Problem$1..$ A sample was taken from the center of a clay layer with a thickness of $6$ m from the ground surface, and a consolidation test was conducted. The following data was obtained $($assume that the groundwater level coincides with the ground surface, and the saturated unit weight of the clay layer, ${}_{\text{s}\text{a}\text{t}},$ is $1\mathrm{.}94t\frac{f}{m^3})$:

Initial void ratio $e_0=0\mathrm{.}83$

Compression index $C_c=0\mathrm{.}44$

Recompression index $C_r=0\mathrm{.}025$

Coefficient of volume compressibility $m_v=0\mathrm{.}195c\frac{m^2}{k}g$

Coefficient of consolidation $C_v=0\mathrm{.}00573c\frac{m^2}{sec}$

Preconsolidation pressure $P_c=6\mathrm{.}24t\frac{f}{m^2}$

$($a$)$ What is the Over Consolidation Ratio $($OCR$)$ of the clay layer?

$($b$)$ Calculate the consolidation settlement when a uniform load of $10t\frac{f}{m^2}$ is applied over a very large area of the ground surface.

$($c$)$ Determine the average degree of consolidation when settlements of $15cm$ and $30$ cm occur, respectively$\mathrm{.}1$