A limit‑equilibrium model that predicts lateral earth pressures on retaining structures by representing the backfill as a rigid wall pushing a planar failure wedge whose geometry is determined by internal soil friction, cohesion, wall friction and wall/backfill inclinations; the active or passive lateral force is obtained by equilibrating the wedge along a trial failure plane and selecting the plane that extremizes (minimizes or maximizes) the resultant. Assumptions: rigid wall, planar failure surface, homogeneous soil, static conditions, and negligible wall deformation.

Principle

Lateral earth pressure results from equilibrium of a potential failure wedge: the magnitude and line of action of the lateral resultant depend on soil strength parameters (φ, c), the wall‑to‑soil friction δ, backfill slope and wall inclination; the governing value (active or passive) is found by optimizing over possible wedge angles.

Demonstration

Illustrative scenario: For a vertical, rough retaining wall of height H retaining a cohesionless backfill of friction angle φ and wall friction δ, an engineer constructs the Coulomb wedge geometry, writes force and moment equilibrium on a trial plane, varies the plane angle to find the minimum active resultant and then computes the total active lateral force and its point of application to design the wall section and overturning resistance.

Misapplication

Using Coulomb’s planar‑wedge solution for flexible, yielding walls, for backfills with significant layering or anisotropy, or for curved failure surfaces treats a model assumption as universal; the semantic error is conflating the planar rigid‑wedge idealization with more complex real failure surfaces.

Consequence

Within its assumptions Coulomb’s theory yields closed‑form estimates for active and passive lateral forces and their lever arms, which are fundamental inputs to retaining‑wall sizing and stability checks; misapplication can misplace design loads, causing inadequate bearing, sliding or overturning resistance.

Reversal

When wall flexibility, non‑planar curved failure surfaces, significant ground stratification, seismic inertial forces, or time‑dependent pore‑pressure changes govern behaviour, Coulomb’s planar rigid‑wedge model is inadequate—numerical methods or specialized seismic earth‑pressure theories are required.

Boundary

Clearly within: a stiff, relatively rigid retaining wall with homogeneous backfill where a planar wedge is plausible. Boundary case: slightly flexible wall or weak layering—Coulomb gives indicative loads but must be checked. Clearly outside: flexible cantilever walls undergoing large rotation, non‑planar failure mechanisms, or soils subject to transient pore‑pressure effects.

Semantic Tension

Tractable limit‑equilibrium simplicity (planar wedge, closed‑form expressions) versus the need to model wall deformability, soil layering, and dynamic pore‑pressure effects for accurate load prediction; the engineer balances analytical convenience against fidelity to observed failure mechanisms.

Synthesis

Coulomb reduces lateral earth pressure to a mechanics‑based wedge equilibrium that explicitly includes wall friction and geometry—powerful for many retaining‑wall designs but an idealization: verify wall stiffness and ground conditions and replace with more sophisticated analyses when assumptions are violated.