Soil mechanics – Assumptions of Rankine’s theory for active earth pressure Identify the set of assumptions underlying Rankine’s earth pressure theory for active case acting on a vertical retaining wall.

Introduction / Context:
Rankine’s theory predicts earth pressure at rest, active, and passive states for cohesionless backfills. For active pressure, the wall yields sufficiently away from the soil to mobilize the minimum lateral stress condition.

Given Data / Assumptions:

• Backfill is idealized as homogeneous and dry (c = 0), with unit weight γ and friction angle φ.
• Back of the wall is vertical and smooth, implying no wall–soil friction effects.
• Failure surface is assumed planar for the active case.

Concept / Approach:
With these assumptions, Rankine derived active earth pressure coefficient Ka = (1 − sin φ) / (1 + sin φ). The active pressure acts at H/3 above the base of the wall for level backfill. The simplifications enable closed-form expressions without wedge equilibrium involving interface friction (as in Coulomb’s theory).

Step-by-Step Solution:
Adopt cohesionless soil (c = 0) and smooth wall → no interface shear.Assume an extended semi-infinite backfill with level surface → uniform conditions.Postulate planar failure → obtain Ka and the triangular pressure distribution.Compute resultant = (1/2) * Ka * γ * H^2 acting at H/3 above base (if needed).

Verification / Alternative check:
Coulomb’s theory relaxes the smooth-wall assumption and permits sloping backfills and wall friction; its results reduce toward Rankine’s when interface friction is set to zero and geometry is simplified.

Why Other Options Are Wrong:
Each of (A), (B), and (C) is correct but incomplete alone; “None of the above” is incorrect because a planar surface is explicitly assumed in Rankine’s formulation.

Common Pitfalls:
Applying Rankine for cohesive or submerged soils without modification; confusing active and passive signs; using Coulomb coefficients unintentionally.

Final Answer:
all of the above