An oedometer test was performed on a peat soil sample from an FDOT project in the Homestead area. The results are shown below. The initial sample thickness was $20mm$ with two way drainage through porous stones, simulating field conditions. The vertical stress increment is $10$ kPa. Use an estimate of the coefficient of consolidation $c_v$ as;

$c_v=\frac{3H_d^2}{4t}$

$\backslash$table$[[$Given Data,$],[$Time$($min$),0\mathrm{.}00,0\mathrm{.}32,0\mathrm{.}64,1\mathrm{.}28,2\mathrm{.}40,4\mathrm{.}80,9\mathrm{.}60,16\mathrm{.}00],[$Settlement $(mm),0\mathrm{.}00,0\mathrm{.}16,0\mathrm{.}23,0\mathrm{.}33,0\mathrm{.}45,0\mathrm{.}65,0\mathrm{.}86,0\mathrm{.}96],[$Time$^1/2($min$)\frac{1}{2},0\mathrm{.}00,0\mathrm{.}57,0\mathrm{.}80,1\mathrm{.}13,1\mathrm{.}55,2\mathrm{.}19,3\mathrm{.}10,4\mathrm{.}00]]$

$($a$)$ Plot a graph of settlement against the square root of time.

$($b$)$ Determine the value of $c,(\frac{m^2}{s}).$

$($c$)$ Estimate what could be a good estimate of the elastic modulus of this soil, $E,($in kPa$).$

$($d$)$ What sort of permeability $)$ could you estimate for this soit $($from $E)?$