QUESTION $2($LO $6$: Consolidation$)$

$2\mathrm{.}1($a$)$ A sand layer of thickness $1$ m overlies a clay layer of thickness $2$ m $($refer diagram$).$ A circular foundation of diameter $2$ m is located on top of the clay layer and exerts a total load of $200$ tonnes $($including self$-$weight$)$ on the surface of the clay. The water table coincides with the top of the clay.

The results of a consolidation test on a representative sample of the clay are attached in the form of a void ratio vs$.$ stress graph. Calculate the primary consolidation settlement, in $\backslash (\backslash$mathbf$\{$m m$\}\backslash ),$ of the foundation. $($b$)$ Repeat the calculation in $($a$)$ with one change namely the shape of the foundation now is a square of dimensions $\backslash (2\backslash$mathrm$\{$~m$\}\backslash$times $2\backslash$mathrm$\{$~m$\}\backslash ).$