Question

A fully saturated sandy soil deposit has water content 20 % and specific gravity 2.65.
The critical hydraulic gradient for seepage through the soil to create the quicksand condition is ______ (rounded off to two decimal places).

Hint:

Find void ratio from e=wGs (since S=1), then use ic=(Gs-1)/(1+e).

Answer 1

Correct Answer: 1.08

Instead of jumping straight to the standard formula, build it up from the physical picture of quicksand: it happens when the upward drag force of water flowing through the soil exactly cancels the submerged weight of the soil grains, so the effective stress between grains drops to zero and the soil behaves like a liquid.

1. Get the void ratio first: for a saturated soil, all the void space is filled with water, so the volume of water per unit volume of solids equals $wG_s$, from the phase relation $Se = wG_s$ with $S=1$. With $w=0.20$ and $G_s=2.65$, $e = 0.20 \times 2.65 = 0.53$.
2. Write the submerged (buoyant) unit weight: $\gamma' = \dfrac{(G_s-1)}{1+e}\gamma_w$. This represents the net downward weight per unit volume of soil once the buoyant push of water is subtracted out.
3. Set the seepage force equal to the submerged weight: the upward seepage force per unit volume at gradient i is $i\gamma_w$. Quicksand starts exactly when this force cancels $\gamma'$, so at the critical gradient $i_c\gamma_w = \gamma' = \dfrac{(G_s-1)}{1+e}\gamma_w$, and the $\gamma_w$ cancels from both sides, leaving $i_c = \dfrac{G_s-1}{1+e}$.

Now plug in numbers: $i_c = \dfrac{2.65-1}{1+0.53} = \dfrac{1.65}{1.53} = 1.0784$.

Let's summarize:

• Saturation condition gives $e = wG_s = 0.53$.
• Quicksand happens when seepage force equals submerged weight, giving $i_c = (G_s-1)/(1+e)$.

The critical hydraulic gradient works out to about $1.08$.