Coulomb’s wedge theory – core assumptions for earth pressure on retaining walls: Which of the following assumptions are inherent in Coulomb’s earth pressure theory for planar failure wedges?

Introduction / Context:
Coulomb’s earth pressure theory provides active and passive pressures on retaining structures by considering a rigid wedge of backfill sliding along a planar surface. Understanding its assumptions clarifies applicability and limitations versus Rankine’s simpler theory and more advanced wedge or numerical methods.

Given Data / Assumptions:

• Backfill is idealized as dry, cohesionless, homogeneous, isotropic (basic Coulomb case).
• Planar failure surface intersects the wall, typically near the heel.
• Wall friction angle and backface inclination are known inputs.

Concept / Approach:
Coulomb analyzes equilibrium of a rigid wedge bounded by the wall backface and a trial plane. The resultant earth force acts at a known inclination to the wall normal depending on wall friction; magnitude comes from maximizing or minimizing the thrust with respect to the plane angle for active or passive conditions. Variants extend the method to c–φ soils, sloping backfills, and submerged conditions but maintain the same core assumptions of planarity and rigid wedge behavior.

Step-by-Step Solution:

Verification / Alternative check:
Comparisons with Rankine (no wall friction, vertical wall, horizontal backfill) show differences arising precisely from these assumptions.

Why Other Options Are Wrong:

• Any single statement alone is incomplete; the theory needs all these assumptions to be well-defined.

Common Pitfalls:
Applying Coulomb to cohesive backfills without modifications; assuming a nonplanar slip surface; ignoring wall friction or backface batter effects.

Final Answer:
All of the above