Q $(50$ pts$)$ A foundation is to be constructed at a site whose soil profile is shown below. The initial void ratio of the overconsolidated 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 be $60$ kPa at the mid$-$height of the clay layer. Find the followings:

a$.$ For the above soil, the effective overburden pressure at the midheight of the clay layer is most nearly?

b$.$ The total effective pressure at the midheight of the clay layer is most nearly?

c$.$ If the overconsolidated pressure of the clay layer is $130$kPa, the primary consolidation settlement for the clay layer is most nearly? PAY ATTENTION TO UNITS

Show all the calculation steps!