Problem $3[25$ points$]$

Recently, a remolded gray lean clay was tested in the UD Soil Mechanics Laboratory. ${?}^1$ A saturated specimen of the clay $10$ cm in diameter and $2\mathrm{.}5$ cm thick is compressed in an oedometer to a $2\mathrm{.}0$ cm thickness. The initial void ratio $(e_0)$ of the specimen is $1\mathrm{.}15,$ its specific gravity of solids $(G_{})$ is $2\mathrm{.}70,$ and the clay is normally consolidated.

Please do the following:

$($a$)$ Determine the initial saturated unit weight $($in units of $k\frac{N}{m^3}).[5$ points$]$

$($b$)$ Assuming that all compression is produced by a reduction in void ratio and loss of pore fluid, determine the void ratio after compression. $[5$ points$]$

$($c$)$ Determine the saturated unit weight after compression $($in units of $k\frac{N}{m^3}).[5$ points$]$

$($d$)$ Determine the change in moisture content $($i$.$e$.,w)$ caused by the compression $($as a percentage$).[5$ points$]$

$($e$)$ If the vertical effective stress $({}_v^{\text{'}})$ corresponding to $e_0$ is $24\mathrm{.}0$ kPa $,$ and if the compression index $(C_c)$ is equal to $0\mathrm{.}385,$ what is the value of ${}_v^{\text{'}}$ after compression to a thickness of $2\mathrm{.}0$ cm $?[5$ points$]$