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

Step 1: Find the void ratio from the saturation condition.
For a fully saturated soil, the degree of saturation S=1 (i.e. 100%), and the relation between water content w, specific gravity Gs, void ratio e, and S is
\[ S\,e = w\,G_s \]
Since S=1, this becomes \( e = w G_s \). Here w = 20% = 0.20 and Gs = 2.65, so
\[ e = 0.20 \times 2.65 = 0.53 \]

Step 2: Recall the critical hydraulic gradient formula.
Quicksand occurs when the upward seepage force on the soil grains equals their submerged weight, at which point the effective stress becomes zero. The hydraulic gradient at which this happens is called the critical hydraulic gradient, given by
\[ i_c = \frac{G_s-1}{1+e} \]
This comes directly from equating the submerged unit weight of soil, \( \gamma' = \dfrac{(G_s-1)\gamma_w}{1+e} \), with the seepage force per unit volume, \( i_c \gamma_w \), and solving for ic.

Step 3: Substitute the values.
\[ i_c = \frac{2.65-1}{1+0.53} = \frac{1.65}{1.53} \]
\[ i_c = 1.0784 \]

Final Answer:
Rounded to two decimal places, the critical hydraulic gradient is 1.08.
\[ \boxed{i_c \approx 1.08} \]