According to the Mohr-Coulomb failure criterion in soils, which of the following statements are INCORRECT? A: Shear strength is attributable to the interlocking of soil particles and cohesion. B: Shear strength is only attributable to the internal friction between particles. C: The Y-intercept represents friction of soils. D: The Mohr-coulomb failure envelope is a straight line.
- AA and C
- BB and CCorrect
- CA and D
- DB and D
Solution
Concept
Mohr-Coulomb: shear strength = cohesion + friction part; the envelope is a straight line with intercept c and slope φ.
Formula
τf = c + σ tanφ
Step-by-step solution
1. Mohr-Coulomb equation: τf = c + σ tanφ. 2. Shear strength has two parts: cohesion (c) and friction/interlocking (σ tanφ). So A is correct. 3. B says strength comes ONLY from friction. This ignores cohesion, so B is incorrect. 4. At σ = 0, τf = c. So the Y-intercept is cohesion, not friction. C is incorrect. 5. τf vs σ is a linear equation, so the envelope is a straight line. D is correct. 6. Incorrect statements are B and C, so the answer is option (B).
Explanation
In the Mohr-Coulomb equation, shear strength comes from both cohesion and internal friction. The Y-intercept of the failure envelope is cohesion c, and the slope angle is φ. So the statements saying 'only friction' and 'intercept is friction' are wrong.
Why the other options are wrong
(A) A is a correct statement. (C) A and D are both correct statements. (D) D is correct, because the Mohr-Coulomb envelope is a straight line.
Shortcut
Intercept = c (cohesion), slope = φ (friction).
Common mistake
Confusing the intercept (cohesion) with the slope (friction angle).
Correct answer: B) B and C