Problem $1)$ A foundation is to be constructed at a site where the soil profile is as shown in the figure below. The base of the foundation, which measures $2$ m each side, exerts a total load $($weight of structure, foundation, and soil surcharge on the foundation$)$ of $1000$ kN$.$ The initial void ratio $($e$)$ in situ of the normally consolidated clay layer is $1\mathrm{.}058,$ and its compression index $($Cc$)$ is $0\mathrm{.}60.$ Using both Boussinesq $($center$)$ and the $2$:$1$ Method, find the estimated primary consolidation settlement for the clay layer by dividing the clay layer up into $4$ equal sublayers and determining the increase in stress due to the footing at the center of each sublayer.