$2.$ Check the stability $($overturning$,$ sliding$)$ of the gravity wall$-$backfill system shown in Figure $2,$ with the data given in Table $2,$ and state if the selected dimensions are safe or not $($Use Coulomb's theory of earth pressures$).$

Figure $2.$ Gravity retaining wall.

Table $2.$ Data for gravity wall stability analysis.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash$multirow$[$t$]\{2\}\{*\}\{$Student No$.\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{$Backfill$\}$ & $\backslash$multicolumn$\{3\}\{|$c$|\}\{$Front and base soil$\}\backslash \backslash$

$\backslash$hline & $\backslash (\backslash$varphi $1^\{\backslash$prime $\backslash$circ$\}\backslash )$ & $\backslash [$

$\backslash$begin$\{$array$\}\{$c$\}$

$\backslash$gamma$\_\{1\}\backslash \backslash$

$\backslash$left$(\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash$right$)$

$\backslash$end$\{$array$\}$

$\backslash ]$ & $\backslash (\backslash$alpha$^\{\backslash$circ$\}\backslash )$ & $\backslash (\backslash$varphi$^\{2\}\{\}^\{\backslash$prime $0\}\backslash )$ & $\backslash ($ c$^\{\backslash$prime$\}\backslash )($kPa$)$ & $\backslash [$

$\backslash$begin$\{$array$\}\{$c$\}$

$\backslash$gamma$\_\{2\}\backslash \backslash$

$\backslash$left$(\backslash$mathrm$\{$kN$\}/\backslash$mathrm$\{$m$\}^\{3\}\backslash$right$)$

$\backslash$end$\{$array$\}$

$\backslash ]\backslash \backslash$

$\backslash$hline $21910274$ & $28$ & $18$ & $10$ & $25$ & $25$ & $20\backslash \backslash$

$\backslash$hline $21910805$ & $30$ & $18$ & $15$ & $20$ & $30$ & $20\backslash \backslash$

$\backslash$hline $22007616$ & $32$ & $18$ & $20$ & $15$ & $40$ & $20\backslash \backslash$

$\backslash$hline $22008497$ & $34$ & $18$ & $15$ & $25$ & $25$ & $20\backslash \backslash$

$\backslash$hline $22008738$ & $36$ & $18$ & $5$ & $20$ & $30$ & $20\backslash \backslash$

$\backslash$hline $22008877$ & $30$ & $18$ & $10$ & $15$ & $40$ & $20\backslash \backslash$

$\backslash$hline $22015403$ & $32$ & $18$ & $15$ & $25$ & $25$ & $20\backslash \backslash$

$\backslash$hline $22018684$ & $34$ & $18$ & $20$ & $20$ & $30$ & $20\backslash \backslash$

$\backslash$hline $22100282$ & $28$ & $18$ & $15$ & $15$ & $40$ & $20\backslash \backslash$

$\backslash$hline $22105692$ & $25$ & $18$ & $12$ & $30$ & $20$ & $20\backslash \backslash$

$\backslash$hline $22108994$ & $28$ & $18$ & $10$ & $25$ & $25$ & $20\backslash \backslash$

$\backslash$hline $22111891$ & $30$ & $18$ & $15$ & $20$ & $30$ & $20\backslash \backslash$

$\backslash$hline $22112648$ & $32$ & $18$ & $20$ & $15$ & $40$ & $20\backslash \backslash$

$\backslash$hline $22113725$ & $34$ & $18$ & $15$ & $25$ & $25$ & $20\backslash \backslash$

$\backslash$hline $22114881$ & $36$ & $18$ & $5$ & $20$ & $30$ & $20\backslash \backslash$

$\backslash$hline $22118073$ & $30$ & $18$ & $10$ & $15$ & $40$ & $20\backslash \backslash$

$\backslash$hline $22201494$ & $32$ & $18$ & $15$ & $25$ & $25$ & $20\backslash \backslash$

$\backslash$hline $22211156$ & $34$ & $18$ & $20$ & $20$ & $30$ & $20\backslash \backslash$

$\backslash$hline $22214202$ & $28$ & $18$ & $15$ & $15$ & $40$ & $20\backslash \backslash$

$\backslash$hline $22307482$ & $25$ & $18$ & $12$ & $30$ & $20$ & $20\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$