Retaining Wall Stability Calculator

A gravity retaining wall stands only because its own dead weight generates a restoring moment larger than the overturning moment produced by soil pushing on its back face. This tool resolves that balance using Rankine active earth pressure, where Ka = tan squared of (45 minus phi/2). For a clean granular backfill with a friction angle of 30 degrees, Ka is 0.333, so horizontal pressure at any depth is one third of the vertical overburden. Integrating the triangular pressure diagram gives Pa = 0.5 x Ka x gamma x H squared per foot of wall, acting at H/3 above the base. Typical inputs are 110 to 130 pcf for compacted backfill, 145 to 150 pcf for concrete, and 0.4 to 0.55 for the base friction coefficient of concrete cast on granular soil. Three checks govern the design: overturning with a minimum factor of safety of 2.0, sliding at 1.5, and bearing at 3.0 against allowable pressure. A fourth condition, the middle third rule, requires base eccentricity to stay under B/6 so the whole footing remains in compression; beyond that the pressure diagram collapses to a triangle over a shortened contact width and the heel lifts. The model here is deliberately narrow. It assumes a vertical back face, level backfill, no wall friction, drained conditions and no surcharge. Water trapped behind the stem, a sloped backfill, seismic inertia or a deep-seated slip surface each change the answer substantially and require separate analysis.

Lateral earth pressure theory begins with Charles-Augustin de Coulomb, whose 1773 memoir to the French Academy of Sciences analysed a sliding soil wedge behind a revetment and searched for the wedge geometry giving maximum thrust. His method, published in 1776, grew out of military fortification work and remains the basis of the Coulomb wedge solution used when wall friction or a sloping backfill matters. In 1857 William John Macquorn Rankine, professor of civil engineering at Glasgow, published On the Stability of Loose Earth in the Philosophical Transactions of the Royal Society, deriving pressure states directly from a stress field in a semi-infinite soil mass rather than from a trial wedge. That approach yields the compact Ka expression used here. Karl Terzaghi's Erdbaumechanik of 1925 established soil mechanics as a quantitative discipline and clarified that the active state requires the wall to yield slightly, roughly 0.001 to 0.004 of the wall height for dense sand. Treatment of eccentrically loaded footings was refined by George Meyerhof in the 1950s through the effective width concept, which underlies the base pressure distribution reported by this calculator. Allowable stress factors of safety of 2.0, 1.5 and 3.0 became standard through mid-century American design manuals, and were later recast as load and resistance factors when AASHTO moved its bridge specifications to LRFD in 1994.