A foundation is to be constructed at a site whose soil profile is shown below. The initial void ratio of the over$-$consolidated clay layer is $0\mathrm{.}9.$ The compression index of the clay layer is $0\mathrm{.}3$ and the swell index is $0\mathrm{.}05.$ The consolidation pressure due to the foundation is calculated to $100$kPa at the mid$-$height of the clay.

For the above problem, if the over$-$consolidation pressure is $80$kPa, what is the primary consolidation settlement for the clay layer? $(20$ points$)$