State of Stress Near a Retaining Wall – Passive Condition in Non-Cohesive Soil In a cohesionless (non-cohesive) soil mass at the passive limit state against a rigid wall, which statement correctly identifies the directions of the principal stresses?

Introduction / Context:
Rankine and Coulomb earth pressure theories describe limiting stress states in backfills. When the wall moves toward the soil (compressing it), the soil reaches the passive condition and mobilizes its maximum lateral resistance, changing the orientation of principal stresses relative to the active case.

Given Data / Assumptions:

• Soil is cohesionless and level ground is assumed for simplicity.
• Rigid wall induces limiting equilibrium (passive).
• Plane strain conditions are approximated.

Concept / Approach:

In the passive state, lateral stress exceeds vertical stress. Therefore the major principal stress σ1 acts horizontally (toward the wall), and the minor principal stress σ3 acts vertically. This is the reverse of the active case, where σ1 is vertical and σ3 is horizontal due to soil dilation under extension as the wall moves away.

Step-by-Step Solution:

Verification / Alternative check:

Mohr’s circle constructions for passive Rankine state confirm the right-shifted circle where horizontal stress is the maximum principal stress.

Why Other Options Are Wrong:

(b) states a true corollary but the question asks for the correct identification in single choice; (c) is the active condition; (d) is incorrect for principal stresses which are mutually orthogonal and not inclined together arbitrarily.

Common Pitfalls:

Mixing up active and passive orientations; forgetting that principal planes carry no shear.

Final Answer:

Major principal stress is horizontal