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 -- 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 tile 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.
Formula and source
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.
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