A straight drilled shaft with a diameter ($D$) of $1.0 \text{ m}$ and a length ($L$) of $15 \text{ m}$ is constructed in a uniform deposit of medium dense sand. The unit weight of the sand is $\gamma = 18 \text{ kN/m}^3$ and $\phi' = 32^\circ$. The water table is very deep. Using the $\beta$-method, assume an average $\beta = 0.40$ along the shaft and $N_q^* = 30$. Calculate the ultimate capacity ($Q_u$). Ignore the critical depth limitation for simplicity.

The drilled shaft from the previous example (sand) carries a working load of $Q_{working} = 3000 \text{ kN}$. It is estimated that $2200 \text{ kN}$ is carried by skin friction and $800 \text{ kN}$ is carried by end bearing. The shaft is made of concrete ($E_c = 25 \times 10^6 \text{ kPa}$), area $A = 0.785 \text{ m}^2$, length $L = 15 \text{ m}$. Calculate the elastic shortening of the shaft ($s_1$). Assume the skin friction distribution is uniform ($\alpha_s = 0.5$).

A drilled shaft ($D = 1.0 \text{ m}$) is subjected to a lateral load ($H$) at the ground surface. The shaft is embedded in a cohesive soil ($s_u = 100 \text{ kPa}$). According to Broms' simplified method for cohesive soils, the ultimate lateral resistance of the soil is assumed to be zero from the surface to a depth of $1.5D$, and then uniform at $9 s_u$ below that depth. Calculate the lateral resisting pressure provided by the soil at a depth of $3.0 \text{ m}$.

A high-rise building is being constructed in an area with a high groundwater table and a thick layer of loose, caving sands.

During the construction of a large drilled shaft for a bridge pier, the concrete supply truck was delayed by traffic for nearly two hours while the tremie pour was halfway completed.