What is the difference between active, at-rest and passive pressure?

Active pressure develops when a wall yields away from the soil (lowest pressure); at-rest applies to an unyielding wall; passive develops when the wall is pushed into the soil (highest pressure).

What earth-pressure theory does this use?

It uses Rankine theory for cohesionless backfill, with Jaky's K0 = 1 − sin φ for the at-rest case on level backfill.

Lateral Earth Pressure

Rankine Preliminary estimate

Rankine active, at-rest and passive lateral earth pressure on a retaining wall — coefficients, the resultant thrust, its line of action, and the overturning moment about the base.

Results update as you type. These are educational estimates — confirm against the governing code and a licensed engineer before design use.

Method & references

Lateral earth pressure on a vertical wall with cohesionless backfill, from Rankine theory. The coefficient K converts vertical effective stress to horizontal pressure:

p = K·γ·z + K·q , P = ½·K·γ·H² + K·q·H

Active K_a = (1 − sin φ)/(1 + sin φ) — wall yields away from the soil
At-rest K₀ = 1 − sin φ (Jaky, normally consolidated, level backfill)
Passive K_p = (1 + sin φ)/(1 − sin φ) — wall is driven into the soil

For a sloping backfill (β), the Rankine coefficient uses the cos β form and the resultant acts parallel to the slope; the horizontal component governs overturning. The triangular soil pressure resultant acts at H/3 above the base; the rectangular surcharge resultant at H/2.

References: Rankine (1857); Jaky (1944); Das, Principles of Foundation Engineering; AASHTO LRFD §3.11.5. For cohesive soils, seismic (Mononobe-Okabe), or layered or submerged profiles, use a fuller analysis.