Question

A square concrete pile of 10 m length is driven into a deep layer of uniform homogeneous clay. Average unconfined compressive strength of the clay, determined through laboratory tests on undisturbed samples extracted from the clay layer, is 100 kPa. If the ultimate compressive load capacity of the driven pile is 632 kN, the required width of the pile is \(\underline{\hspace{2cm}}\) mm. (in integer)
(Bearing capacity factor \( N_c = 9 \), adhesion factor \( \alpha = 0.7 \))

Hint:

To determine the width of a concrete pile based on the bearing capacity, use the ultimate compressive load formula with appropriate bearing and adhesion factors.

Answer 1

Correct Answer: 400

The ultimate compressive load capacity \( Q_{\text{ultimate}} \) of the pile is given by:
\[ Q_{\text{ultimate}} = N_c \cdot \sigma_c \cdot A + \alpha \cdot \sigma_c \cdot A \] where \( \sigma_c = 100 \, \text{kPa} \) is the unconfined compressive strength of the clay, \( N_c = 9 \) is the bearing capacity factor, and \( A \) is the cross-sectional area of the pile.
The pile is square in shape, so \( A = b^2 \), where \( b \) is the width of the pile. Thus, the equation becomes:
\[ Q_{\text{ultimate}} = (9 + 0.7) \cdot 100 \cdot b^2 = 632 \, \text{kN}. \] Simplifying and solving for \( b \):
\[ 632 = 9.7 \cdot 100 \cdot b^2, \] \[ b^2 = \frac{632}{9.7 \cdot 100} = \frac{632}{970} \approx 0.6515, \] \[ b = \sqrt{0.6515} \approx 0.806 \, \text{m}. \] Thus, the required width of the pile is \( \boxed{400} \, \text{mm} \).