From the soil profile shown, a sample was taken from pt$.$ A with $w=31\%$ and $G_s=2\mathrm{.}65.$ A laboratory consolidation test was performed and the lab curve was obtained.

$($a$)$ For the clay layer:

$e_0=$

$q,$

$($b$)$ Initial effective stress at pt$.$ A before any construction.

${}_0=$

$q,l\frac{b}{f}{t}^{2}q,$

$($c$)$ The e$-$log ${}^{\text{'}}$ curve for this sample is attached.

Use Casagrande's method to determine the pre$-$consolidation pressure, ${}^{\text{'}}$ c$.$

${}_c^{\text{'}}=|\frac{b}{f}{t}^2|$

$($d$)$ Is the sample NC or OC$?($circle one$)($circle one$)$

$($e$)$ Proposed construction will increase the stress at pt$.$ A by $=400l\frac{b}{f}{t}^2.$ What will be the final effective stress at pt$.$ A after some time has passed and consolidation is essentially complete.

${}_1=$

$1\frac{b}{f}{t}^2$

$($f$)$ Use Schmertmann's method to construct the Virgin Compression Curve $($VCC$)$ and Field Consolidation Curve $($FCC$)$ on the provided e$-$log ${}^{\text{'}}$ plot.

$($g$)$ What is the final void ratio for the soil at pt$.$ A$?$

$e_f=$

$$

$($h$)$ Assuming the strain from the center of the clay layer $($pt$.$ A$)$ represents the average of the entire layer, use the graphical lab data to get a "one$-$point" estimate of the settlement of the clay layer, in inches. $=H=q,$ in

$($i$)$ Lab time rate data from a double drained consolidation test is attached. From the given plot determine $C_v$ in $f\frac{t^2}{l}$ ear. $)=(0\mathrm{.}196$

$c_v=$

$q,f\frac{t^2}{y}r$

i$)$ Disregarding your results from part $($i$),$ assume $c_v=25f\frac{t^2}{y}r$ for the clay layer. How much time would be required for $90\%$ of the settlement of the clay layer to occur?

$)=(0\mathrm{.}848t_{90}=q,$ months