A $3 \times 3$ square group of 9 identical friction piles is driven into deep clay. Each pile has an ultimate individual capacity ($Q_{single}$) of $400 \text{ kN}$. The spacing ($s$) between pile centers is 3 times the pile diameter ($d$). Using a simplified block failure analysis, the geotechnical engineer determines the group capacity acting as a single large block ($Q_{block}$) is $2800 \text{ kN}$. Determine the design capacity of the pile group and its efficiency.

A 15 m long precast concrete pile ($0.4 \text{ m} \times 0.4 \text{ m}$ square cross-section) is driven entirely into a uniform layer of saturated clay. The clay has an undrained shear strength ($s_u$) of $80 \text{ kPa}$. The adhesion factor ($\alpha$) is estimated to be 0.55. The bearing capacity factor $N_c^*$ for deep foundations is 9. Calculate the ultimate load capacity ($Q_u$) of the pile.

A 12 m long circular steel pipe pile (diameter $D = 0.5 \text{ m}$) is driven into a deep deposit of medium dense sand. The water table is deep. The sand has a unit weight of $18.5 \text{ kN/m}^3$ and $\phi' = 35^\circ$. Assume the unit skin friction ($f_s$) increases linearly to the pile tip. Use $K = 1.2$, $\delta = 25^\circ$, and $N_q^* = 40$. Estimate the ultimate capacity ($Q_u$).

A drop hammer is used to drive a timber pile. The hammer weight ($W_R$) is $25 \text{ kN}$, and the drop height ($h$) is $1.2 \text{ meters}$. The pile is driven until the final set ($S$, average penetration per blow for the last few blows) is $5 \text{ mm/blow}$ ($0.005 \text{ m/blow}$). Using the Engineering News Record (ENR) formula with $C = 0.0254 \text{ m}$ (for drop hammers) and a Factor of Safety of 6.0, determine the allowable pile capacity ($Q_{allow}$).

A bridge abutment was supported on steel H-piles driven through a $6 \text{ m}$ layer of soft, highly compressible organic clay, terminating in a dense gravel bearing layer.

A new commercial pier was planned in a coastal estuary. The soil profile consisted of loose sands overlying soft silts.