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From a flow-net diagram drawn under a concrete dam, following information are obtained: (i) The head difference between upstream and downstream side of the dam is 9 m. (ii) The total number of equipotential drops between upstream and downstream side of the dam is 10. (iii) The length of the field nearest to the toe of the dam in the downstream side is 1 m.
If the soil below the dam is having a saturated unit weight of 21 kN/m³ and unit weight of water is 9.81 kN/m³, then the factor of safety against the quick condition will be _____ (round off to two decimal places).
- 1.00
- 1.15
- 1.25
- 1.35
Correct answer: 1.25
Solution
Critical hydraulic gradient i_c = (gamma_sat - gamma_w)/gamma_w = (21-9.81)/9.81 = 1.14. Exit gradient i_e = head loss per drop / field length = (9/10)/1 = 0.9. Factor of safety = 1.14/0.9 = 1.27, closest to 1.25 (index 2), not 1.15.
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