Retaining Wall Pressure Calculator (Rankine and Coulomb)

Retaining walls hold back soil that would otherwise slide or spread under its own weight. The lateral force that soil applies to the wall, the active earth pressure, depends on the soil’s unit weight, strength, any surcharge load on top, and geometry such as backfill slope and wall friction. This calculator computes that pressure two ways, the classic Rankine method and the more general Coulomb method, then works out the resulting force and overturning moment on the wall.

Rankine active and passive pressure

Rankine’s theory assumes a smooth vertical wall and a level, cohesionless backfill, giving simple closed form coefficients based only on the soil friction angle phi’:

Ka = tan^2(45 – phi’/2) (active), Kp = tan^2(45 + phi’/2) (passive)

Active pressure resists lateral spreading and is what a retaining wall must be designed to hold back. Passive pressure develops when soil is pushed toward a structure, such as against an embedded footing or wall toe, and is much larger for the same friction angle, which is why passive resistance is a valuable but often unreliable line of defense against sliding.

Coulomb’s general method

Coulomb’s method extends the active pressure coefficient to account for wall friction delta, a sloped backfill surface beta, and a battered (non-vertical) wall face theta:

Ka = cos^2(phi’ – theta) / [ cos^2(theta) cos(theta+delta) (1 + SQRT[ sin(phi’+delta) sin(phi’-beta) / (cos(theta+delta) cos(theta-beta)) ])^2 ]

Setting delta, beta, and theta all to zero reduces this exactly to the Rankine coefficient, which is a useful check, wall friction generally reduces the active coefficient somewhat, while a sloped backfill increases it.

Force, cohesion, and surcharge

For a wall of height H, the resultant active force from the soil’s own weight is 0.5 x Ka x gamma x H^2, acting at H/3 above the base for a simple triangular pressure distribution. Cohesion reduces near surface pressure by a term of 2c x SQRT(Ka), which can make the pressure diagram negative near the top, in practice a tension crack forms there instead of the soil pulling on the wall, so this calculator holds that portion at zero. A uniform surcharge q adds a rectangular pressure of Ka x q over the full wall height, acting at H/2.

Worked example

For a 12 ft wall retaining soil with unit weight 115 pcf, friction angle 30 degrees, cohesion 100 psf, a 250 psf surcharge, 15 degrees of wall friction, and a 5 degree backfill slope, the Rankine active coefficient is 0.333 and the Coulomb active coefficient is about 0.320, slightly lower due to wall friction. The resulting total active force is roughly 2,254 lb per foot of wall, producing an overturning moment of about 10,935 lb-ft per foot of wall about the base.

Retaining Wall Pressure Calculator

Related Calculator and Reference

For slip circle stability on the same site, see the Slope Stability Factor of Safety Calculator. Formula reference: Rankine and Coulomb lateral earth pressure theory.