Question

A single under-reamed pile is to be installed in a hard clay deposit. The undrained strength obtained from a series of vane tests at different depths have shown linear relationship, $C_u=75+5DinkN/m^2$, where 'D' is the depth in metres. The dia of pile shaft and the bulb are 1.5 m & 3 m respectively. The centre of under-ream is located at 10 m from ground surface. The allowable load on the pile to ensure an overall factor of safety 2.5.
$(given\alpha =0.4)$
(Neglect resistance offered by shaft beneath bulb)

• A. 3935 kN
• B. 1743 kN
• C. 6471 kN
• D. 5286 kN

Answer 1

The correct option is A 3935 kN


$D=10m$

$:Givenequation{C}_u=75+5D$

At $D=0m\Rightarrow 75kN/m^2=C_u$

$D=10m\Rightarrow 125kN/m^2=C_u$

$\therefore \text{Average cohesion of shaft}=\frac{75+125}{2}$

$=100kPa$

$Given,d=1.5m,D_u=3m$

$A_b=\frac{\pi }{4}{D}_u^2$

$=\frac{\pi }{4}\times 3^2=7.068m^2$

$A_s=\pi dL=\pi \times 1.5\times 10$

$\therefore A_s=47.124m^2$

$Q_u=f_b{A}_b+f_s{A}_s$

$=C{N}_c{A}_b+\alpha c^{\prime }{A}_s$

$=125\times 9\times 7.068+0.4\times 100\times 47.124$

$Q_u=9836.46kN$

$Q_s=\frac{Q_u}{F}=\frac{9836.46}{2.5}=3934.58$