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Lateral Earth Pressure — AASHTO LRFD §3.11.5–3.11.6 (U.S. units)

Coulomb active coefficient for inclined walls, sloping backfill and wall friction; at-rest coefficient for normally and overconsolidated soil; passive coefficients with the log-spiral warning; resultant force with surcharge and water.

Backfill and wall

φ′ deg

Moist unit weight γ pcf

Wall height H ft

θ — back of wall from horizontal deg

β — backfill slope deg

δ — wall friction deg

θ follows AASHTO Fig. 3.11.5.3-1: θ = 90° is a vertical back; θ < 90° means the back of the wall leans so that the backfill rests on it (larger wedge, larger pressure); θ > 90° means the back overhangs the backfill. Entering the mirror angle by mistake can change k_a by about 40%.

Uniform surcharge q psf

Live-load h_eq (Table 3.11.6.4) ft

OCR (at rest)

Water depth below top (blank = dry) ft

Saturated unit weight pcf

Results

k_a (Coulomb) · Rankine · k_o—

Active pressure at base—

Active force P_a · horizontal · vertical (per ft)—

Resultant height above base—

At-rest force P_o (per ft)—

k_p: Coulomb · Rankine—

AASHTO LRFD§3.11.5.1 (p = kγz), 3.11.5.2 (k_o), 3.11.5.3 and Fig. 3.11.5.3-1 (Coulomb k_a, θ convention), 3.11.5.4 and Fig. 3.11.5.4-1 (passive, log spiral), 3.11.6.1 and 3.11.6.4 (surcharge, h_eq). OC at rest: Mayne & Kulhawy (1982). Clause numbers only.

VerifiedCaltrans Bridge Design Practice 11.2 (2022): Rankine coefficients, pressures and live-load surcharge reproduced; the Coulomb active and passive formulas agree with an independent numerical trial-wedge solution to 0.01% for vertical and inclined walls.

Preliminary calculation tool. Final design requires the full text of the referenced standard (see the sources on this page) and review by a licensed PE.