in accordance with the invention, a bore is drilled with a special drill rod and a sacrificial drill bit. After the drilling has been completed, the drill rod is rotated and grout is applied through it at high pressure. The wall of the rod has axially and circumferentially staggered discharge openings through which the grout is injected to enlarge and fill the bore. The drill rod is left in place centered in the bore to structurally reinforce the grout column.