Spacing of nine piles for efficiency 1

Given: 9 piles (3 × 3, square pattern), $d = 0.30$ m, $L = 12$ m, $q_u = 75$ kN/m² so $c_u = 37.5$ kN/m². Point bearing is neglected, and the efficiency is to be 1. The adhesion factor is not given, so $\alpha = 1.0$ is assumed.

For efficiency $= 1$, block capacity = sum of individual pile capacities (skin friction only).

Individual piles

$$\sum Q_u = 9\,\alpha c_u\pi dL = 9 \times 1.0 \times 37.5 \times \pi \times 0.3 \times 12 = 3817.0\ \text{kN}$$

Block

$$Q_{block} = 4B_g\,L\,c_u = 4 \times B_g \times 12 \times 37.5 = 1800\,B_g$$

Equate

$$\begin{aligned} 1800\,B_g &= 3817.0 \Rightarrow B_g = 2.12\ \text{m} \\ B_g &= 2s + d \Rightarrow s = \frac{2.12 - 0.30}{2} = 0.91\ \text{m} \end{aligned}$$

Thus $s/d = 3.0$. In general $B_g = \dfrac{9\alpha\pi d}{4}$.

Answer: centre-to-centre spacing $\approx 0.91$ m ($\approx 3d$) for an efficiency of 1.