A post-tensioned concrete cap foundation has helical anchors with pipes having several helical discs welded around the pipe perimeter to spin drill deep into subsurface soils or other soft materials with holes in the pipe for high pressure-grouting in place. The helical anchor pipes include a tensioning element for pulling and post-tensioning the helical anchor. The helical anchors are tension anchors which can be converted to compression anchors. The helical anchors in tension serve to pull the foundation cap down to compress the underlying soil while the compression anchors limit the maximum settlement of the concrete foundation cap. The foundation also includes perimeter-forming and interior corrugated metal pipes with upper and lower sleeved horizontally extending radial bolts that are secured to the pipes and post-tensioned to provide lateral foundation compression.