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