$3.$ The average effective overburden pressure within a $4$ m thick normally consolidated and twoway drained clay layer at a site is $80$ kN$/$m$2.$ The void ratio and the compression index of the clay are $0\mathrm{.}72$ and $0\mathrm{.}5,$ respectively. The coefficient of consolidation of the clay is $2\mathrm{.}5$ m$2/$year$.$ A proposed building at the site is expected to increase the average vertical stress at the clay layer by $50$ kN$/$m$2.(5$ marks$)($a$)$ determine the expected primary consolidation settlement $($b$)$ it is proposed to apply precompression through application of a total surcharge of $60\mathrm{.}0$ kN$/$m$2$ before the construction of the proposed building. For how long should the surcharge be applied sot that there is no more primary consolidation settlement on the removal of the surcharge? $($c$)$ Due to the time constraints, it is required to limit the preloading period to $6$ months. What should be the surcharge pressure that would eliminate the primary consolidation settlements beyond the preloading period