Example Problems

A square concrete pile ($0.4m \times 0.4m$) is driven 15m deep into a homogeneous clay layer with an undrained shear strength $c_u = 100 \, kPa$. Calculate the theoretical ultimate capacity ($Q_u$). Assume an adhesion factor $\alpha = 0.5$ and a bearing capacity factor $N_c^* = 9$.

Example Problem 2: A group of 9 friction piles ($3 \times 3$ arrangement) is driven into a soft clay. Each pile is $0.4 \, m$ in diameter and $15 \, m$ long. The spacing is $1.2 \, m$. The undrained shear strength of the clay is $40 \, kPa$, and the adhesion factor is $0.8$. Calculate the ultimate load-carrying capacity of the pile group. Neglect end-bearing.

Example Problem 3: A concrete pile is driven into a sandy soil. The rated energy of the hammer is $45 \, kN \cdot m$. The final penetration resistance is $5 \, mm/blow$. Assuming an efficiency of $0.80$ and an elastic compression loss of $2.5 \, mm$, estimate the ultimate bearing capacity of the pile using the dynamic formula.