Pile groups

A pile’s shaft and toe resistances give its ultimate capacity and, from it, the group’s. Units, symbols and assumptions are set out in Method and assumptions.

A single pile

The pile’s ultimate capacity is $Q_u = Q_s + Q_p$. A pile on its own must have $\mathrm{FS} = Q_u/Q \ge 3.0$. In a group, $Q_u$ is not checked by itself: it is the base of the group’s capacity.

The group: piles or block

A group of $n = n_x n_y$ piles can fail in two ways, and the weaker governs:

• As individual piles, each one reaching its own $Q_u$: $n \, Q_u$.
• As a block: the piles and the soil between them, as one large pile bounded by the outer faces of the outer piles, $B_g = (n_x - 1)\,s + D$ by $L_g = (n_y - 1)\,s + D$, with perimeter $p_g = 2(B_g + L_g)$ and toe area $A_g = B_g L_g$.

The block’s capacity, $Q_{block}$, is calculated like a pile’s, with $p_g$ and $A_g$ in place of $p$ and $A_p$, and with the block’s smaller side, $\min(B_g, L_g)$, in place of $D$ in $z_c = 15D$ and in the 0.3 m rule for $K$. Its sides are soil against soil, so $\alpha = 1$ in clay ($f_s = c_u$) and $\delta = \phi'$ in sand. Its toe in sand bears like a pile’s.

The block’s toe in clay

In clay, the block’s toe is a deep rectangular footing: Skempton’s factor, as Das & Sivakugan take it for block failure, in place of a pile’s 9,

$$N_c^{\ast} = 5\left(1 + 0.2\,\frac{L}{B_g}\right)\left(1 + 0.2\,\frac{B_g}{L_g}\right), \qquad \frac{L}{B_g} \le 2.5$$

with $L$ the length of the piles and $B_g \le L_g$ the sides of the block: 9 for a deep square block, 7.5 for a long one.

Efficiency: which one governs

The group efficiency is $\eta = Q_{block}/(n \, Q_u)$, and the group’s capacity is $Q_g = \min(\eta, 1) \, n \, Q_u$: the smaller of $n \, Q_u$ and $Q_{block}$. With $\eta \le 1$ block failure governs; with $\eta > 1$, the individual piles do. The group must have $\mathrm{FS} = Q_g/Q \ge 3.0$.