A $100$kPa vertical load will be imposed on a soil profile consisting of sand overlying clay, as illustrated below. To anticipate the settlement of the clay layer upon loading, a consolidation test was performed on a sample of clay from the center of the clay layer and $c_c,c_r,$ and ${}_p^{\text{'}}$ are calculated as $0\mathrm{.}3,0\mathrm{.}03,$ and $120$kPa, respectively.

Weathered rock

Assuming these coefficients are representative coefficients for the entire clay layer, compute the total amount of consolidation settlement due to the vertical load increase. For your calculation, divide the clay layer into at least $2$ sublayers.

The void ratio table with time is shown below for one load stage from the consolidation test for the specimen sampled at the center of the clay layer. The height of the specimen was approximately $20mm,$ and the specimen was loaded using double$-$drained conditions.

A$.$ Using Casagrande method, compute the coefficient of consolidation, $c_v.$

B$.$ Compute a settlement versus time plot for the $100$kPa surcharge imposed on the sand layer. You may choose $U=20,40,60,80,$ and $90\%$ for plotting.

C$.$ Plot vertical total stress, hydraulic water pressure, pore water pressure, and vertical effective stress from the surface to the bottom of the clay layer at $6$ months after $100$ kPa surcharge

U$(\%)$:$20->$Tv:$0\mathrm{.}0314$

$40->0\mathrm{.}126$

$60->0\mathrm{.}286$

$80->0\mathrm{.}567$

$80->0\mathrm{.}848$

plz solve this problem as detailas you can$($no$\mathrm{.}1$ and A$,$B$,$C of no$\mathrm{.}2)$