Question

The ultimate load capacity of a $10\text{m}$ long concrete pile of square cross-section $500\text{mm}\times 500\text{mm}$ driven into a homogeneous clay layer having undrained cohesion value of $40\text{kPa}$ is $700\text{kN}$. If the cross-section of the pile is reduced to $250\text{mm}\times 250\text{mm}$ and the length of the pile is increased to $20\text{m}$, the ultimate load capacity will be

• A. $350\text{kN}$
• B. $632.5\text{kN}$
• C. $722.5\text{kN}$
• D. $1400\text{kN}$

Answer 1

The correct option is B $632.5\text{kN}$

Ultimate load capacity = Ultimate bearing capacity $\times$ Area
At first condition,
$700=q_u\times A_{\text{base}}+q_{\text{fs}\times A_{\text{surface}}}$
$=C{N}_c\times 0.5\times 0.5+\alpha C_u\times \text{perimeter}\times L$
$700=40\times 9\times 0.5\times 0.5+\alpha \times 40\times 4\times 0.5\times 10$
$\alpha =0.763$
Second condition
When cross section of pile is reduced to $0.25\text{m}\times 0.25\text{m}$ and length is increased to $20\text{m}$
Ultimate load capacity = Ultimate bearing capcity $\times$ Area $=q_u\times A_b+q_{\text{fs}}\times A_s$
$=C{N}_c\times 0.25\times 0.25+\alpha C_u\times \text{perimeter}\times L$
$=40\times 9\times 0.25\times 0.25+0.763\times 40\times 4\times 0.25\times 20$
$=632.5\text{kN}$