Question

The relationship between the specific gravity of sand (G) and the hydraulic gradient (i) to initiate quick condition in the sand layer having porosity of 30% is

1. G = 0.7i + 1
2. G = 1.43i − 1
3. G = 1.43i + 1
4. G = 0.7i – 1

Answer 1

Correct Answer - Option 3 : G = 1.43i + 1

Concept:

The relation between porosity (n) and voids ratio (e) is given by,

\(n = \frac{e}{{1 + e}}\)

The critical hydraulic gradient is given by,

\(i\; = \frac{{G - 1}}{{1 + e}}\)

Calculation:

n = 0.3

\(\begin{array}{l} e = \frac{n}{{1 - n}} = \frac{{0.3}}{{1 - 0.3}} = \frac{3}{7}\\We \ know \ that\\ i = \frac{{G - 1}}{{1 + e}}\\ \therefore i = \frac{{G - 1}}{{1 + \frac{3}{7}}} \end{array}\)

G - 1 = 1.43i

G = 1.43i + 1