Question $2$

Soil samples were taken from the clay layer shown in the figure. The results of the laboratory consolidation test are summarized in the table. The initial void ratio of the clay is known to be $e_0=2\mathrm{.}38.$

$\backslash$table$[[p^{\text{'}}(kPa),$Void Ratio, e$],[12\mathrm{.}5,2\mathrm{.}33],[25,2\mathrm{.}32],[50,2\mathrm{.}26],[100,2\mathrm{.}21],[200,1\mathrm{.}90],[400,1\mathrm{.}56],[50,1\mathrm{.}62],[400,1\mathrm{.}54]]$

a$)$ Plot the $e-log{p}^{\text{'}}$ laboratory curve for the specimen. $[$here$,p^{\text{'}}={}_{v{o}^{\text{'}}}]$

b$)$ Determine the preconsolidation pressure, $P_c^{\text{'}}($or ${}_p^{\text{'}}),$ using the Casagrande's construction.

c$)$ Compute the compression index, $C_c,$ and the recompression index, $C_r,$ using $e-log{p}^{\text{'}}$ curve.

d$)$ Estimate the settlement of the clay layer in the figure when a uniform surface load of $80$ kPa is applied. Assume the stress increase in the clay layer is constant and use the $1-$D approximation. Use $C_c$ and $C_r$ determined in $($c$).$