Intuitively, the lateral stress must influence the amount of vertical settlement. As BigHarvey pointed out, ground improvements increase the "locked-in" lateral stresses - compaction with a large vibratory roller will increase the normally accepted 0.5 to over 0.7 or more. For a material to decrease in vertical "thickness" it has to expand in the horizontal directions as well. The larger the horizontal stress - at rest or "locked-in" - the more resistance it has to being squeezed - picture a soil, one having relative density of, say, 50% and the other of 85% - certainly, you would expect that the settlement under the footing in the latter case would be less than the former. This also manifests itself in compression testing. It is well known that when a lateral confining pressure is added (triaxial) compared to the "open air" test, the strength will be higher. While this might be construed for cohesionless soils, it would also apply to cohesive soils - think normally consolidated vs lightly overconsolidated to heavily overconsolidated soils (where you, Kushtian, might actually have negative porepressures develope).
Again, I would relate back to 3-D consolidation theory . . . BigHarvey - going for a Ph.D? or double?