Which of the following statements are correct with respect to Mohr-Coulomb failure criteria on soils. I: Mohr failure envelope is approximated as 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.
- AI and IV
- BII and III
- CI and IIICorrect
- DII and IV
Solution
Concept
The real Mohr failure envelope is curved. Mohr-Coulomb approximates it as a straight line τ = c + σ tanφ, and a stress circle can at most touch it.
Formula
τf = c + σ tanφ
Step-by-step solution
1. Statement I: The actual failure envelope is curved, but it is approximated as a straight line (Coulomb's equation). This is TRUE. 2. Statement II: This is the reverse of I. It is FALSE. 3. Statement III: A Mohr circle touching the envelope means failure. A circle cannot go beyond it, because the soil would have failed already. This is TRUE. 4. Statement IV: c and φ depend on drainage, test type, stress level and density. They are not fundamental properties. This is FALSE. 5. So the correct statements are I and III, which is option C.
Explanation
Mohr gave a curved failure envelope, and Coulomb's straight line is a simple approximation of it. A Mohr circle can only touch the envelope at failure and cannot cross it. The values of c and φ change with test conditions (UU, CU, CD), so they are not fixed soil properties.
Why the other options are wrong
A: IV is wrong because c and φ depend on test conditions. B: II is wrong because the actual envelope is curved, not straight. D: Both II and IV are wrong.
Shortcut
Real envelope is curved, the assumed one is straight. The circle only touches the envelope. c and φ are not constants.
Common mistake
Thinking c and φ are fixed soil properties. They change with drainage condition and type of test.
Correct answer: C) I and III