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?

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:

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