Active, passive, and at-rest earth pressure: three different states, not one number

If a wall genuinely cannot move at all — braced rigidly top and bottom, like a basement wall cast tightly between two floor slabs — the soil behind it settles into an intermediate at-rest pressure, neither the highest nor the lowest state that soil can exert. If a wall is instead free to move even slightly away from the soil, the soil behind it relaxes as it moves, dropping to its lowest stable pressure: active pressure. This is the condition a free-standing retaining wall design normally assumes, since a cantilever or gravity wall is expected to deflect and rotate a small amount under load — enough to fully mobilize the active state. Push a wall into the soil instead, and the soil resists at a much higher passive pressure — but it takes considerably more wall movement to fully mobilize passive resistance than it takes to reach active pressure, which is exactly why design practice only credits a reduced fraction of full passive capacity unless that movement is actually demonstrated.

Rankine and Coulomb: two classical ways to calculate active (and passive) pressure

Rankine's theory (1857) and Coulomb's earlier theory (1776) are both classical soil-mechanics methods for computing active and passive earth-pressure coefficients from a soil's friction angle. Rankine assumes a frictionless wall-soil interface and a specific failure-wedge geometry, which keeps it simple but strictly valid only for a vertical wall with a level or uniformly sloped backfill; Coulomb's method additionally accounts for friction between the wall face and the soil (wall friction δ) and allows a sloped wall face, at the cost of a somewhat more involved calculation. Neither is a Eurocode- or ACI-specific formula — both predate either code by well over a century — which is why EC7 and ASCE 7/IBC-referenced US practice both simply point to established earth-pressure theory rather than defining their own. Retaining Wall Design lets you choose either Rankine or Coulomb directly, and optionally include a reduced fraction of passive resistance in front of the wall via a mobilization-reduction factor — it does not compute an at-rest (K0) case, since that applies to a genuinely different wall condition (a rigid, non-yielding wall, like a braced basement wall) than the free-standing cantilever and gravity walls the tool models (see the related tool below).