An isotropically$-$consolidated drained triaxial compression test $($ICD$-$TXC$)$ is performed in the More Hall geotechnical lab. A relatively fine dune sand specimen from Florence, OR is isotropically$-$consolidated in a triaxial test apparatus to ${}_{\text{c}\text{e}\text{l}\text{l}}=420$kPa and is then sheared with the drainage valve open. At failure, the deviator stress $({}_{1^{\text{'}}}-{}_{3^{\text{'}}})$ is $1046$kPa.

a$.$ Determine the major principal stress $({}_{{11}^{\text{'}}})$ at failure $($in units of kPa $).$

b$.$ Determine the minor stress $({}_{3f^{\text{'}}})$ at failure $($in units of kPa $).$

c$.$ Determine the friction angle at failure $({}^{\text{'}})$ for this sample $($assuming that $c=0).$ Provide your answer in units of degrees.

d$.$ Determine the shear stress acting on the failure plane at failure $({}_{ff})$ for this sample $($assuming that $c=0).$ Provide your answer in units of kPa.

e$.$ Plot two Mohr Circles for the specimen: $($i$)$ after consolidation and $($ii$)$ at failure $($both in $$ and $$ space$).$ Include an M$.$C$.$ failure envelope. You are not required to write anything here. Instead, simply attach your plot and clearly label axes and your figures.