Rankine Earth Pressure
Active earth pressure coefficient and resultant force on a retaining wall.
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The engineering
Rankine's active case with its assumptions in the open: cohesionless, dry, level backfill; a smooth vertical wall that yields enough to mobilize the soil's strength; no surcharge and no water. Under those conditions the pressure grows linearly with depth (a triangle), the resultant acts at H/3 above the base, and typical sands (φ ≈ 30–35°) give Ka around 0.27–0.33 — the soil pushes with roughly a third of its weight.
Every dropped assumption adds load: water behind an undrained wall roughly triples the pressure (which is why weep holes exist), surcharge adds a uniform strip, and sloped backfill raises Ka. This card is the sanity-check number; the wall design belongs to a geotechnical engineer.
Where this math comes from
Charles-Augustin de Coulomb, then a military engineer building fortifications on Martinique, published the first wedge theory of earth pressure in 1776 — soil as a sliding triangle held by friction. William Rankine re-derived the problem in 1857 from stress states inside the soil mass itself, giving the closed-form coefficient this card evaluates.
Karl Terzaghi's Erdbaumechanik (1925) founded modern soil mechanics and showed where the classical theories hold and where pore water wrecks them — but for a quick check on a yielding wall with drained granular backfill, Rankine's 1857 triangle is still the number every geotech quotes first.
- 1776Charles-Augustin de CoulombWedge theory of earth pressure — soil mechanics begins.
- 1857William RankineStress-state earth pressure theory; Ka in closed form.
- 1925Karl TerzaghiErdbaumechanik — modern soil mechanics, effective stress, and the limits of the classics.
See the full timeline of the math behind every calculator →
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