A $4\mathrm{.}7-$m thick sand layer overlies a $6\mathrm{.}9-$m thick layer of clay, the water table being at the surface; the permeability of the clay is very low. The saturated unit weight of the sand is $17\mathrm{.}5$ kN$/$m$3$ and that of the clay is $19\mathrm{.}3$ kN$/$m$3.$ A $4\mathrm{.}5-$m thick layer of fill material of unit weight $19\mathrm{.}6$ kN$/$m$3$ is placed on the surface over an extensive area. Determine the effective vertical stress $($in kPa$)$ at the centre of the clay layer many years after the fill has been placed.