A new structure is planned to be constructed in an offshore location and will apply an estimated surface load of $250$kPa directly to the seafloor. The seafloor consists of a $20m$ thick layer of normally consolidated marine clay which overlies an impermeable rock formation $($see figure below$).$ The clay has a saturated density of $1\mathrm{.}9M\frac{g}{m^3}$

A sample of the clay layer is tested in the lab and was found to have an initial void ratio of $0\mathrm{.}63,$ a compression index of $C_c=0\mathrm{.}27,$ and a coefficient of consolidation of $C_v=2\mathrm{.}1**{10}^{-4}c\frac{m^2}{s}.$

Assume that the water level remains constant during and after loading $(5m$ above seafloor$).$ Consolidation charts can be found on the last page of the exam.

a$)$ Calculate the total amount of settling that will occur due to consolidation of the clay layer

b$)$ How long will it take the clay layer to reach $50\%$ of the total consolidation?

c$)$ Calculate the effective stress at a point in the middle of the clay layer $($red circle in the plot$)$ when the soil reaches $50\%$ consolidation

d$)$ If the clay was actually over$-$consolidated $($rather than normally consolidated$),$ would the total amount of settling increase or decrease compared to your answer in a$)?$ How do you know?