Question

The width of a square footing and the diameter of a circular footing are equal. If both the footings are placed on the surface of sandy soil, the ratio of the ultimate bearing capacity of circular footing to that of square footing will be

• A.
  $$\frac{4}{3}$$
• B.
  1
• C.
  $$\frac{3}{4}$$
• D. $$\frac{2}{3}$$

Answer 1

The correct option is C

$$\frac{3}{4}$$
Given ;
width of square footing (B) = diameter of circular footing (D)
$$\text{depth of foundation}\left(D_f\right)=0$$
(Since both footing are place on the surface)
For sandy soil, C = 0
Ultimate bearing capacity of circular footing
$$(q_u{)}_{circular}=1.3C{N}_c+\gamma D_f{N}_q+0.3D\gamma N\gamma$$
$$=0.3D\gamma N\gamma$$
Ultimate bearing capacity of square footing
$$(q_u{)}_{square}=1.3C{N}_c+\gamma D_f{N}_q+0.4\gamma B{N}_{\gamma }$$
$$=0.4B\gamma N\gamma$$
$$\therefore \frac{(q_u{)}_{circular}}{(q_u{)}_{square}}=\frac{0.3D\gamma N\gamma }{0.4B\gamma N\gamma }=\frac{3}{4}(\because B=D)$$