Mohr–Coulomb (Mohr’s straight line) failure concept: Which statements correctly characterize the basis of the Mohr's straight theory used in soil and rock strength?
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AMaterial fails essentially by shear along a plane
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BUltimate strength is determined by the stresses acting on the potential slip plane
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CThe failure criterion is independent of the intermediate principal stress (two-parameter form)
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DAll the above
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ENone of the above
Answer
Correct Answer: All the above
Explanation
Introduction / Context:The Mohr–Coulomb failure criterion represents shear failure by a straight line envelope in shear-normal stress space: τ = c + σ′ tan φ. It is widely applied to geomaterials due to its simplicity and reasonable approximation of strength behavior in many practical problems.
Given Data / Assumptions:
- Material fails along a plane when shear stress reaches a critical combination with normal stress.
- Criterion is defined by two parameters: cohesion intercept c and friction angle φ.
- Intermediate principal stress is ignored in the basic form.
Concept / Approach:Mohr’s circles represent stress states; failure is predicted when the circle touches the straight-line envelope. The theory assumes shear-dominated failure, with the envelope calibrated from tests such as triaxial compression where principal stresses are controlled and the critical plane is inferred from the Mohr representation.
Step-by-Step Solution:
Construct Mohr’s circle for the stress state at failure.Draw the linear envelope τ = c + σ′ tan φ.Intersection indicates the shear stress and normal stress on the slip plane at failure.Predict strength on other planes or stress paths using the same two parameters.Verification / Alternative check:Comparison with triaxial data at varying confining pressures shows approximate linearity for many soils within practical ranges.
Why Other Options Are Wrong:Each statement A–C is a defining feature of the Mohr–Coulomb model; dismissing any one would misstate the criterion.
Common Pitfalls:Applying the linear envelope at very low or very high confining pressures where curvature exists; neglecting the role of intermediate principal stress addressed by more advanced criteria (e.g., Drucker–Prager).
Final Answer:All the above