Question

From a flow-net diagram drawn under a concrete dam, the following information is 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 on the downstream side is 1 m.
If the soil below the dam is having a saturated unit weight of 21 kN/m\(^3\) and the unit weight of water is 9.81 kN/m\(^3\), then the factor of safety against the quick condition will be __________ (round off to two decimal places).

Hint:

To assess piping safety in soil under hydraulic structures, use \( {FOS} = i_c / i_{{exit}} \) with exit gradient from flow net geometry.

Answer 1

The factor of safety (FOS) against quick condition is given by: \[ {FOS} = \frac{i_c}{i_{{exit}}} \] Where,
\[ i_{{exit}} = \frac{\Delta h}{N_d \cdot L} = \frac{9}{10 \cdot 1} = 0.9 \] \[ i_c = \frac{\gamma'}{\gamma_w} = \frac{21 - 9.81}{9.81} = \frac{11.19}{9.81} \approx 1.14 \] \[ {FOS} = \frac{1.14}{0.9} \approx 1.27 \] Thus, the factor of safety against the quick condition is \( \boxed{1.27} \).