A gravity retaining wall, shown in Figure E$15\mathrm{.}3$a$,$ is required to retain $5$ m of soil. The backfill is a coarse$-$grained soil with ${}_{\text{s}\text{t}\text{I}}=18k\frac{N}{m^3},{}_G^{\text{'}}=30.$ The existing soil $($below the base$)$ has the following properties: ${}_{\text{s}\text{t}\text{a}\text{t}}=20k\frac{N}{m^3},{}_p^{\text{'}}=36.$The wall is embedded $1$ m into the existing soil and a drainage system is provided, as shown. The groundwater level is $4\mathrm{.}5$ m below the base of the wall. Determine the stability of the wall for the following conditions $($assume $=20)$:

$($Use coulomb's theory for estimating earth forces$)$