Problem $1(35$ points$)$

Silty clay sample was retrieved from a construction site which natural water content was $40\mathrm{.}5\%.$

Atterberg limit tests were performed on the silty clay. The water contents obtained in the plastic limit test

were $31\mathrm{.}6\%,33\mathrm{.}5\%$ and $30\mathrm{.}9\%.$ Table $1$ shows the results of liquid limit test. Sieve and hydrometer

analyses were also performed on the clay which shows the percentage of clay$-$size fraction $(\%$ finer than $2$

$m$ by weight$)$ of $50\%.$ Provide the following variables:

$($a$)$ Liquid limit$,$ LL $($b$)$ Flow index, I $I_F($c$)$ Plastic limit$,$ PL $($d$)$ Plasticity index, PI $($e$)$ Activity, A $($f$)$

Liquidity index, LI $($g$)$ Potential clay mineral $($h$)$ Estimated shrinkage limit$,$ SL

Table $1.$ Results of liquid limit test