If the cohesion value of soil is zero, the Mohr envelope will pass through:

Asked in SSC JE 11/10/2023 (Morning)

Detailed Explanation

The Mohr–Coulomb envelope is τ = c + σ tan φ. Its intercept on the τ (y) axis is c.

Why “the origin” Is Correct

If c = 0 the intercept is zero, so the line starts at the origin and rises at angle φ. Such soils (clean sands and gravels) are called φ-soils or cohesionless soils.

Failure envelopes for the three kinds of soil. Pure clay under undrained loading (φ = 0): horizontal line at τ = c. Clean sand (c = 0): straight line through the origin at angle φ. Most real soils (c–φ soils): line with intercept c and slope φ.

Why the Other Options Are Wrong

A. some distance on positive y-axis: A positive y-intercept means c > 0, which contradicts c = 0.
C. some distance on negative x-axis: An intercept on the negative σ-axis would imply tensile strength (a positive c).
D. some distance on positive x-axis: An envelope starting on the positive σ-axis would mean the soil has no strength until some normal stress is applied, which is not the Mohr–Coulomb model.

Key Point

c = 0 → envelope through origin. φ = 0 → horizontal envelope at τ = c.

Key Concepts for Students

Clean sand and gravel are typical c = 0 soils.
Apparent cohesion in moist sand from suction disappears when it dries or is submerged.
Effective-stress parameters of NC clays also often have c′ ≈ 0.

Practice more: this is question 9 in Shear Strength of Soils MCQs – Part 1. Try the whole set and check every answer instantly.