Allowable load of 4×4 pile group, layered sand

Given: 16 driven concrete piles (4 × 4), $B = 0.40$ m, spacing $2.5B = 1.0$ m, FOS $= 2.5$, critical depth $D_{cr} = 12B = 4.8$ m, water table at ground level. Layers: loose sand 0–3 m ($\gamma = 16$, $\phi = 30^\circ$); medium dense sand 3–9 m ($\gamma_{sat} = 19$, $\phi = 35^\circ$); dense sand 9–14 m ($\gamma_{sat} = 20$, $\phi = 40^\circ$). The pile length is 14 m.

Assumptions: the given $\gamma$ values are saturated unit weights, $\gamma_w = 9.81$ kN/m³; concrete pile $\delta = 0.75\phi$; $K = 1$ (loose), $1.5$ (medium dense, interpolated) and $2$ (dense); $N_q$ for $\phi = 40^\circ$ is read from the Berezantsev curve as about 130 (an approximate chart reading). Effective stress is constant below $D_{cr}$.

Effective stresses

$\gamma' = 6.19,\ 9.19,\ 10.19$ kN/m³ for the three layers.

$$\sigma'_v(3\text{ m}) = 6.19 \times 3 = 18.57,\qquad \sigma'_v(D_{cr}) = 18.57 + 9.19 \times 1.8 = 35.11\ \text{kN/m}^2$$

Shaft friction ($Q_s = K\sigma'_{avg}\tan\delta\,P\,\Delta L$, $P = \pi \times 0.4 = 1.257$ m)

$Q_s = 451.2$ kN.

End bearing

$$\begin{aligned} q' &= 35.11\ \text{kN/m}^2 \ (\text{at } D_{cr}) \\ q_p &= q'N_q = 35.11 \times 130 = 4564.6\ \text{kN/m}^2 \le 50N_q\tan\phi = 5454\ \text{kN/m}^2 \\ Q_p &= 4564.6 \times 0.1257 = 573.6\ \text{kN} \end{aligned}$$

Capacity

$$\begin{aligned} Q_u &= 451.2 + 573.6 = 1024.8\ \text{kN} \\ Q_{all} &= \frac{1024.8}{2.5} = 409.9\ \text{kN per pile} \end{aligned}$$

For driven piles in sand at 2.5B spacing the group efficiency is taken as $\eta = 1$ (soil is compacted), so

$$Q_{g,all} = 16 \times 409.9 = 6559\ \text{kN}$$

Answer: allowable load of the group $\approx 6560$ kN (410 kN per pile). If the conservative Converse–Labarre efficiency ($\theta = 21.8^\circ$, $\eta = 0.637$) were used, the group value would be about 4176 kN.