Test: The Mohr - Coulomb Failure Envelope - Civil Engineering (CE) MCQ

Mohr’s theory of failure can be symbolically expressed as:
σmax–σmin =f (σmax +σmin) or τmax=f (σn).

the effect of intermediate principal was studied by D.C. Drucker and W. Prager in 1952, who proposed the concept of a three dimensional yield envelope.

 The major drawback of Mohr criterion is that the curved shape of the envelope, hence the functional form of the equation τmax=F (σn) is not amendable to mathematical computation.

The yield criterion may be expressed as f (I1, I2, I3) =0
Where I1, I2, I3 are the invariant of stress.

 If the auxiliary plane passes through the origin its equation is σ1+σ2+σ3=0 and equation will be σ1+σ2+σ3=constant if the plane is perpendicular to the hydrostatic axis.

The intersection of yield surface with octahedral plane is called the failure locus .A point on the failure locus represents the stress state at incipient failure.

Experiments conducted by Cross land in 1965 have demonstrated that a pure state of hydrostatic pressure is unable to produce failure even under enormous pressure.

According to cross land σ1=σ2=σ3 represent hydrostatic pressure in its purest form.

The Mohr-Coulomb criterion implicitly assumes that the strength is independent of the intermediate principal stress σ2.

Since all the points in the auxiliary plane represent deviatorial state of stress, the plane is also called the deviatoric plane.