$2-$ A level site has the following soil profile:

$0-3$m Dry gravel $$d $=16$kN$/$m$3$

$3-5$m Dry sand $$d $=14$kN$/$m$3$

$5-8$m Dry clay $$d $=17$kN$/$m$3$

$8$m $+$ Rock

The following construction sequence is then carried out. The uppermost $2$m of gravel is

excavated and a very large diameter oil storage tank is built at the new surface. The depth of oil

in the tank is $6$m and the specific gravity of the oil is $0\mathrm{.}8.$ The mass of steel in the tank is

negligible compared to the mass of oil in the tank. Determine the change in vertical stress caused

by construction at the bottom of the clay layer.