Question $5$:

$($Value: $20$ marks$)$

A silty sand specimen's shear strength was found to be equal to $25$ kPa when it was tested

in a direct shear apparatus under drained loading conditions without application of any

normal load. An identical specimen was then subjected a normal stress of $200$ kPa $,$ which

failed at $130$ kPa $.$ Determine the following:

$($a$)$ The angle of friction?

$($b$)$ Magnitude of the principal stresses at failure under the normal stress of $200$ kPa $.$

$($c$)$ The normal and shear stresses the failure plane.