Question $1_{?}$

$($a$)$ Draw a clear labelled diagram of a falling head permeability test and derive an

expression which enables the coefficient of permeability of a soil to be determined

from the test.

$($b$)$ A falling head permeability test is carried out on a sample of silt $100mm$ in diameter

and $150mm$ in length taken from Site $x.$ If the standpipe diameter is $10mm$ and

water level in the standpipe drops from $1500mm$ to $600mm$ over $2\mathrm{.}5$ minutes,

calculate the coefficient of permeability of the silt in $\frac{m}{s}.$

$($c$)$ A sheet pile wall is driven at Site $x$ to a depth of $5m$ into silt that extends to a depth

of $10\mathrm{.}3m$ below ground level, where there is an impermeable rock stratum. The

depths of water over the ground level are $8\mathrm{.}6m$ on one side of the wall and $1\mathrm{.}7m$

on the other.

$($i$)$ Draw a neat flow net to represent seepage around the sheet pile wall.

$($ii$)$ Calculate the pore pressure at the lower end of the sheet piles.

$($iii$)$ Calculate the quantity of seepage through the silt under the sheet pile wall in

$\frac{m^3}{?}$ day per $m$ run.

$($iv$)$ Determine the exit hydraulic gradient and the factor of safety against piping if

the unit weight of the silt is $18k\frac{N}{m^3}.$