Shear Strength MCQ with answer and solution

Concept

For c = 0, the Mohr-Coulomb envelope τ = σ tanφ is a straight line through the origin.

Formula

τ_f = c + σ tanφ; for c = 0, τ_f = σ tanφ

Step-by-step solution

1. Mohr-Coulomb equation: τ_f = c + σ tanφ. 2. Put c = 0: τ_f = σ tanφ. 3. At σ = 0, τ_f = 0. 4. So the envelope starts at the origin.

Explanation

Cohesion c is the intercept of the Mohr envelope on the shear stress (y) axis. If c = 0, the intercept is zero, so the line passes through the origin. This is the case for dry sand and other cohesionless soils.

Why the other options are wrong

A and B: The envelope never cuts the normal stress (x) axis away from the origin in the standard c-φ form. C: A positive y-intercept means c > 0, which applies to cohesive soils.

Shortcut

y-intercept = c. If c = 0, the line goes through the origin.

Common mistake

Confusing the x-axis (normal stress σ) with the y-axis (shear stress τ) when locating c.