Apparatuses for constructing displacement aggregate piers are disclosed. In one example, a mandrel is provided comprising a tamper head that has cutting teeth on the leading edge thereof. In another example, hydrojet nozzles are provided within one or more of the cutting teeth of the tamper head. In yet another example, the mandrel comprises grout tubes (or grout injection lines) and/or grout inspection lines. In yet another example, the mandrel and/or tamper head can comprise cutting teeth, hydrojet nozzles, grout tubes (or gout injection lines), grout inspection lines, and any combinations thereof.