$*****$ Please use the values given and solve the question$***($

b$)$ For the oedometer test show on Figure $2($NB X$-$axis is plotted on a log scale$)$ determine:

$($i$)$ the preconsolidation stress $(P_p),$

$($ii$)$ the overconsolidation ratio $($OCR$)$

$($iii$)$ the compression index $(C_c),$

$($iv$)$ The recompression index $(C_r)$

To determine $C_c$ or $C_r$ you can use the following expression for strain $()$ :

$=\frac{C^{**}}{1+e_0}lo{g}_{10}[\frac{{}_{v0}^{}+{}_v^{}}{{}_{v0}^{}}]$

where:

$C^{**}$ is either $C_c$ or $C_r$ as appropriate

$e_0=$ initial void ratio $=1\mathrm{.}776$

${}_v{o}^{\text{'}}=$ initial vertical effective stress

${}_v^{\text{'}}=$ change in vertical effective stress

Ons$$y clay has unit weight $=16\mathrm{.}5k\frac{N}{m^3}$ and water table is at $0\mathrm{.}5m$

Figure $2-$ Oedometer test

$(50\%)$