$[10$ Points$]$ A direct shear test was performed on a specimen of dry sand under a $($vertical$)$ normal stress of $80$kPa. The effective$-$stress friction angle was determined to be $=32.$

$($i$)$ Find the horizontal shear stress required to cause failure.

$($ii$)$ Draw the effective$-$stress Mohr's circle for the stress state at failure. Indicate the location of the pole and the Mohr$-$Coulomb failure envelop.

$($iii$)$ Determine the major and minor principal stresses at failure.

$($iv$)$ Find the normal stress on the vertical plane at failure.

$($v$)$ If the same dry sand specimen is subjected to a consolidated drained triaxial test, do you expect the friction angle determined from the triaxial test to be small than, equal to or larger than $32?$ Give a brief explanation to your answer.