Q1: In a drained triaixal compression test, a saturated specimen of a cohesionless sand fails under a deviatoric stress of 3 kgf/cm² when the cell pressure is 1 kgf/cm² . The effective angle of shearing resistance of sand is about

ANS:A - 37°

Deviated stress = 3 kgf/cm^2, cell pressure=1 kgf/cm^2.
Effective stress = d.s+c.p,
Then eff.stress = 4.

We have an equation at plastic equibilibrium.
Eff.stress=cell pressure x tan^2(x)+2c x tan(x),
For sand(cohesionless), c=0,
Eff.str = c.p x tan^2(x).

4 = 1*tan^2(x), x = tan^-1(4/2) = 63.43,

We known that x = 45+(frin.ang)/2,

Then fri.angle = (63.43-45)*2 = 36.8.