Retaining Wall Calculator: Overturning, Sliding and Bearing

Loads and the pressure plane

A unit length of wall is analyzed in drained effective stress. The gravity wall has a vertical back and a tapered front. The cantilever has a uniform stem, a horizontal footing, and a vertical pressure plane at the heel. Height H runs from the base underside to ground at that plane; stem height is H minus footing thickness and the rise of the backfill over the heel.

Mass densities convert to unit weights using g = 9.81 m/s². The active coefficient is the total thrust coefficient. Rankine uses the sloping-backfill expression and directs thrust parallel to the slope; Coulomb uses the vertical-face special case of FHWA GEC 6 Eq. 6-2, with thrust inclined downward by the chosen interface angle. A cantilever Coulomb analysis follows the virtual heel-plane convention illustrated by MnDOT (attached pp. 100–102); interface friction there describes soil interaction.

Earth, surcharge and groundwater

For level backfill with groundwater height h_w, submerged unit weight is γ′ = γ_sat − γ_w. Integration of effective stress gives soil thrust K_a[γH² + (γ′ − γ)h_w²]/2 and its moment K_a[γH³ + (γ′ − γ)h_w³]/6, before resolving horizontally. Uniform vertical surcharge adds K_a q H at H/2; water adds γ_w h_w²/2 at h_w/3, horizontally. These integrations and the wall centroids are derived here from statics. USACE EM 1110-2-2502 (1989), Chapter 3, supplies the classical framework; its superseding 2022 hydraulic-wall guidance is a separate, broader design procedure.

Equilibrium and bearing

Wall and heel-soil weights, credited permanent surcharge and downward earth thrust stabilize the wall. Uplift varies linearly from zero at the drained toe to r_u γ_w h_w at the heel. Its resultant is U = r_u γ_w h_w B/2 at 2B/3 from the toe.

Sliding FS = μN/P_h, with N = total downward force − U. Overturning FS = stabilizing moments / overturning moments about the toe; uplift belongs in the overturning denominator. The base resultant is x = (M_resist − M_drive)/N and e = B/2 − x.

For |e| ≤ B/6, effective contact pressure is N/B(1 ± 6e/B). Outside that range, a compression-only triangle has contact width 3(B/2 − |e|) and peak pressure 2N/contact width. This is a linear contact-stress screening model, not a bearing-capacity solution. Compare its peak with a compatible site-specific allowable stress. See FHWA GEC 6, attached pp. 124–125, for the distinction between a linear contact distribution and an effective-area capacity calculation. Force and moment closure are checked for both contact regimes. Arrows in the section are symbolic; the separate pressure envelope is normalized to its own maximum.

• Homogeneous cohesionless backfill, constant drained friction angle, planar ground, and enough wall movement to mobilize active pressure.
• A horizontal base on soil, with no anchorage, shear key, base adhesion or passive resistance. Base friction is a separate site-specific input.
• Groundwater is horizontal and permitted only with level backfill; no front-face water, ponding above ground, seepage gradients in the backfill or rapid drawdown.
• The uplift model assumes a drained toe. Lowering its fraction requires evidence from drainage or seepage analysis; it is not an automatic drainage credit.
• Soil over the cantilever heel uses total moist/saturated weight. Earth thrust is applied at the virtual heel plane; top-of-stem lateral design is not calculated.
• Lateral surcharge always acts over the full active wedge. The heel-weight setting defines the selected vertical load case: excluded heel weight is favorable for sliding/overturning screening but may be unfavorable for bearing. Check both settings when a surcharge can act over the heel.
• The sketch uses a common geometry scale and a separate relative lateral-pressure scale. H includes the base thickness. Positive eccentricity is toward the toe.

Use for preliminary external stability checks and teaching, not construction authorization. Default targets (sliding 1.5 and overturning 2.0) are editable screening assumptions, not universal requirements. The allowable bearing pressure must come from a geotechnical assessment and must be compatible with effective contact stress, settlement, base inclination and the selected load case. Do not divide an allowable pressure by another bearing safety factor.

Global/slope stability, seismic loading, structural reinforcement, stem and footing bending/shear, masonry/block interlock, settlement, internal wall failure, frost, scour, layered/cohesive/expansive soil and construction-stage loads are outside scope. Restrained basement walls may require at-rest pressure. A partial-contact result fails this tool's middle-third screening criterion even if its calculated peak pressure is below the allowance; separation can also change seepage and uplift.

Walls taller than about 1.2 m (4 ft) usually need an engineer and a permit; local thresholds vary, and surcharges or nearby structures may require review at smaller heights. Confirm local requirements. Installation and excavation work belongs to qualified people following an engineered plan.

This is a classical unfactored service-load calculation. It does not implement AASHTO LRFD or the complete USACE hydraulic-wall procedure. Source editions are FHWA GEC 6 (2002), the MnDOT worked example (July 2016), and the classical USACE manual (1989, superseded in 2022). Check against the standard and local rules in force; source/edition review date: 26 October 2026.