Problem $2(40)$

For a given laboratory data from a $1$D consolidation test,

a$.$ Calculate $C_v,$ for the load of $512kg$ using $t_{50}$ and t$90$ method.

b$.$ Plot void ratio $($e$)$ versus $log({}_v^{\text{'}})$ for the test and calculate $C_c.$ include the completed table in your answers.

Height of the specimen $=38\mathrm{.}10mm$

Area of the specimen $=90\mathrm{.}1c{m}^2$

Mass of dry specimen $=475\mathrm{.}1g$

Density of solids $(G_s)=2\mathrm{.}8$

Hint $1$: $C_v,$ has to be calculated only for the load of $512kg.$ All you need is the elapsed time and dial reading numbers for this load to calculate $C_v.$

Hint $2$: For plotting the void ratio $($e$)$ versus $log({}_v^{\text{'}}),$ you should follow these steps:

Calculate void ratio for each load increment. For the load of $512kg,$ we only interested in the final dial reading which is $5\mathrm{.}753.$

${}_d=\frac{W_s}{V}=\frac{G_s{}_w}{1+e}$ obtain $e$

Calculate the pressure which is Load$/$Area in kPa units.

Plot the pressure $($on X$-$axis$)$ versus void ratio $($on Y$-$axis$).$ The X$-$axis is log scaled

Find the part of the graph where the curve gets steeper and draw a straight line $($trendline$)$ through these points. The steepness of this line, or its slope,