Principal Stresses – Plane of Maximum Normal Stress in a Loaded Soil Element At a given point within a loaded soil mass, on which principal plane is the maximum normal (principal) stress acting?

Introduction / Context:
Understanding principal stresses and planes is essential for interpreting failure criteria, earth pressure states, and stress paths. Principal planes are mutually orthogonal planes on which shear stress is zero and normal stress is extreme (max, min, intermediate).

Given Data / Assumptions:

• Continuum mechanics applies; stress tensor symmetric.
• Three principal stresses σ1 ≥ σ2 ≥ σ3 and corresponding principal planes exist.

Concept / Approach:

The major principal plane is the plane on which the major principal stress σ1 acts normal to the plane, with zero shear. By definition, σ1 is the maximum normal stress at the point. Hence, the maximum normal stress acts on the major principal plane, not on the intermediate or minor ones.

Step-by-Step Solution:

Verification / Alternative check:

Mohr’s circle shows σ1 at the far right; the corresponding plane orientation yields zero shear and maximum normal stress, confirming the selection.

Why Other Options Are Wrong:

Minor and intermediate principal planes carry σ3 and σ2 respectively, which are lower than σ1. Equal normal stress on all planes occurs only under hydrostatic conditions, not general loading.

Common Pitfalls:

Confusing “plane of σ1” with “direction of σ1”; mixing up shear-free condition with failure plane orientation.

Final Answer:

Major principal plane