$($Q$1)$

The gravity wall shown below is to support backfill with unit weight of $19\mathrm{.}5k\frac{N}{m^3}$ and shear strength parameters $c^{\text{'}}=0$kPa and $\frac{O}{{?}^{\text{'}}}=36($shear strength parameters were determined using triaxial laboratory tests$).$ The unit weight of the wall material is $24k\frac{N}{m^3}$ and the friction angle between the wall and the backfill $=27$ and at the base of the wall it is $25.$ Determine the factors of safety against $($i$)$ sliding on the base $($ii$)$ overtuming, and $($iii$)$ bearing capacity failure, and compare these against minimum desirable values of $1\mathrm{.}5,1\mathrm{.}5$ and $3\mathrm{.}0$ respectively $($the soil below the wall can be assumed as similar to the backfill soil$).$ If any of the FOS are inadequate, redesign the wall $($while maintaining the same height and concrete volume$)$ so as to satisfy the minimum FOS requirements. Show a dimensioned sketch and clearly set out all necessary calculations for your modified design.