If the footing is in contact with the water table, the reduction in bearing capacity may be as high as:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2015
Detailed Explanation
The γ terms in the bearing capacity equation use the effective unit weight of the soil. Water reduces that effective unit weight through buoyancy.
Why “50%” Is Correct
Since γ′ ≈ γ/2, the most that the water table can reduce the γ terms is to about half. The reduction factor Rw varies between 1 (water table deep) and 0.5 (water table at or above the level considered). So the reduction may be as high as 50%.
| Water table position | Reduction factor on the γ terms | Effect on bearing capacity of sand |
|---|---|---|
| At depth ≥ B below the footing base | 1.0 (no reduction) | None |
| At the footing base | Rw2 = 0.5 for the ½BγNγ term | Reduced |
| At the ground surface | 0.5 for both γDfNq and ½BγNγ | About half (50% reduction) |
Rw = 0.5(1 + zw/B or Dw/Df). The submerged unit weight is roughly half the saturated unit weight, which is why the maximum reduction is about 50%.
Why the Other Options Are Wrong
- A. 25%: 25% is a partial reduction, not the maximum.
- C. 65%: 65% would need γ′ to fall to about a third of γ.
- D. 75%: 75% would need γ′ = γ/4, which is unrealistic.
Key Point
Maximum water table reduction factor = 0.5, i.e. up to 50% loss for sand.
Key Concepts for Students
- R_w2 for the Nγ term = 0.5(1 + z_w/B).
- R_w1 for the Nq term = 0.5(1 + D_w/D_f).
- Cohesive term c·Nc is not reduced by the water table.
Practice more: this is question 36 in Shallow and Deep Foundation MCQs – Part 3. Try the whole set and check every answer instantly.