Problem $2(30$ points$)$:

A geotechnical investigation at the site of a proposed warehouse has disclosed that the site was once a marsh. The previous owner excavated most of the soft organic soils and replaced them with engineered fill. However, to save money on excavating costs, the lower two feet of organic soil was left in place. The proposed ware house will have maximum column loads of $400$kips, and the designer has tentatively sized the footings to be $9ft9ft.$

Compute the consolidation settlement in the soft organic layer. Treat this layer as a single layer $($i$.$e$.,$ do not subdivide$).[$Hint: To answer the following sub$-$questions will help you solve this problem$]$

a$.$ The initial vertical effective stress at the midpoint of the organic soil layer;

b$.$ The induced vertical effective stress at the midpoint of the organic soil layer by using the simplified method proposed by Poulos and Davis $1974,$ whose equations are provided at the end of exam paper$)$;

c$.$ Determine the final vertical effective stress at the midpoint of the organic soil layer;

d$.$ Calculate the consolidation settlement from the organic soil layer by using the Classic Method $($Use $1\mathrm{.}0$ for the rigidity factor $r$; note that $)$;

e$.$ If the coefficient of consolidation of the organic soil layer is$,f\frac{t^2}{y}r,$ how much consolidation settlement would be developed after $3$ years of the footing construction?