$10\mathrm{.}9$ A consolidation test on a sample of clay produced the following data:

$\backslash$table$[[{}_z^{\text{'}}(kPa),8,16,32,64,128,256,512,1024,16],[{}_z,0\mathrm{.}032,0\mathrm{.}041,0\mathrm{.}051,0\mathrm{.}069,0\mathrm{.}109,0\mathrm{.}173,0\mathrm{.}240,0\mathrm{.}301,0\mathrm{.}220]]$

The initial void ratio of the sample was $1\mathrm{.}21,$ and ${}_{z0}^{\text{'}}$ at the sample depth was $40$kPa.

$($a$)$ Plot these data on an arithmetic diagram similar to that in Figure $10\mathrm{.}10($a$)$

$($b$)$ Plot these data on a semilogarithmic diagram similar to that in Figure $10\mathrm{.}10($b$).$

$($c$)$ Using Casagrande's method, find ${}_c^{\text{'}}.$

$($d$)$ Using Schmertmann's method, adjust the test results.

$($e$)$ Determine $C_c$ and $C_r.$

$($f$)$ The soil has a plasticity index of $23.$ Based on Kulhawy and Mayne's correlations, do the consolidation test results seem reasonable?