# If e represents the void ratio of the soil and G is its specific gravity, the critical gradient is:

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If e represents the void ratio of the soil and G is its specific gravity, the critical gradient is:
1. G +1 / 1 - e
2. G + 1 / 1 + e
3. G - 1 / 1 - e
4. G - 1 / 1 + e

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Correct Answer - Option 4 : G - 1 / 1 + e

Explanation:

Void ratio of soil mass = e

specific gravity of soil mass = G

The hydraulic gradient under which quick sand condition occurs is termed as critical hydraulic gradient. If void ratio and specific gravity of soil is known.

$i_{cr} = \dfrac{\gamma'}{\gamma_w}=\dfrac{\dfrac{(G-1)}{1+e}\gamma_w}{\gamma_w}$

$i_cr = \dfrac{G-1}{1+e}$

Quick Sand condition:

If the seepage pressure is such that it equals the submerged weight of the soil mass, then effective stresses at that location reduced to zero.

Under such condition cohesionless soil mass loses all shear strength. Now soil mass has a tendency to move also with the flowing water in the upward direction. This process in which soil particles are lifted over the soil mass is called quick sand condition or boiling of sand.