$[18$ Points$]$ Consider the following soil deposit. A consolidation test is performed on a sample that is retrieved from the fat clay layer in the field.

$($i$)$ The average height of the clay specimen during the consolidation test is $2,24cm.$ There are porous stones at the top and bottom of the specimen. Suppose that it takes $19$ minutes for $50\%$ consolidation to occur, estimate the coefficient of consolidation in $c\frac{m^2}{m}in.$

$($ii$)$ Suppose that a $4-$meter fill with ${}_m=19\mathrm{.}5k\frac{N}{m^3}$ is to be placed on the ground surface, estimate the ultimate settlement of the fat clay layer in the field due to primary consolidation. You may assume that the fat clay is normally consolidated.

$($iii$)$ Find the excess pore pressure, total pore pressure and effective vertical stress at locations $T$ and $R$ five years after the placement of the fill. You may assume that the water in the clay layer can drain through the silty sand above and the clayey sand below.

$($iv$)$ What is the amount of settlement after five years?

$($v$)$ What should be the new thickness of the proposed fill if double amount of the settlement in $($iv$)$ is desired after five years?

$\backslash$table$[[,$Soil Properties$],[$Silty Sand,$\backslash$table$[[\backslash$table$[[$ above g$.$w$.$t