Compensated foundation and types of mat

Compensated (floating) foundation

A compensated foundation is a raft or mat placed at a depth such that the weight of soil excavated is equal to (fully compensated) or a large part of (partially compensated) the weight of the structure. The net pressure on the soil is then zero or small, so settlement is very small, like a ship floating in water.

Net pressure: $q_{net} = \dfrac{Q}{A} - \gamma D_f$. When $q_{net} = 0$, $D_f = \dfrac{Q}{\gamma A}$. It is used on soft, compressible clays and for buildings with basements.

Types of mat foundation

 (a) Flat plate              (b) Thickened under columns
     |     |     |               |     |     |
 ===================         ====[=====[=====[====   <- slab
                                  \___/ \___/        <- thickened pads

 (c) Beam and slab           (d) Cellular (box) raft
     |     |     |               |     |     |
 ===================         ====================   <- top slab
  |||   |||   |||            |  [  ] | [  ] | [  ] |  <- walls, hollow cells
 -------------------         ====================   <- bottom slab
   (beams below slab)

1. Flat plate (uniform thickness) mat: a plain slab of uniform thickness. Suitable for light loads and closely spaced columns.
2. Flat plate thickened under columns: pedestals or drop panels increase the punching shear resistance. For heavier column loads with uniform spacing.
3. Beam and slab mat: beams in both directions with a slab below or above. Stiff and economical for heavy and unequal column loads and large spans.
4. Slab with basement walls (rigid frame): the basement walls act as stiffeners. Used where a basement is needed.
5. Cellular (box) raft: a bottom slab, a top slab and walls forming hollow cells. Very stiff, reduces differential settlement, and the hollow space reduces net pressure. For high-rise buildings on compressible soils.
6. Piled raft: the mat is supported on piles, used when settlement is large or the soil is very weak.

Suitability

Mats are used where the allowable pressure is low (spread footings would cover more than about 50% of the plan area), where the soil is erratic or compressible, for uplift due to a high water table, and for tall or heavy buildings needing uniform settlement.