Аңдатпа
The Müller-Breslau closed-form solution for the active earth pressure coefficient Ka(φ, α, β, δ) remains the standard design tool for cohesionless backfill, yet its parameter domain is documented only fragmentarily and the error of its planar failure-surface assumption is rarely isolated from other sources of discrepancy between calculation methods. This study maps the admissible domain over the practical range of soil friction angles, φ = 20-45°, and wall inclinations α = -20° to +20° and quantifies the planar-surface error in a unified computational framework. Direct numerical maximization of the Coulomb trial wedge, formulated with the admissibility conditions ρ ≤ 90° + α and R ≥ 0, reproduces the closed form to within 0.015% over 8 970 parameter combinations, so that the difference from Sokolovski's method of characteristics measures the planar failure-surface error alone. This error is governed primarily by the wall inclination rather than by wall friction: its median does not exceed about 1% for vertical walls and for α = +10° but reaches 6.6-16% at α = -20°, locally above 30%, consistently on the unsafe side - a finding verified independently by a rotational log-spiral upper-bound mechanism. The results are condensed into applicability maps dividing the parameter space into safe, caution and significant-error zones, and a step-by-step design procedure with a worked example shows how the maps are used to decide whether the closed form may be applied directly or must be replaced by a rigorous solution.