Problem $8$

A dry sand specimen is hydrostatically consolidated in a triaxial test apparatus to $9400psf$ and then sheared by increasing the vertical stress while the horizontal stress remains constant $($i$.$e$.,$ this is the traditional compression test$).$ At failure, $({}_1-{}_3)$ is $23,400psf.$

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

$($b$)$ Determine the angle of shearing $($or friction angle$)$ resistance.

$($c$)$ Determine the angle of the failure plane with the horizontal direction.

$($d$)$ Plot the Mohr diagram.

The same sand is then tested in a direct shear apparatus under a normal stress of $9400psf.$ Assuming that the friction angle is the same on both triaxial and direct shear tests.

$($e$)$ Determine the shear stress at failure.

$($f$)$ Plot the Mohr diagram for the direct shear test.

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