c$)$ Stone columns are constructed in a deep saturated deposit of clay with a cohesion of $40$kPa using Vibro replacement technique to facilitate the construction of a multi$-$storey building at a foundation level of $3$m below the ground surface. The geotechnical report indicated that groundwater level is permanent at $2$m below the ground surface. Compacted stone columns with a diameter of $1\mathrm{.}0$m are to be placed at a spacing of $3\mathrm{.}5$m in a square grid. The Geotechnical report indicated that the angle of internal friction and unit weight of soil in the treated columns are $35$and $19$k$($N$)/($m$^(3))$ respectively. Determine the degree of improvement and the ultimate bearing capacity of the treated ground. $(30$