Pile spacing for 100% efficiency, 16 piles

Given: 16 square piles in a 4 × 4 group, side $b = 0.30$ m, $L = 12$ m, soft clay, $\alpha = 0.8$. The value of $c_u$ is not legible, but it cancels out, as both the individual and block capacities are proportional to $c_u$. Point bearing and skin friction are both considered.

For 100% efficiency, block capacity = sum of individual pile capacities.

Individual pile

$$\begin{aligned} Q_u &= \alpha c_u(4bL) + 9c_ub^2 \\ &= c_u\left[0.8(4)(0.3)(12) + 9(0.3)^2\right] \\ &= c_u(11.52 + 0.81) = 12.33\,c_u \end{aligned}$$

Sum for 16 piles $= 16 \times 12.33\,c_u = 197.28\,c_u$.

Block of side $B_g$ (square)

$$Q_{block} = c_u(4B_g)L + 9c_uB_g^2 = c_u\left(48B_g + 9B_g^2\right)$$

Equate

$$\begin{aligned} 9B_g^2 + 48B_g - 197.28 &= 0 \\ B_g &= \frac{-48 + \sqrt{48^2 + 4(9)(197.28)}}{2(9)} = 2.721\ \text{m} \end{aligned}$$

For a 4 × 4 group $B_g = 3s + b$:

$$s = \frac{2.721 - 0.30}{3} = 0.807\ \text{m}$$

Answer: centre-to-centre spacing of piles $\approx 0.81$ m ($\approx 2.7b$) for 100% efficiency. A larger spacing also gives an efficiency of 100%.