According to the Mohr–Coulomb theory of failure, useful in case of soils, which of the following statements is INCORRECT?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 06/11/2024 (Morning)
Detailed Explanation
The Mohr–Coulomb theory is built on a few simple ideas: failure is a shear failure on a particular plane, the shear stress that causes failure depends on the normal stress on that plane and on the material (c and φ), and failure is judged using the Mohr circle drawn from the major and minor principal stresses.
Why “The failure criterion depends on the intermediate principal stress” Is Correct
A Mohr circle is drawn using only σ₁ and σ₃, so the theory ignores the intermediate principal stress σ₂ completely. Saying the failure criterion depends on σ₂ is therefore incorrect. Statements (a), (b) and (d) are all basic assumptions of the theory.
Why the Other Options Are Wrong
- A. The ultimate strength of material is determined by the stresses on the potential failure plane: Correct: failure is decided by the stresses (σ, τ) acting on the potential failure plane.
- B. Material fails essentially by shear: Correct: the theory assumes failure is essentially by shear.
- D. The critical shear stress causing failure depends upon the properties of the material as well as on normal stress on the failure plane: Correct: τf = c + σf tan φ depends on the material (c, φ) and the normal stress σf on the failure plane.
Key Point
Mohr–Coulomb ignores σ₂. Failure circle uses σ₁ and σ₃ only.
Key Concepts for Students
- Experiments show σ₂ does have a small effect (plane-strain φ is a little higher than triaxial φ).
- Failure plane is inclined at 45° + φ/2 to the major principal plane.
- Other criteria (e.g. Lade–Duncan) include σ₂ but are not used at SSC JE level.
Practice more: this is question 13 in Shear Strength of Soils MCQs – Part 1. Try the whole set and check every answer instantly.