$(25$ points$)$ The soil profile at a site consists of a layer of fine sand $5m$ thick above a layer of clay $4m$

thick. Below the clay is a layer of impermeable rock. The groundwater table was observed at $2m$ below

ground level. The unit weight of the sand above and below the water table is $20K\frac{N}{m^3}.$ The water

content of the clay is $25\%$ and its dry unit weight is $15K\frac{N}{m^3}.$ The compression and recompression

indices of the clay are $0\mathrm{.}2$ and $0\mathrm{.}05,$ respectively. The building will impose a vertical stress of $150$KPa.

Estimate the primary consolidation settlement of the clay. The over$-$consolidation margin of this soil is

$80$KPa.

$(25$ points$)$ What is the total stress, effective stress and pore pressure $1m$ within the clay layer after $6$

years? The coefficient of consolidation is $0\mathrm{.}20\frac{m^2}{y}r.$

$(10$ points$)$ In Problem $2,$ what would be the average degree of consolidation after $9$ years?

$(10$ points$)$ In Problem $2,$ if a piezometer is installed at a depth of $1m$ in the clay layer, what would be

the height of water in the piezometer after $9$ years.

This is one big question with $4$ parts to it$.$ Please make sure to show work for every single part. Will give thumbs up$,$ if correct and neat work!