Question

Which one of the following equations correctly gives the relationship between the specific gravity of soil grains (G) and the hydraulic gradient (i) to initiate 'quick' condition in sand having a void ratio of 0.5?
1. G = 0.5i + 1
2. G = i + 0.5
3. G = 1.5i + 1
4. G = 1.5i - 1

Answer 1

Correct Answer - Option 3 : G = 1.5i + 1

Concept:

Quick sand condition:

(i) This process in which soil particles are lifted over the soil mass is called quick sand condition. It is also known as 'boiling of sand' as the surface of sand looks it is boiling.

(ii) At quick sand condition, net effective stress is reduce to zero, i.e.

σ̅  = 0

∴ γ'z = p_s = 0     {p_s = Seepage pressure}

or, γ'z - izγ_w = 0

i = i_cr = γ'/γ_w

(iii) The hydraulic gradient inder which quick sand condition occurs is termed as critical hydraulic gradient. If void ratio and specific gravity of soil is known, then

\(i = {i_{cr}} = \frac{{\gamma '}}{{{\gamma _w}}} = \frac{{\frac{{\left( {G - 1} \right){\gamma _w}}}{{1 + e}}}}{{{\gamma _w}}}\)  

⇒ \(i = \frac{{\left( {G - 1} \right)}}{{1 + e}}\)

Calculation:

Given,

Void ratio (e) = 0.5

∵ We know that, \(i = \frac{{\left( {G - 1} \right)}}{{1 + e}}\)

⇒ \(i = \frac{{\left( {G - 1} \right)}}{{1 + 0.5}}\)

1.5i = G - 1

G = 1.5i + 1