c$)$ A constant$-$head permeameter test has been run on a sand sample $250mm$ in length and $2000m{m}^2$ in area. With a head$-$loss of $400mm,$ the discharge was found to be $260ml$ in $130$ seconds.

i$)$ Determine the coefficient of permeability of the soil. $(3$ marks$)$

ii$)$ If the specific gravity of the grains was $2\mathrm{.}65$ and the dry weight of the sand $925\mathrm{.}0g,$ find the void ratio of the sample.

$(3$ marks$)$

d$)$ Discuss the difficulties of estimating the site value for the coefficient of permeability of a soil in laboratory tests.

$(8$ marks$)$