Soil mechanics — basis of Coulomb’s earth pressure theory Coulomb’s classical theory for active and passive earth pressure on retaining walls is fundamentally based on which underlying approach?

Introduction / Context:
Coulomb’s earth pressure theory is one of the earliest and most widely taught methods for estimating lateral earth pressures on retaining walls. Understanding its foundational assumptions clarifies when the method is applicable and what limitations it has compared with more advanced approaches.

Given Data / Assumptions:

• Rigid wall supporting a granular backfill (often with wall–soil friction and sloping backfills considered).
• Soil is assumed to fail along a planar surface.
• Limit equilibrium conditions are invoked at failure (active or passive states).
• Soil is treated as a weight-only, cohesionless (or simple c–φ) mass with constant properties.

Concept / Approach:
Coulomb’s method treats a potential soil wedge behind (or in front of) the wall as a rigid body in limiting equilibrium. The method searches for the critical wedge angle that extremizes the lateral thrust, accounting for soil weight, wall friction, and surcharge. This is a wedge-theory, limit-equilibrium approach—not an elasticity solution (continuous small-strain stress field) and not a full plasticity solution with yield surfaces and flow rules.

Step-by-Step Solution:
Idealize a planar failure wedge adjoining the wall.Write force equilibrium of the wedge including weight, reaction on the slip plane, and wall reaction with friction.Vary the assumed plane angle to find the maximum or minimum wall thrust (passive or active).Compute the corresponding lateral earth pressure on the wall.

Verification / Alternative check:
Rankine’s theory is also a limit-state approach but assumes no wall friction and a vertical wall; both are not elasticity solutions. Modern numerical plasticity analyses can check Coulomb results for complex geometries.

Why Other Options Are Wrong:
Elasticity and plasticity frameworks are different solution classes; Coulomb does not solve the full stress field. Empirical rules alone are not the basis. Finite-element analysis is a modern numerical method, not the foundation of Coulomb’s classic theory.

Common Pitfalls:

• Assuming curved failure surfaces; Coulomb assumes planar.
• Applying Coulomb blindly to cohesive or layered backfills without caution.

Final Answer:
Wedge theory (limit equilibrium of a planar sliding wedge)