Fully compensated raft and its depth

Fully compensated raft: a raft placed at such depth that the weight of the soil excavated is equal to the total weight of the structure, including the raft. The net pressure on the soil is then zero, and, in principle, no extra settlement or shear failure occurs.

Derivation of depth

Let $Q$ = total load of the structure (including the raft), $A$ = area of the raft, $\gamma$ = unit weight of the excavated soil, $D_f$ = depth of the raft.

Gross pressure at foundation level: $q = \dfrac{Q}{A}$

Weight of soil removed per unit area (overburden pressure): $\gamma D_f$

Net pressure on the soil: $q_{net} = \dfrac{Q}{A} - \gamma D_f$

For a fully compensated raft $q_{net} = 0$:

$$\frac{Q}{A} = \gamma D_f$$ $$D_f = \frac{Q}{\gamma A} = \frac{q}{\gamma}$$

If the water table is above the raft, the buoyancy reduces the soil weight, so $\gamma D_f$ is replaced by the vertical effective stress at base, or the buoyant uplift is subtracted from $Q$.