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

Step 2: Shape factors.
- For square footing: $s_\gamma = 1.3$.
- For circular footing: $s_\gamma = 1.3 \times 1.3 \approx 1.65$.

Step 3: Ratio of bearing capacities.
Since $B$ and $\gamma$ are the same, ratio depends on shape factor only: \[ \frac{q_{ult}(\text{circular})}{q_{ult}(\text{square})} = \frac{1.65}{1.3} \approx 1.27 \approx 1.3. \]

Step 4: Conclusion.
Thus, the ratio is approximately 1.3.