Methods for augmenting the load bearing characteristics of short aggregate piers include preloading matrix soils, adding chemical additives to matrix soils and using mesh reinforcement in matrix soils and in cooperation with the aggregate lifts associated with pier constructions. Methods for expanding the feasibility of short aggregate piers include the use of gradations of aggregate, reducing friction between the short aggregate pier and adjacent matrix soils using liners or lubricating materials, controlling liquefaction by employing aggregate drains in short aggregate pier constructions, the use of non-impact forces alone or in conjunction with vibratory forces in construction short aggregate pier lifts, and the use of indigenous materials in short aggregate pier constructions. Other methods for augmenting the construction of short aggregate piers include the use of variable dimensioned lifts, the use of interlocking aggregates and recycled materials, such as recycled concrete, the use of temporary casings to protect pier cavities, and the use of load sensors to monitor stresses within short aggregate pier constructions and pressure cells to measure load/deformation characteristics. The invention also includes systems for lateral load stabilization and uplift anchoring utilizes short aggregate pier construction techniques; systems to apply preload to short aggregate piers to increase their stiffness. The invention also includes an apparatus for applying preload to short aggregate pier and matrix soils and other constructions incorporates a pair of half shells operatively associated with an actuator for moving them outward. Once inserted into the pier cavity, the half shells are forced outward to apply preload forces to the pier cavity walls and matrix soil.