Question

A circular concrete pile of 3 m diameter carries a gross load of 4000 kN. The supporting soil is a clayey sand having the following properties : $C=5kN/m^2,\varphi ={30}^{0}and\gamma =18.5kN/m^3$. Find the depth at which the pier is to be located such that a factor of safety 3.0 (in m).
Bearing capacity factor for $\varphi ={30}^{0}are{N}_c=30.1,N_q=18.4$ & $N_{\gamma }=22.4$

• A. 2 m
• B. 2.5 m
• C. 3 m
• D. 1.5 m

Answer 1

The correct option is C 3 m

Given
Circular footing

$B=3m,Q_g=4000kN,C=5k{P}_a$

$For\varphi ={30}^0\to N_c=30.1,N_q=18.4,N_{\gamma }=22.4$

$\gamma =18.5kN/m^3$

$\therefore q\le q_s$

$\therefore q=\frac{q_{nu}}{F}+\gamma D$

For circle
$q_u=1.3C{N}_c+\gamma D{N}_q+0.3\gamma B{N}_{\gamma }$
$=1.3C{N}_c+\gamma D(N_q-1)+0.3\gamma B{N}_{\gamma }$

$\therefore q=\frac{q_{nu}}{F}+\gamma D$

$=\frac{4000}{\frac{\pi }{4}\times 3^2}=\frac{1.3\times 5\times 30.1+18.5\times D\times (18.4-1)+0.3\times 18.5\times 3\times 22.4}{3}+18.5\times D$

565.88 = 189.536 + 107.3 D +18.5 D

$D=2.99m\approx 3m$