Problem $4.$ Consolidation and Time$-$settlement curve $(40$ pts $)$

a$.$ A laboratory consolidation test was performed and yielded the following results. Use the results to make a plot of the effective stress vs void ratio. Use your plot and the information given to determine the maximum past pressure, Coefficient of Compression $($Cc$)$ and Coefficient of Re$-$compression $($Cr$).$

$\backslash$table$[[$Effective Stress ${}_v(kPa),$Void Ratio e$],[50,0\mathrm{.}841],[100,0\mathrm{.}826],[200,0\mathrm{.}774],[400,0\mathrm{.}696],[800,0\mathrm{.}612],[1150,0\mathrm{.}524],[1700,0\mathrm{.}435],[2100,0\mathrm{.}365]]$

b$.$ The sample was collected from the middle of a $20$ meter thick clay layer with a total $($saturated$)$ unit weight of $16\mathrm{.}4k\frac{N}{m^3}$ at a site where a new highway embankment is proposed. The proposed highway embankment will raise the current ground level up by $5$ meters and the proposed fill will have a unit weight of $18\mathrm{.}8k\frac{N}{m^3}.$ Use this information and your results from part $($a$)$ to determine the overconsolidation margin $($refer to problem $4$ in assignment $7).$ Assume the water table is at the ground surface and stays at the top of the ground surface.

c$.$ Use the information in parts $($a$)$ and $($b$)$ to determine the maximum amount of settlement you expect after the embankment is built. You should break the layer into at least $4$ sub$-$layers and use your overconsolidation margin to predict the maximum past pressure in the middle of every sub$-$layer. The in$-$situ void ratio for this sample is very near $0\mathrm{.}99.$

d$.$ At this site the $20$ meter thick layer lies just above a sandy layer. Results from one of the loading stages resulted in a coefficient of consolidation value, $c_v=6\mathrm{.}34{10}^{-3}c\frac{m^2}{sec}.$ Determine how long it will take to reach $95\%$ average degree of consolidation, please report you answer in years.

e$.$ The owner of the project would like to be able to monitor the settlement at the site and compare the settlement to your predicted total settlement. $($A time settlement curve is a plot of the predicted settlement as a function of time, usually this is plotted with the time on the $x-$axes and the total settlement on the $y-$axes. The $y-$axes is usually oriented with $0$ at the top of the axis with settlement getting bigger going down $[$reverse the $y-$axis$]).$