Problem $7$ HKS$11-31($modified$).$

A sand specimen is consolidated non$-$hydrostatically, with ${}_v^{\text{'}}=150$kPa and ${}_h^{\text{'}}=100$kPa, and

then it is sheared by holding the vertical stress constant and increasing the horizontal stress $($this

is a lateral compression test$).$ The angle of internal friction is $30$ and the cohesion is $0.$

$($a$)$ Draw the Mohr circles for both initial and $"$at failure" conditions.

$($b$)$ What will be the major and minor principal stresses at failure?