Question

If \( \gamma \) is the unit weight of soil, \( D_f \) is the depth of foundation, and \( F \) is the factor of safety, the difference in gross safe bearing capacity and net safe bearing capacity is expressed as ............

• A. \( \gamma D_f \)
• B. \( 0.5 \gamma D_f \)
• C. \( \frac{\gamma D_f}{F} \)
• D. \( \frac{0.5(\gamma D_f)}{F} \)

Hint:

Gross bearing capacity includes overburden pressure; subtracting it gives the net safe bearing capacity which is more useful for design purposes.

Answer 1

The Correct Option is A

The gross safe bearing capacity (q\_safe(gross)) is the total pressure that can be safely applied at the base of the foundation,
while the net safe bearing capacity (q\_safe(net)) is the gross capacity minus the pressure due to the overburden (soil above the foundation base).
The pressure due to overburden (also called surcharge) is given by: \[ q = \gamma D_f \] where:
- \( \gamma \) = unit weight of soil
- \( D_f \) = depth of foundation
Hence, \[ q_{\text{safe(gross)}} - q_{\text{safe(net)}} = \gamma D_f \] This is the additional pressure exerted by the soil above the foundation level, and it must be subtracted from the gross bearing capacity to obtain the net value.
So, the correct answer is \( \boxed{\gamma D_f} \).