A sand lying below a masonry dam has a porosity of 40% and a specific gravity of 2.67. The maximum permissible upward gradient, if a factor of safety of 4 is considered, will be
- A0.50
- B0.75
- C1.00
- D0.25Correct
Solution
Concept
Critical gradient and factor of safety against piping
Formula
ic = (G − 1)/(1 + e), e = n/(1 − n), ipermissible = ic / FS
Step-by-step solution
1. e = n/(1 − n) = 0.40/0.60 = 0.667. 2. ic = (G − 1)/(1 + e) = 1.67/1.667 = 1.0. 3. Permissible gradient = ic / FS = 1.0 / 4 = 0.25.
Explanation
Piping or boiling occurs when the upward gradient reaches the critical value. For safety, the gradient allowed is the critical gradient divided by the factor of safety.
Shortcut
ic ≈ 1 for sands. Permissible = 1/FS.
Common mistake
Reporting the critical gradient without dividing by the FS.
Correct answer: D) 0.25