A uniform collapsible sand stratum, 2.5 m thick, has specific gravity of its sand as 2.65, with a natural void ratio of 0.65. The hydraulic head required to cause quick collapsible sand condition is

Concept:

The quick collapsible sand condition will occur when hydraulic gradient under given conditions become critical hydraulic gradient and critical hydraulic gradient, icr is given by,

$i_{cr}=\frac{G-1}{1+e}$

Where G = specific gravity of soil solids and e = void ratio

Calcutation:

Given, H = 2.5 m, G = 2.65; e =0.65

$i_{cr}=\frac{2.65-1}{1+0.65}=1$

Further, critical hydraulic gradient is the head loss per unit length of flow or total head available under critical conditions and it is given by:

${\mathrm{i}}_{\mathrm{c}\mathrm{r}}=\frac{\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}\left(\mathrm{h}\right)}{\mathrm{T}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{d}\left(\mathrm{H}\right)}$

$1=\frac{\mathrm{h}}{2.5}$

h = 2.5 m

∴ The hydraulic head required to cause quick collapsible sand condition is 2.5 m.