Problem $2(25/100)$:

A foundation is to be constructed at a site where the soil profile is as shown in figure. The base of the foundation, which is $2m$ square, exerts a total load $($weight of structure, foundation, and soil surcharge on the foundation$)$ of $5000kN.$ The initial void ratio of the clay layer is $1\mathrm{.}06,$ its compression index is $0\mathrm{.}35,$ and its recompression index is $0\mathrm{.}08.$ Water table is $3$ meters below the ground level. Find the estimated primary consolidation settlement for the clay layer if:

a$)$ The clay soil is normally consolidated.

b$)$ The clay is over$-$consolidated and the over consolidation pressure is $165$kPa.