An embankment with side slope angle $($beta$)=$ pm$5^*$ constructed with a soil that has varphi $^*=20^*$ and c $24$ kPa. The compacted unit weight of the $19$kN $/($m $^3)$

$1.$ Find the critical height of the slope?

ii$.$ Find the factor of safety $($with respect to strength$)$ of the slope for a height of $10$ m

iii. Discuss the effect of tension crack and rapid draw down on the slope stability

$($h$).$ Draw and discuss the contact pressure and settlement distribution for rigid and