The figure below shows a subsoil profile obtained from boring logs$.$ The water table in th upper sand layer is found to be at Elev. $-1\mathrm{.}0$ meter. Additional investigations revealed tha the sand below Elev. $-7\mathrm{.}0$ meters is part of an aquifer and that the water table in this aquife is at Elev. $-3\mathrm{.}0$ meters.

$($a$)$ Determine the initial vertical stress ${}_v$ at point A in the middle of the clay later $($i$.$e$.,$ a Elev. $-6\mathrm{.}0$ meters$).$

$($b$)$ Determine the initial pore water pressure and effective vertical stress ${}_v^{\text{'}}$ at the sam point A$,$ respectively.

$($c$)$ Assuming that the value of coefficient of later stress is $K=0\mathrm{.}5,$ determine the total an effective horizontal tresses at the same point A$.$

$($d$)$ If the water table in the upper sand layer is lowered to Elev. $-3\mathrm{.}0$ meters, what would b the long$-$term vertical effective stress at point A$?$ Assume that the sand above the wate table dries up when the table is lowered.