Q$1(5$ marks$)$ A normally consolidated clay was subjected to a consolidated$-$drained triaxial test under a chamber pressure of ${}_3=241$kPa, resulting in the deviator stress at failure of ${}_{d,f}=289\mathrm{.}5$kPa. Draw the Mohr's circle $(2$ marks$)$ and determine:

$($a$)$ the angle of friction ${}^{\text{'}}(1$ mark$)$

$($b$)$ the angle $$ that the failure plane makes with the major principal plane $(1$ mark$)$

$($c$)$ the normal stress ${}_f^{\text{'}}$ and the shear stress ${}_f$ on the failure plane $(1$ mark$)$

Q$2(5$ marks$)$ Following are the results of consolidated$-$undrained triaxial tests on undisturbed soils retrieved from a $4-$m thick saturated clay layer in the field