$.$ A site is underlain by an $8$m thick clay layer with void ratio $=1.$ Rock lies below the clay layer. The water table is located at the ground surface. The consolidation parameters of mid$-$layer sample are: coefficient of consolidation $=0\mathrm{.}018$ m$^2/$day$,$ compression index $=0\mathrm{.}3,$ recompression index $=0\mathrm{.}02,$ and preconsolidation stress $=50$ kPa. A $3$m fill with unit weight $=17$ kN$/$m$^3$ will be placed on the ground surface. Find the ultimate consolidation settlement of the clay layer. Make sure to draw the generic consolidation curve and mark the relevant stresses with arrows.