Two footings, one circular and or strip, are founded on surface of a purely Cohesionless soil. Diameter of circular footing and width of strip footing is same. Then, ratio of ultimate bearing capacity of circular to strip footing is:

Concept:

According to Tarzaghi,

Ultimate bearing capacity of circular footing, 

$q_u=1.3C{N}_c+q{N}_q+0.3D\gamma N_{\gamma }$

Ultimate bearing capacity of strip footing, 

$q_u=C{N}_c+q{N}_q+0.5B\gamma N_{\gamma }$

For square footing, ultimate bearing capacity,

qu = 1.3 CNc + γDfNq + 0.4 γBNγ

Where,

C = cohesion 

Nc, Nq, Nγ = Bearing capacity factors

q = overburden pressure = γDf

Df = depth of the footing, B = width of footing, D = diameter of circular footing

γ = unit weight of soil

Calculation:

Given,

D = B

Surface footing ⇒ Df = 0 ⇒ q = 0

Purely cohesionless ⇒ C = 0

$Ratio=\frac{q_{u,circular}}{q_{u,strip}}=\frac{0.3D\gamma N_{\gamma }}{0.5B\gamma N_{\gamma }}=0.60$