Problem $2$:

Plot the data below from a consolidation test on a specimen of saturated normally consolidated

clay in both linear and semi$-$log scales by Excel:

TABLE J

A $10m-$thick layer of this clay lies below a $4m$ depth of sand, and the water table is very near the

ground surface. The saturated unit weight for both soils is $19k\frac{N}{m^3}.$ A $3\mathrm{.}5m$ depth of sandy fill

of unit weight $21k\frac{N}{m^3}$ is placed on the surface over an extensive area.

Determine the final settlement after clay's consolidation is complete. If the fill were to be removed

some time after the completion of consolidation, what would the surface heave eventually be from

the rebound of the clay?

Note: To account for the variation of the soil's initial void ratio due to variation of the in situ

vertical stress with respect to depth,

$($a$)$ divide the clay into at least $4$ layers

$($b$)$ calculate the in$-$situ vertical effective stress ${}_0^{\text{'}}$ at their mid$-$points

$($c$)$ determine their corresponding initial void ratios e using the 'virgin compression' data by

the fact that it is a normally consolidated clay

$($d$)$ determine the change due to the sandy fill of the vertical total stress ${}_1^{\text{'}}$ as a function of

depth which will translate to the final effective stress ${}_v^{\text{'}}$ and $e_1$ for the resulting final

${}_1^{\text{'}}$ at the $4$ mid$-$points due to the fill

$($e$)$ calculate using $($a$)-($d$)$ the vertical settlement of each of the $4$ layers and sum them to

determine the total surface settlement and heave.