Allowable load of 400 mm pile, layered soil

Given: driven concrete pile $D = 0.40$ m, length 14 m, water table at 3 m. Layers: loose sand 0–3 m ($\gamma = 16$, $\phi = 30^\circ$); soft clay 3–9 m ($\gamma = 16$, $c = 15$ kN/m²); dense sand 9–14 m ($\gamma = 20$, $\phi = 40^\circ$). For concrete: $\delta = 0.75\phi$, $K = 1$ (loose) and $2$ (dense).

Assumptions: $\gamma_w = 9.81$ kN/m³; below the water table the given $\gamma$ values are saturated values; effective stress is limited at the critical depth $L' = 15D = 6$ m (Das/Meyerhof) for both shaft friction and the tip; $N_q$ for $\phi = 40^\circ$ is read from the Berezantsev curve as about 130 (approximate chart reading); $\alpha = 1.0$ for soft clay ($c < 25$ kPa); factor of safety $= 3$ (not given). Pile area $A_p = 0.1257$ m², perimeter $P = 1.257$ m.

Effective stress

$$\sigma'_v(3\ \text{m}) = 16 \times 3 = 48\ \text{kN/m}^2,\qquad \sigma'_v(6\ \text{m}) = 48 + (16 - 9.81)(3) = 66.57\ \text{kN/m}^2 \ (\text{constant below})$$

Shaft resistance

$Q_s = 37.5 + 113.1 + 483.0 = 633.6$ kN.

End bearing

$$\begin{aligned} q_pN_q &= 66.57 \times 130 = 8654\ \text{kN/m}^2 \\ q_l &= 50N_q\tan\phi = 50(130)\tan 40^\circ = 5454\ \text{kN/m}^2\ (\text{limiting value governs}) \\ Q_p &= 5454 \times 0.1257 = 685.4\ \text{kN} \end{aligned}$$

Capacity

$$Q_u = 633.6 + 685.4 = 1318.9\ \text{kN},\qquad Q_{all} = \frac{1318.9}{3} = 439.6\ \text{kN}$$

Answer: allowable pile load capacity $\approx 440$ kN (ultimate $\approx 1319$ kN). The result depends on the chart value of $N_q$.