SSC JE Civil Engineering 30-Oct-2020 Shift 1 Paper

Failure plane is one at which angle of obliquity is maximum.
Failure shear stress is one at which difference of shear stress and shear strength is minimum.
${\mathrm{\theta }}_{\mathit{c}}$ = Angle of the critical plane to the major principal plane
From triangle property, External angle = Sum of internal angle


where, ${\mathrm{\beta }}_{\max }=$ Angle between resultant stress and normal stress on critical plane $=$ Friction angle of soil $=\mathrm{\varphi }$
Calculation:
the angle of failure plane relative to the major principle plane in a triaxial test,
$\mathrm{\theta }=\frac{\mathit{\pi }}{4}+\frac{30}{2}=60°$