Question

It is proposed to drive H-piles up to a depth of 7 m at a construction site. The average surface area of the H-pile is $3{\text{m}}^2$ per meter length. The soil at the site is homogeneous sand, having an effective friction angle of ${32}^{\circ }$. The ground water table (GWT) is at a depth of 2m below the ground surface. The unit weights of the soil above and below the GWT are $16{\text{kN/m}}^3$ and $19{\text{kN/m}}^3$, respectively. Assume the earth pressure coefficient, $K=1.0$, and the angle of wall friciton, $\delta ={23}^{\circ }$. The total axial frictional resistance (in kN, up to one decimal place) mobilized on the pile against the driving is

• A. 390.78

Answer 1

The correct option is A 390.78
(390.8)

Stress at $B$ level $=16\times 2=32{\text{kN/m}}^2$
Average stress in $AB=16{\text{kN/m}}^2$
Axial frictional resistance in
$AB=\left(K{\sigma }_{\text{avg}}\tan \delta \right)A_{AB}$
$A_{AB}=$ Area of AB
$=3\times 2=6{\text{m}}^2$
$=\left(K{\sigma }_{\text{avg}}\tan \delta \right)\times 6$
$=(1\times 16\times \tan {23}^{\circ })\times 6$
$=40.75\text{kN}$
In part $BC$:
Effective vertical stress variation

${\sigma }_{\text{avg}}=\frac{32+77.95}{2}$
$=54.975{\text{kN/m}}^2$
$A_{BC}=3\times 5$
$=15{\text{m}}^2$
Axial frictional resistance in part $BC$
$=\left(K{\sigma }_{\text{avg}}\tan \delta \right)A$
$=(1\times 54.975\times \tan {23}^{\circ })\times 15$
$=350.03\text{kN}$
Total axial frictional resistance
$=350.03+40.75$
$=390.78\text{kN}$