Meaning of plastic equilibrium in soils: A soil mass is said to be in plastic equilibrium when which condition holds?

Introduction / Context:
Limit equilibrium methods in geotechnical engineering evaluate stability by assuming that along a potential surface the soil is at “plastic equilibrium.” Understanding this phrase is crucial for interpreting slope stability and bearing capacity analyses.

Given Data / Assumptions:

• Mohr–Coulomb shear strength criterion governs failure: τ_f = c + σ′ tan φ.
• Plastic equilibrium implies critical conditions along a failure plane.
• Small-strain elasticity elsewhere is not the focus.

Concept / Approach:

Plastic equilibrium means the mobilized shear stress τ equals the available shear strength τ_f. The soil is neither safely below failure nor post-failure flowing; it is exactly at the threshold—“on the verge of failure.” This is the state assumed on slip surfaces in limit equilibrium analyses.

Step-by-Step Solution:

Verification / Alternative check:

In bearing capacity solutions (Prandtl–Terzaghi) and slope stability, yield lines or slip circles are taken at plastic equilibrium.

Why Other Options Are Wrong:

(a) is vague and not tied to strength; (c) “in plastic stage” does not guarantee limit state; (d) describes post-failure flow; (e) refers to elastic behavior, not plasticity.

Common Pitfalls:

Equating plastic range with plastic equilibrium; confusing onset of flow with limit state.

Final Answer:

It is on the verge of failure (mobilized shear stress equals shear strength)