Question

Two footings (one is circular and the other is square) are founded on the surface of a purely cohesionless soil. The diameter of the circular footing is the same as that of the side of the square footing. The ratio between ultimate bearing capacity of circular footing to that of the square footing (using Terzaghi equation) will be:

• A. 1.0
• B. 1.4
• C. 1.3
• D. 0.75

Hint:

For Terzaghi's bearing capacity, shape factors vary with footing geometry: circular footings generally have higher capacity than square footings of same size.

Answer 1

The Correct Option is C

Step 1: State Terzaghi's bearing capacity equation.
For cohesionless soil ($c = 0$): \[q_{ult} = \gamma D_f N_q + 0.5 \gamma B N_\gamma s_\gamma,\] $s_\gamma$ represents the shape factor.

Step 2: Define shape factors.
- Square footing: $s_\gamma = 1.3$.
- Circular footing: $s_\gamma = 1.3 \times 1.3 \approx 1.65$.

Step 3: Calculate the ratio of bearing capacities.
Given that $B$ and $\gamma$ are constant, the ratio is solely determined by the shape factor: \[\frac{q_{ult}(\text{circular})}{q_{ult}(\text{square})} = \frac{1.65}{1.3} \approx 1.27 \approx 1.3.\]

Step 4: Final result.
The ratio is approximately 1.3.