Example $7\mathrm{.}8$: A saturated soil has a compression index of $0\mathrm{.}25.$ Its void ratio at a stress of

$10k\frac{N}{m^2}$ is $2\mathrm{.}02$ and its permeability is $3\mathrm{.}4{10}^{-7}m\frac{m}{s}.$ Compute:

$($i$)$ Change in void ratio if the stress is increased to $19k\frac{N}{m^2}$;

$($ii$)$ Settlement in $($i$)$ if the soil stratum is $5$ m thick; and

$($iii$)$ Time required for $40\%$ consolidation if drainage is one$-$way.