At-Rest Earth Pressure on a Braced Wall (Jaky K0)
The push of retained soil on a wall that cannot yield -- a basement wall, a braced excavation, a rigid box culvert.
Example
You enter
- Friction angle phi (deg) 30
- Soil unit weight (pcf) 120
- Retained height H (ft) 10
You get
- At-rest coefficient K0 0.500
- At-rest pressure at base 600 psf
- P0 soil 3000
- Resultant height above base 3.33 ft
Details, formula, and sources
Where the Rankine active pressure does not apply because the soil never relaxes to its active limit: Jaky's K0 = 1 - sin phi, the triangular at-rest thrust P0 = 0.5 x K0 x gamma x H^2 at H/3, the uniform-surcharge term K0 x q x H at H/2, the combined resultant and its height. A 10 ft wall of phi = 30 sand carries 3,000 lb/ft at rest against only 2,000 lb/ft active -- exactly 1.5x more, the error a designer makes reaching for the active case on a braced wall. Normally-consolidated cohesionless, dry; an overconsolidated or submerged case needs its own analysis. A design aid, not a substitute for a geotechnical engineer's report.
K0 = 1 - sin phi (Jaky, normally consolidated); P0 = 0.5 K0 gamma H^2 at H/3, plus surcharge K0 q H at H/2; P0_tot and its resultant height y_bar.
Jaky (1944) at-rest earth pressure, as compiled in Das, Principles of Foundation Engineering, and NAVFAC DM-7.02 (Foundations and Earth Structures), by name.
NAVFAC DM-7.02 is a free public US Navy design manual; Jaky's K0 = 1 - sin phi is public and printed in every soil-mechanics text.
Estimate. AHJ and licensed professional govern.
Field names used by the API: phi, gamma, h_ft, k0, p0_base, p0_soil, y_bar
- Non-yielding wall the at-rest state governs only when the wall is restrained from deflecting to the active limit (braced cut, basement wall, rigid culvert); a wall free to yield sheds to the lower Rankine activeJaky 1944 / Das / NAVFAC DM-7.02
- Normally consolidated cohesionless K0 = 1 - sin phi is the NC form; an overconsolidated deposit carries a higher K0 that rises with OCRDas / NAVFAC DM-7.02