Design pile group for 2000 kN

Given: consolidated clay 16 m deep, $c_u = 30$ kN/m², $\gamma = 22$ kN/m³, load $Q = 2000$ kN, $\alpha = 0.6$, FS $= 3$.

Trial pile: diameter $D = 0.40$ m, length $L = 12$ m (the pile stays in the clay, with 4 m of clay below the tip).

Capacity of one pile

$$\begin{aligned} Q_s &= \alpha c_u\pi DL = 0.6 \times 30 \times \pi(0.4)(12) = 271.4\ \text{kN} \\ Q_p &= 9c_uA_p = 9 \times 30 \times 0.1257 = 33.9\ \text{kN} \\ Q_u &= 305.4\ \text{kN} \end{aligned}$$

Number of piles

$$n = \frac{FS \times Q}{Q_u} = \frac{3 \times 2000}{305.4} = 19.6 \ \Rightarrow\ 20\ \text{piles}$$

Arrange them in a 5 × 4 pattern at spacing $s = 3D = 1.2$ m.

Group check

• Sum of individual piles: $20 \times 305.4 = 6107$ kN.
• Block: $B_g = 3(1.2) + 0.4 = 4.0$ m, $L_g = 4(1.2) + 0.4 = 5.2$ m.

$$Q_{block} = 2(B_g + L_g)Lc_u + 9c_uB_gL_g = 2(9.2)(12)(30) + 9(30)(4.0)(5.2) = 6624 + 5616 = 12\,240\ \text{kN}$$

• Group capacity $=$ the smaller $= 6107$ kN, so $\eta = 1$.
• Allowable group load $= 6107/3 = 2036$ kN $> 2000$ kN. O.K.

Answer: provide 20 piles of 0.40 m diameter and 12 m length in a 5 × 4 group at 1.2 m c/c (allowable load 2036 kN > 2000 kN), joined by a pile cap of about 5.2 m × 4.0 m plus edge distance. Check the settlement of the group.