Question

Consider the following statements:

1. The ultimate bearing capacity of a footing on sand increases with an increases in its width.

2. The settlement of the footing on sand increases with increase in its width.

Which of the above statements are correct?

1. 1 only
2. Both 1 and 2
3. 2 only
4. Neither 1 nor 2

Answer 1

Correct Answer - Option 2 : Both 1 and 2

Concept:

For a plate load test for sands.

\({q_f} = {q_p} \times \frac{{{B_f}}}{{{B_p}}}\)

Where,

q_f = ult bearing capacity of footing

q_p = ult. Bearing capacity of plate.

B_f, B_p = width of footing & plate respectively so

q_f ∝ B_f

⇒ Ultimate bearing capacity of a footing on sand increases with increase in its width.

Settlement of footing (S_f) on sand increases with increase in width (B_f), can be explained as

\(\frac{{{S_{{f_1}}}}}{{{S_p}}} = {\left[ {\frac{{{B_{{f_1}}}\left( {{B_p} + 0.3} \right)}}{{{B_p}\left( {{B_{{f_1}}} + 0.3} \right)}}} \right]^2}\)  (for 1^st footing)

\(\frac{{{S_{{f_2}}}}}{{{S_p}}} = {\left[ {\frac{{{B_{{f_1}}}\left( {{B_p} + 0.3} \right)}}{{{B_p}\left( {{B_{{f_2}}} + 0.3} \right)}}} \right]^2}\)  (for 2^nd footing)

\(\therefore \frac{{{S_{{f_1}}}}}{{{S_{{f_2}}}}} = {\left[ {\frac{{{B_{{f_1}}}\left( {{B_{{f_2}}} + 0.3} \right)}}{{{B_{{f_2}}}\left( {{B_{{f_1}}} + 0.3} \right)}}} \right]^2} = {\left( {\frac{{1 + \frac{{0.3}}{{{B_{{f_2}}}}}\;}}{{1 + \frac{{0.3}}{{{B_{{f_1}}}}}}}} \right)^2}\)

If \({B_{{f_2}}} > {B_{{f_1}}}\;;\;\frac{{{S_{{f_1}}}}}{{{S_{{f_2}}}}} < 1\) 

∴  \({S_{{f_2}}} > {S_{{f_1}}}\)

Hence settlement increases.