# Geotechnical Engineering Questions and Answers – The Mohr – Colomb Failure Envelope

This set of Geotechnical Engineering Multiple Choice Questions & Answers (MCQs) focuses on “The Mohr – Colomb Failure Envelope”.

1. The Mohr’s theory of failure can be symbolically expressed as ____________
a) τmax=F(σn) and σmax–σmin = f(σmax +σmin)
b) τmax = σmax– σmin
c) None of the mentioned
d) All of the mentioned

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

2. The concept of a three dimension yield envelope was presented by _________
a) D.C. Drucker and Prager
b) Mohr
c) None of the mentioned
d) All of the mentioned

Explanation: 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.

3. A major drawback of Mohr criterion is ____________
a) Shape of the envelope
b) Principal stress
c) Shape of the plane
d) All of the mentioned

Explanation: 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.

4. The yield or failure criterion can be expressed as ____________
a) f(I1,I2)=0
b) f(I1,I2,I3)=0
c) f(σ1,σ2,σ3)=0
d) f(σmax +σmin)

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

5. If the auxiliary plane in hydrostatic axis passes through the origin, then its equation is _____________
a) σ1+σ2+σ3=0
b) σ1+σ2+σ3=constant
c) I1+ I2+I3 =0
d) f(σ1,σ2,σ3)=0

Explanation: 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.
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6. The intersection of the yield surface or envelope with octahedral plane is called ____________
a) Yield point
b) Deviation point
c) Failure locus
d) Space diagonal

Explanation: 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.

7. The hydrostatic pressure’s inability to produce failure under normal pressure was first demonstrated by ___________
a) Cross land
b) W. Pager
c) D.C. Drucker
d) Mohr

Explanation: 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.

8. Which of the following equation represent hydrostatic pressure in its purest form?
a) σ1+σ2+σ3=0
b) σ1+σ2+σ3=constant
c) σ1=σ2=σ3
d) σmax+ σmin

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

9. The Mohr-Coulomb criterion assumes that the strength of the soil is independent of ____________
a) σ1
b) σ2
c) σ3
d) All of the mentioned

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

10. The auxiliary plane in the hydrostatic axis can also be called as ___________
a) Failure plane
b) Octahedral plane
c) Deviatoric plane
d) Principal plane

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

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