Problem $4$:

Natural water contents $($i$.$e$.,$ the water content for the in$-$situ soil$)$ and Atterberg limits were determined for the following fine$-$grained soils. Determine their classifications according to the Unified Soil Classification System and compute their liquidity indices for their in$-$situ condition.

$($a$)$ natural water content $=25\%,$ liquid limit $=20,$ plastic limit $=11.$

$($b$)$ natural water content $=68\%,$ liquid limit $=28,$ plastic limit $=$ nonplastic.

$($c$)$ natural water content $=72\%,$ liquid limit $=60,$ plastic limit $=25,$ strong odor and black color, so sample was oven$-$dried and a new liquid limit of $42$ obtained

$($d$)$ natural water content $=48\%,$ liquid limit $=60,$ plastic limit $=25.$