A foundation for a structure is to be constructed on soft clay of $10\mathrm{.}0$ m thick. Below the soft clay is very hard overconsolidated clay. The calculated settlement cannot be tolerated and it was decided that the soft soil should be preconsolidated by an embankment equivalent to the building load. The PVD drains with $100$ mm wide and $3$mm thick are to be installed with $1\mathrm{.}0$ m spacing in a triangular pattern to speed of the consolidation. The following data are available: mv $=0\mathrm{.}2$ m$2/$MN$,$ Cv$=3\mathrm{.}5$ m$2/$yr$,$ Ch$=6\mathrm{.}2$ m$2/$yr$.($i$)$ Calculate the degree of consolidation achieved in $180$ days due to radial and vertical drainage without considering smearing and discharge effect, and $($ii$)$ Calculate the degree of consolidation achieved in $180$ days due to radial drainage considering smearing and discharge effect $($assume: smeared ratio $=3,$ kh$/$ks$=3$; qw$=0\mathrm{.}00081$m$3/$s; kh $=1\mathrm{.}0$ x $10-8$ m$/$s$).$