Earth Pressure Fundamentals
Soil behind a retaining wall exerts lateral pressure that the structure must resist to prevent collapse. The magnitude of this pressure depends on whether the wall yields away from the soil (active condition), stays perfectly still (at-rest condition), or pushes into the soil (passive condition). Rankine's theory provides closed-form expressions for the limiting active and passive states, assuming the soil reaches plastic equilibrium along planar failure surfaces inclined at 45°±φ/2 from horizontal.
Active Pressure Distribution
Under active conditions, lateral pressure increases linearly with depth: σ_h = K_a·γ·z. The resulting triangular pressure diagram produces a resultant force P_a = 0.5·K_a·γ·H² acting at H/3 from the base. Surface surcharges add a uniform rectangular pressure K_a·q_s over the full height. The simulation draws both components and shows how the point of application shifts upward as surcharge increases, changing the overturning moment profile on the wall.
Passive Resistance
On the toe side of a retaining wall, soil provides passive resistance when the wall base pushes forward. Passive pressure coefficients K_p are the inverse of K_a: for φ = 30°, K_p = 3.0 compared to K_a = 0.33. This asymmetry — passive resistance is 9 times stronger — is nature's gift to retaining wall designers. However, mobilizing full passive pressure requires significant wall movement (2-6% of wall height), so design often uses only a fraction of the theoretical passive force.
Design Stability Checks
Retaining wall design requires checking three failure modes: overturning about the toe (active moments vs. restoring moments from wall weight and passive resistance), sliding along the base (active horizontal force vs. friction plus passive resistance), and bearing capacity of the foundation soil. Adequate factors of safety — typically 2.0 for overturning, 1.5 for sliding, and 3.0 for bearing — ensure the wall performs safely throughout its service life.