Which of the following statements are correct with respect to Mohr–Coulomb failure criteria on soils? I. Mohr failure envelope is approximated as a straight line but in actual, it is curved. II. Mohr failure envelope is approximated as a curved line but in actual, it is straight. III. The Mohr circle drawn for soil cannot cross the Mohr failure envelope. IV. Cohesion c and angle of internal friction φ are fundamental properties of soil and are independent of testing conditions.

Asked in SSC JE 07/06/2024 (Morning)

Detailed Explanation

Mohr's theory says a soil fails when the shear stress on some plane reaches a limiting value that depends on the normal stress on that plane. Plotting the limiting (τ, σ) pairs gives the failure envelope. Coulomb's straight-line equation, τ = c + σ tan φ, is used to represent it.

Why “I and III” Is Correct

I is true: tests over a wide stress range show the real envelope curves slightly (φ falls a little at high stresses), but over the working range a straight line is accurate enough.

III is true: a Mohr circle touching the envelope represents failure. A circle crossing it would mean some plane carries more shear stress than the soil can resist, which is impossible.

IV is false: c and φ are not fixed soil constants; they change with drainage conditions (UU, CU, CD), stress history, density and rate of loading. So the correct pair is I and III.

Mohr circles at failure for tests at different confining pressures. The line touching all the circles is the Mohr–Coulomb failure envelope: its intercept is the cohesion c and its slope angle is φ. A circle for a stable state lies wholly below the line; no circle can cross it.

Why the Other Options Are Wrong

A. II and III: Statement II reverses the truth: the envelope is curved in reality and approximated as straight.
B. I and IV: Statement IV is false: c and φ depend on how the soil is tested (drained or undrained, stress history and so on).
C. II and IV: Both II and IV are false.

Key Point

Real envelope: slightly curved. Design envelope: straight, τ = c + σ tan φ. A Mohr circle can touch but never cross it.

Key Concepts for Students

A circle below the envelope = stable; touching = failure; crossing = impossible.
Undrained parameters (cu, φu) and effective parameters (c′, φ′) of the same clay are very different.
Always state which test gave c and φ when you quote them.

Practice more: this is question 1 in Shear Strength of Soils MCQs – Part 1. Try the whole set and check every answer instantly.