Calculate the axial stress sigma1 when the sample fails

Question

1. A type of rock is supposed to follow the Mohr-Coulomb linear strength criterion, the strength of the rock sample under uniaxial compression test is σ_c = 40 MP_a, the angle between failure plane and the maximum principal stress σ₁ is θ = 60^o. If triaxial compression test is conducted on this rock sample with confining pressure σ₃ = 3MPa, please calculate:

(a) The axial stress σ₁ when the sample fails;

(b) The normal stress (σ) and shear stress (Τ) on the failure plane.