Apparatus for construction of a soil reinforcement pier in a soil matrix comprising, in combination: an elongate hollow tube having a longitudinal axis, a top material entrance end, an open bottom material discharge end and a first outer surface diameter; and a unitary, shaped bottom head element at the open discharge end having a second outside surface diameter greater than the first surface outside diameter and configured to provide a combination of axial and transaxial stress components onto the soil matrix surrounding the bottom head element upon lowering the hollow tube into the soil matrix, said head element comprising a unitary attachment of the hollow tube; wherein said head element includes a leading bottom end having a generally frustoconical configuration shaped for facilitating outward lateral compaction of soil when lowered and a trailing end having a generally frustoconical configuration shaped for facilitating raising of the hollow tube and outward lateral compaction of soil when being raised; said bottom head element having an effective diameter larger than the effective diameter of the hollow tube to reduce frictional forces on the hollow tube when penetrating into and withdrawing from the soil matrix; a head element cap closing the open end of said bottom head element; said bottom head element with said cap and said hollow tube being shaped for insertion in a soil matrix to effect displacement of the soil as the hollow tube with the bottom head element and said cap are lowered into the soil matrix to form a cavity in the soil matrix, characterized in that said head element is solid between its internal diameter and its outside diameter and the head element cap is a sacrificial cap; and said cap being removable from the bottom discharge opening as the hollow tube is subsequently raised from said formed cavity to allow material flow through the bottom discharge opening into the portion of the cavity vacated by the hollow tube and bottom head element. an elongate hollow tube having a longitudinal axis, a top material entrance end, an open bottom material discharge end and a first outer surface diameter; and a unitary, shaped bottom head element at the open discharge end having a second outside surface diameter greater than the first surface outside diameter and configured to provide a combination of axial and transaxial stress components onto the soil matrix surrounding the bottom head element upon lowering the hollow tube into the soil matrix, said head element comprising a unitary attachment of the hollow tube; wherein said head element includes a leading bottom end having a generally frustoconical configuration shaped for facilitating outward lateral compaction of soil when lowered and a trailing end having a generally frustoconical configuration shaped for facilitating raising of the hollow tube and outward lateral compaction of soil when being raised; said bottom head element having an effective diameter larger than the effective diameter of the hollow tube to reduce frictional forces on the hollow tube when penetrating into and withdrawing from the soil matrix; a head element cap closing the open end of said bottom head element; said bottom head element with said cap and said hollow tube being shaped for insertion in a soil matrix to effect displacement of the soil as the hollow tube with the bottom head element and said cap are lowered into the soil matrix to form a cavity in the soil matrix, characterized in that said head element is solid between its internal diameter and its outside diameter and the head element cap is a sacrificial cap; and said cap being removable from the bottom discharge opening as the hollow tube is subsequently raised from said formed cavity to allow material flow through the bottom discharge opening into the portion of the cavity vacated by the hollow tube and bottom head element.