Rankine earth pressure
active earth pressurepassive earth pressureat-rest pressure
Active, passive and at-rest earth pressure coefficients, and the thrust a retaining wall has to carry — three states set by which way the wall moves.
Rankine Active Earth Pressure Coefficient
Rankine coefficient of active earth pressure for a smooth vertical wall retaining level cohesionless backfill that has yielded away from the soil.
Rankine Passive Earth Pressure Coefficient
Rankine coefficient of passive earth pressure, the resistance mobilised when a wall or footing is pushed into level cohesionless soil.
At-Rest Earth Pressure Coefficient (Jaky)
Jaky's 1944 empirical coefficient of earth pressure at rest for a normally consolidated soil that is not permitted to strain laterally.
Active Thrust on a Retaining Wall
Total Rankine active thrust per unit length of wall from a dry cohesionless backfill, acting at one third of the wall height above the base.
How they fit together
Which coefficient applies depends entirely on which way the wall moves. Let it yield away from the soil and the soil mobilises its own shear strength to hold itself up, so the pressure drops to the active case. Push the wall into the soil and the pressure climbs to the passive case, which can be an order of magnitude larger. A wall that does not move at all sits between them at rest.
The asymmetry matters: active pressure is reached after a few millimetres of movement, but passive resistance needs centimetres of displacement to develop fully. Designs that count on full passive resistance without checking the deflection required are counting on something the soil has not yet been asked to give.