Earth Pressure Theories – Coulomb’s wedge assumptions Which statement matches a core assumption in Coulomb’s earth pressure theory?

Introduction / Context:
Classical earth pressure theories—Rankine and Coulomb—rely on different sets of assumptions. Recognizing which conditions belong to which theory is essential when selecting formulas for active or passive lateral pressures on retaining structures.

Given Data / Assumptions:

• Backfill is dry, cohesionless for the basic derivation (extensions exist).
• Wall may be inclined; backfill surface may be sloping.
• Static conditions (no seismic loads) unless otherwise specified.

Concept / Approach:

Coulomb’s wedge theory considers the equilibrium of a rigid soil wedge sliding on a planar failure surface. It explicitly accounts for the wall–soil friction (rough interface), wall inclination, and backfill slope, leading to general expressions for active and passive earth pressure coefficients. In contrast, Rankine theory assumes a vertical wall with a smooth back (no wall friction) and considers the soil mass away from the wall, with stress states at failure without explicit wall friction—making the assumptions distinct.

Step-by-Step Solution:

Verification / Alternative check:

Mohr–Coulomb failure and wedge geometry yield closed-form coefficients K_a and K_p including wall friction angle δ and wall inclination—hallmarks of Coulomb’s approach.

Why Other Options Are Wrong:

(a) describes Rankine assumptions, not Coulomb. (b) Coulomb typically assumes homogeneous, isotropic soil for the basic derivation. (c) Circular slips are associated with slope stability (e.g., clays with undrained behavior), not Coulomb earth pressure. (e) Pore pressure is not universally neglected; separate treatment is required when water is present.

Common Pitfalls:

Using Rankine coefficients where wall friction is significant, or assuming a circular failure surface for granular backfills behind rigid walls.

Final Answer:

The wall–soil interface is rough and the failure plane is planar