Usually "slabs on grade" only require a minimum amount of excavation, which is generally limited to removal of the topmost, unconsolidated soil layer containing organic debrie, live vegetation and roots. Often no more than 300 to 400mm is removed. Slab thickness will be the removal depth plus an allowance to extend above the original surface elevation to permit backfill around the slab to drain rainfall away from the structure. Total thickness of the slab may be as thin as 300mm. 450mm is often the maximum thickness, 150mm or so, above the original grade elevation. If good soil bearing is found lower than 450mm, the slab thickness is usually kept at the required thickness, say the 300mm, then the excavated depth will be built back up with compacted fill, usually sand, to the bottom of the slab's thickness, approximately the original surface elevation, then only the edge of the slab, 300 to 450mm or so, will be dropped down to soil bearing depth, making a "turned down slab on grade" type foundation. The turn down portion is provided to retain the compacted fill under the slab and keep it from being washed away from under the slab's edges.
Block pier, is a short column of CMU blocks resting on a minimum concrete pad embedded in the soil below grade where the soil is hard enough to provide the required bearing capacity. The CMU blocks could equally be made as a concrete pier, resulting in the typical pier, or pedestal, or plinth type foundation constructed on top of a embedded concrete footing a meter or two below ground surface.
It is also common to see both slab on grade and pedestal-footings being used together when there are usually light bearing wall and floor loads placed on the slab with heavier column loads placed on the pedestals.
You might want to read Chapter 4 on foundation Design here
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