$10\mathrm{.}13$ A consolidation test has been performed on a sample obtained from a saturated clay at a point $6\mathrm{.}5m$ below the ground surface. The groundwater table is at the ground surface and the unit weight of the clay is $18\mathrm{.}5k\frac{N}{m^3}.$ The measured preconsolidation stress was $260$kPa.

$($a$)$ Determine if the soil is normally consolidated or overconsolidated.

$($b$)$ Compute the overconsolidation margin and the overconsolidation ratio.

$($c$)$ Compute ${}_c^{\text{'}}$ at depth of $12m$ in the same soil.