Question

Two footings, one circular and the other square, are founded on the surface of a purely cohesionless soil. The diameter of the circular footing is same as that of the side of the square footing. The ratio of their ultimate bearing capacities is

• A. $\frac{3}{4}$
• B. $\frac{4}{3}$
• C. 1.0
• D. 1.4

Answer 1

The correct option is A $\frac{3}{4}$

Given,
c = 0
$D_f=0$, (Because footing is surface footing)
D = B
$q=\gamma D_f=0$

For circular footing
$q_{uc}=1.3c{N}_c+q{N}_q+0.3D\gamma N_{\gamma }=0.3D\gamma N_{\gamma }$ ... (i)
For square footing
$q_{us}=1.3c{N}_c+q{N}_q+0.4B\gamma N_{\gamma }=0.4B\gamma N_{\gamma }$ ...(ii)
From (i) & (ii)

$\frac{q_{uc}}{q_{us}}=\frac{0.3D\gamma N_{\gamma }}{0.4B\gamma N_{\gamma }}=\frac{3}{4}$