Allowable pressure of raft 3 m × 12 m

Given: raft $B = 3$ m, $L = 12$ m, $D_f = 2$ m, corrected $N = 22$, cohesionless soil, water table 4 m below GL.

Method (Meyerhof/Bowles, SPT-based, for raft): for a raft the settlement is nearly independent of width, so the net allowable pressure for a settlement $S_a$ is

$$q_{na} = 19.16\,N\,F_d\,\frac{S_a}{25.4}\ \ \text{(kN/m}^2\text{, } S_a \text{ in mm)},\qquad F_d = 1 + 0.33\frac{D_f}{B} \le 1.33$$

Allowable settlement: the differential settlement is limited to 20 mm. As the total settlement is at least equal to the differential settlement, the conservative value $S_a = 20$ mm is used.

Calculation

$$\begin{aligned} F_d &= 1 + 0.33\times\frac{2}{3} = 1.22 \\ q_{na} &= 19.16 \times 22 \times 1.22 \times \frac{20}{25.4} = 404.9\ \text{kN/m}^2 \end{aligned}$$

Water table correction

The water table lies at 4 m, which is within a depth $B$ below the base ($D_f + B = 5$ m), so

$$C_w = 0.5 + 0.5\frac{D_w}{D_f + B} = 0.5 + 0.5\times\frac{4}{5} = 0.90$$ $$q_{na}' = 404.9 \times 0.90 = 364.4\ \text{kN/m}^2$$

Answer: net allowable bearing pressure of the raft $\approx 365$ kN/m² (settlement criterion governs; the shear failure check will have a large margin in sand).