Problem $(10$ points$)$ For the given in$-$situ conditions below,

a$)$ calculate the total settlement of the given foundation $($immediate $+$ primary consol $+$ secondary consol$).$ For consolidation settlements, use $2$:$1$ method, and weigh the top, middle and bottom stress increases due to foundation loading with proportions of $1$:$4$:$1$ respectively. Assume that the primary consolidation takes $4$ years, and the secondary consolidation time is $7$ years $(7$ points$)$

b$)$ calculate the consolidation coefficient by assuming that $\backslash (99\backslash \%\backslash )$ of the primary consolidation was completed in $3\mathrm{.}9$ years, and estimate the soil type based on the given common $\backslash (\backslash$mathrm$\{$C$\}\_\{$v$\}\backslash )$ values below $(3$ points$)$

Assumptions: The weight of the foundation plus the fill lying above the foundation equals approximately to the soil weight excavated, so that the net contact pressure between foundation and soil can be assumed by using the given column load $(100$ kips$)$ only.