Pile group 16 piles, 0.40 m, soft clay

Given: 16 piles (4 × 4), $D = 0.40$ m, $L = 12$ m, $c_u = 35$ kPa, spacing $s = 0.80$ m (c/c, $= 2D$), $\alpha = 0.8$, FoS $= 2.5$.

1. Individual pile

$$\begin{aligned} A_p &= \frac{\pi}{4}(0.4)^2 = 0.1257\ \text{m}^2,\quad P = \pi(0.4) = 1.257\ \text{m} \\ Q_s &= \alpha c_uPL = 0.8 \times 35 \times 1.257 \times 12 = 422.2\ \text{kN} \\ Q_p &= 9c_uA_p = 9 \times 35 \times 0.1257 = 39.6\ \text{kN} \\ Q_u &= 461.8\ \text{kN} \end{aligned}$$

Sum of 16 piles $= 16 \times 461.8 = 7389.0$ kN.

2. Block failure

$$\begin{aligned} B_g = L_g &= 3(0.8) + 0.4 = 2.8\ \text{m},\quad P_g = 4(2.8) = 11.2\ \text{m} \\ Q_{block} &= P_gLc_u + 9c_uB_gL_g \\ &= 11.2 \times 12 \times 35 + 9 \times 35 \times 2.8^2 \\ &= 4704.0 + 2469.6 = 7173.6\ \text{kN} \end{aligned}$$

3. Group capacity

The block capacity (7173.6 kN) is smaller than the sum of individual piles (7389.0 kN), so the block failure governs. Efficiency $= 7173.6/7389.0 = 0.97$.

$$Q_{all} = \frac{7173.6}{2.5} = 2869.4\ \text{kN}$$

Answer: allowable load of the pile group $\approx 2869$ kN.